We consider the evolution of an arbitrary quantum dynamical semigroup of a finite-dimensional quantum system under frequent kicks, where each kick is a generic quantum operation. We develop a generalization of the Baker-Campbell-Hausdorff formula allowing to reformulate such pulsed dynamics as a continuous one. This reveals an adiabatic evolution. We obtain a general type of quantum Zeno dynamics, which unifies all known manifestations in the literature as well as describing new types.

The quantum dynamics of a Jˆ2=(jˆ1+jˆ2)2-conserving Hamiltonian model describing two coupled spins jˆ1 and jˆ2 under controllable and fluctuating time-dependent magnetic fields is investigated. Each eigenspace of Jˆ2 is dynamically invariant and the Hamiltonian of the total system restricted to any one of such (j1+j2)−|j1−j2|+1 eigenspaces, possesses the SU(2) structure of the Hamiltonian of a single fictitious spin acted upon by the total magnetic field. We show that such a reducibility holds regardless of the time dependence of the externally applied field as well as of the statistical properties of the noise, here represented as a classical fluctuating magnetic field. The time evolution of the joint transition probabilities of the two spins jˆ1 and jˆ2 between two prefixed factorized states is examined, bringing to light peculiar dynamical properties of the system under scrutiny. When the noise-induced non-unitary dynamics of the two coupled spins is properly taken into account, analytical expressions for the joint Landau–Zener transition probabilities are reported. The possibility of extending the applicability of our results to other time-dependent spin models is pointed out.

A novel recipe for exactly solving in finite terms a class of special differential Riccati equations is reported. Our procedure is entirely based on a successful resolution strategy quite recently applied to quantum dynamical time-dependent SU(2) problems. The general integral of exemplary differential Riccati equations, not previously considered in the specialized literature, is explicitly determined to illustrate both mathematical usefulness and easiness of applicability of our proposed treatment. The possibility of exploiting the general integral of a given differential Riccati equation to solve an SU(2) quantum dynamical problem, is succinctly pointed out. (C) 2017 Elsevier Inc. All rights reserved.

Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical mechanism that forces the system to oscillate at a single frequency with a predictable and tunable phase difference. Finally, the scheme is generalized to the case of N oscillators and M(< N) two-level systems.

In a recent work (Burgarth et al 2014, Nat. Commun. 5 5173), it was shown that a series of frequent measurements can project the dynamics of a quantum system onto a subspace in which the dynamics can be more complex. In this subspace, even full controllability can be achieved, although the controllability over the system before the projection is very poor since the control Hamiltonians commute with each other. We can also think of the opposite: any Hamiltonians of a quantum system, which are in general noncommutative with each other, can be made commutative by embedding them in an extended Hilbert space, thus the dynamics in the extended space becomes trivial and simple. This idea of making noncommutative Hamiltonians commutative is called 'Hamiltonian purification.' The original noncommutative Hamiltonians are recovered by projecting the system back onto the original Hilbert space through frequent measurements. Here, we generalise this idea to open-system dynamics by presenting a simple construction to make Lindbladians, as well as Hamiltonians, commutative on a larger space with an auxiliary system. We show that the original dynamics can be recovered through frequently measuring the auxiliary system in a non-selective way. Moreover, we provide a universal pair of Lindbladians that describe an 'accessible' open quantum system for generic system sizes. This allows us to conclude that through a series of frequent non-selective measurements a nonaccessible open quantum system generally becomes accessible. This sheds further light on the role of measurement backaction on the control of quantum systems.

© 2016 American Physical Society.Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional subdynamics. Each of the subdynamics is shown to be brought into an exactly solvable form by appropriately engineering the magnetic fields and thus we obtain an exact time evolution of the compound system. Several physically relevant and interesting quantities are evaluated exactly to disclose intriguing phenomena in such a system.

© 2016 American Physical Society.On the basis of the quantum Zeno effect, it has been recently shown [D. K. Burgarth, Nat. Commun. 5, 5173 (2014)2041-172310.1038/ncomms6173] that a strong-amplitude-damping process applied locally on a part of a quantum system can have a beneficial effect on the dynamics of the remaining part of the system. Quantum operations that cannot be implemented without the dissipation become achievable by the action of the strong dissipative process. Here we generalize this idea by identifying decoherence-free subspaces (DFSs) as the subspaces in which the dynamics becomes more complex. Applying methods from quantum control theory, we characterize the set of reachable operations within the DFSs. We provide three examples that become fully controllable within the DFSs while the control over the original Hilbert space in the absence of dissipation is trivial. In particular, we show that the (classical) Ising Hamiltonian is turned into a Heisenberg Hamiltonian by strong collective decoherence, which provides universal quantum computation within the DFSs. Moreover, we perform numerical gate optimization to study how the process fidelity scales with the noise st

© 2016 American Physical Society.In the Hong-Ou-Mandel interferometric scheme, two identical photons that illuminate a balanced beam splitter always leave through the same exit port. Similar effects have been predicted and (partially) experimentally confirmed for multiphoton Fock-number states. In the limit of large photon numbers, the output distribution follows a (1-x2)-1/2 law, where x is the normalized imbalance in the output photon numbers at the two output ports. We derive an analytical formula that is also valid for imbalanced input photon numbers with a large total number of photons, and focus on the extent to which the hypothesis of perfect balanced input can be relaxed, discussing the robustness and universal features of the output distribution.

The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of noncommuting Hamiltonians {h(1),..., h(m)} operating on a d-dimensional quantum system H-d, the problem consists in identifying a set of commuting Hamiltonians {H-1,..., H-m} operating on a larger d(E)-dimensional system H-dE which embeds Hd as a proper subspace, such that h(j) = PHjP with P being the projection which allows one to recover Hd from HdE. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided. (C) 2015 AIP Publishing LLC.

Interference is observed when two independent Bose-Einstein condensates expand and overlap. This phenomenon is typical, in the sense that the overwhelming majority of wave functions of the condensates, uniformly sampled out of a suitable portion of the total Hilbert space, display interference with maximal visibility. We focus here on the phases of the condensates and their (pseudo) randomization, which naturally emerges when two-body scattering processes are considered. Relationship to typicality is discussed and analyzed.

A simple systematic way of obtaining analytically solvable Hamiltonians for quantum two-level systems is presented. In this method, a time-dependent Hamiltonian and the resulting unitary evolution operator are connected through an arbitrary function of time, furnishing us with new analytically solvable cases. The method is surprisingly simple, direct, and transparent and is applicable to a wide class of two-level Hamiltonians with no involved constraint on the input function. A few examples illustrate how the method leads to simple solvable Hamiltonians and dynamics.

The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once 'observed' as outlined above. Conversely, we show that any complex quantum dynamics can be 'purified' into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.

After reviewing the earlier ideas to measure the purity of a quantum system, a new scheme for the measurement of purity is presented, which aims at providing a simple, direct and efficient procedure without resorting to quantum state tomography. The scheme is also illustrated in the Bloch-vector representation for a two-level quantum system (qubit) and for a general D-level quantum system. As a variant, a simple example implemented in a one-dimensional scattering process to measure the purity of the target qubit is also given.

When a Bose-Einstein condensate is divided into two parts that are subsequently released and overlap, interference fringes are observed. We show here that this interference is typical, in the sense that most wave functions of the condensate, randomly sampled out of a suitable ensemble, display interference. We make no hypothesis of decoherence between the two parts of the condensate.

Eigenvalues of a density matrix characterize well the quantum state's properties, such as coherence and entanglement. We propose a simple method to determine all the eigenvalues of an unknown density matrix of a finite-dimensional system in a single experimental setting. Without fully reconstructing a quantum state, eigenvalues are determined with the minimal number of parameters obtained by a measurement of a single observable. Moreover, its implementation is illustrated in linear optical and superconducting systems.

A connection is established between the non-Abelian phases obtained via adiabatic driving and those acquired via quantum Zeno dynamics induced by repeated projective measurements. In comparison to the adiabatic case, the Zeno dynamics is shown to be more flexible in tuning the system evolution, which paves the way for the implementation of unitary quantum gates and applications in quantum control. © 2013 American Physical Society.

In this paper, we investigate the possibility of measuring the purity of a quantum state (and the overlap between two quantum states) within a minimal model where the measurement device is minimally composed. The minimality is based on the assumptions that (i) we use a yes-no measurement on a single system to determine the single value of the purity in order not to extract other redundant information and (ii) we use neither ancilla nor random measurement. We show that the measurability of the purity within this model critically depends on the parity of dimension of the quantum system: The purity measurement is possible for odd-dimensional quantum systems, while it is impossible for even-dimensional cases. © 2013 American Physical Society.

A scheme for measuring the purity of a quantum system with a finite number of levels is presented. The method makes use of two root SWAP gates and hinges only on measurements performed on a reference system, prepared in a certain pure state and coupled with the target system. Neither tomographic methods, with the complete reconstruction of the state, nor interferometric setups are needed.

A simple two-qubit model showing quantum phase transitions as a consequence of ground-state-level crossings is studied in detail. Using the system's concurrence as an entanglement measure and heat capacity as a marker of thermodynamical properties, we obtain an analytical expression giving the latter in terms of the former. A protocol allowing an experimental measure of entanglement is then presented and compared with a related proposal recently reported by Wiesniak, Vedral, and Brukner.

The dynamics of an open quantum system, consisting of three superconducting qubits interacting with independent reservoirs, is investigated to elucidate the effects of the environment on a unitary generation scheme of W states (Migliore R et al 2006 Phys. Rev. B 74 104503). To this end a microscopic master equation is constructed and its exact resolution predicts the generation of a Werner-like state instead of the W state. A comparison between our model and a more intuitive phenomenological model is also considered, in order to find the limits of the latter approach in the case of structured reservoirs.

Repeated measurements on one part of a bipartite system strongly affect the other part that is not measured, the dynamics of which is regulated by an effective contracted evolution operator. When the spectrum of this operator is discrete, the nonmeasured system is driven into a pure state, irrespective of the initial state, provided that the spectrum satisfies certain conditions. We show here that, even in the case of continuous spectrum, an effective distillation can occur under rather general conditions. We confirm it by applying our formalism to a simple model. © 2010 The American Physical Society.

A Lindblad master equation for a harmonic oscillator, which describes the dynamics of an open system, is formally solved. The solution yields the spectral resolution of the Liouvillian, that is, all eigenvalues and eigenprojections are obtained. This spectral resolution is discussed in depth in the context of the biorthogonal system and the rigged Hilbert space, and the contribution of each eigenprojection to expectation values of physical quantities is revealed. We also construct the ladder operators of the Liouvillian, which clarify the structure of the spectral resolution. (C) 2010 American Institute of Physics. [doi:10.1063/1.3442363]

A scheme for generating an entangled state in a two spin-1/2 system by means of a spin-dependent potential scattering of another qubit is presented and analyzed in three dimensions. The entanglement is evaluated in terms of the concurrence both at the lowest and in full order in perturbation with an appropriate renormalization for the latter, and its characteristics are discussed in the context of (in)distinguishability of alternative paths for a quantum particle.

A scheme for preparing two fixed noninteracting qubits in a maximally entangled state is presented. By repeating on-and off-resonant scattering of ancilla qubits, the target qubits are driven from an arbitrary initial state into a singlet state with probability 1 (perfect efficiency). Neither the preparation nor the post-selection of the ancilla spin state is required. The convergence from an arbitrary input state to the unique fixed point (mixing property) is proved rigorously, and its robustness is investigated by scrutinizing the effects of imperfections in the incident wave of the ancillasuch as mistuning to a resonant momentum, imperfect monochromatization, and fluctuation of the incident momentum-as well as detector efficiency.

The dynamics of a system, consisting of a particle initially in a Gaussian state interacting with a field mode, under the action of repeated measurements performed on the particle, is examined. It is shown that regardless of its initial state the field is distilled into a squeezed state. The dependence on the physical parameters of the dynamics is investigated.

We discuss the state tomography of a fixed qubit (a spin-1/2 target particle), which is in general in a mixed state, through one-dimensional scattering of a probe qubit off the target. Two strategies are presented by making use of different degrees of freedom of the probe, i.e. spin and momentum. Remarkably, the spatial degree of freedom of the probe can be utilized for optimizing the tomographic schemes.

The dynamics of a system made of a particle interacting with a field mode "thwarted" by the action of repeated projective measurements on the particle is examined. The effect of the partial measurements is discussed by comparing it with the dynamics in the absence of the measurements.

A qubit (a spin-1/2 particle) prepared in the up state is scattered by local spin-flipping potentials produced by the two target qubits (two fixed spins), both prepared in the down state, to generate an entangled state in the latter when the former is found in the down state after scattering. The scattering process is analyzed in three dimensions, both to lowest order and in full order in perturbation, with an appropriate renormalization for the latter. The entanglement is evaluated in terms of the concurrence as a function of the incident and scattering angles, the size of the incident wave packet, and the detector resolution to clarify the key elements for obtaining an entanglement with high quality. The characteristics of the results are also discussed in the context of (in)distinguishability of alternative paths for a quantum particle.

We investigate the critical short-time scaling of the two-dimensional lattice phi(4) field theory with a Langevin dynamics. Starting from a "hot" initial configuration but with a small magnetization, the critical initial increase of the magnetization is observed through which we determine the critical point. From the short-time relaxation dynamics of various quantities at the critical point obtained, the dynamic critical exponents theta, z and the static exponent beta/nu are evaluated. In executing a Langevin simulation, an appropriate discretization method with respect to the time degree of freedom becomes essentially important to be adopted and we show that the well-know second-order form of discretized Langevin equation works well to investigate the short-time dynamics.

Under appropriate circumstances the electrons emitted from a superconducting tip can be entangled. We analyze these nonlocal correlations by studying the coincidences of the field-emitted electrons and show that electrons emitted in opposite directions violate Bell's inequality. We scrutinize the interplay between the bosonic nature of Cooper pairs and the fermionic nature of electrons. We further discuss the feasibility of our analysis in the light of present experimental capabilities.

As a possible physical realization of a quantum information processor, a system with stacked self-assembled InAs quantum dots buried in GaAs adjacent to the channel of a spin field-effect transistor has been proposed. In this system, only one of the stacked qubits, i.e., the edge qubit (the qubit closest to the channel), is measurable via "spin-blockade measurement." It is shown that the state tomography of the whole chain of the qubits is still possible even under such a restricted accessibility. The idea is to make use of the entangling dynamics of the qubits. A recipe for the two-qubit system is explicitly constructed and the effect of an imperfect fidelity of the measurement is clarified. A general scheme for multiple qubits based on repeated measurements is also presented.

Lateral effects are analyzed in the antibunching of a beam of free noninteracting fermions. The emission of particles from a source is dynamically described in a three-dimensional full quantum-field-theoretical framework. The size of the source and the detectors, as well as the temperature of the source are taken into account and the behavior of the visibility is scrutinized as a function of these parameters.

Decoherence is believed to deteriorate the ability of a purification scheme that is based on the idea of driving a system to a pure state by repeatedly measuring another system in interaction with the former and hinder for a pure state to be extracted asymptotically. Nevertheless, we find a way out of this difficulty by deriving an analytic expression of the reduced density matrix for a two-qubit system immersed in a bath. It is shown that we can still extract a pure state if the environment brings about only dephasing effects. In addition, for a dissipative environment, there is a possibility of obtaining a dominant pure state when we perform a finite number of measurements.

Repeated observations of a quantum system interacting with another one can drive the latter toward a particular quantum state, irrespective of its initial condition, because of an effective nonunitary evolution. If the target state is a pure one, the degree of purity of the system approaches unity, even when the initial condition of the system is a mixed state. In this paper we study the behavior of the purity from the initial value to the final one, that is, unity. Depending on the parameters, after a finite number of measurements, the purity exhibits oscillations that brings about a lower purity than that of the initial state, which is a point to be taken care of in concrete applications.

A quantum system put in interaction with another one that is repeatedly measured is subject to a nonunitary dynamics, through which it is possible to extract subspaces. This key idea has been exploited to propose schemes aimed at the generation of pure quantum states (purification). All such schemes have so far been considered in the ideal situations of isolated systems. In this paper, we analyze the influence of non-negligible interactions with environment during the extraction process, with the scope of investigating the possibility of purifying the state of a system in spite of the sources of dissipation. A general framework is presented and a paradigmatic example consisting of two interacting spins immersed in a bosonic bath is studied. The effectiveness of the purification scheme is discussed in terms of purity for different values of the relevant parameters and in connection with the bath temperature.

A theoretical scheme to generate multipartite entangled states in a Josephson planar-designed architecture is reported. This scheme improves the one published by Migliore [Phys. Rev. B 74, 104503 (2006)] since it speeds up the generation of W entangled states in an MxN array of inductively coupled Josephson flux qubits by reducing the number of necessary steps. In addition, the same protocol is shown to be able to transfer the W state from one row to the other.

We analyze some solvable models of a quantum mechanical system in interaction with a reservoir when the initial state is not factorized. We apply Nakajima-Zwanzig's projection method by choosing a reference state of the reservoir endowed with the mixing property. In van Hove's limit, the dynamics is described in terms of a master equation. We observe that Markovianity becomes a valid approximation for timescales that depend both on the form factors of the interaction and on the observables of the reservoir that can be measured. (c) 2006 Elsevier Inc. All rights reserved.

We analyze the dynamics of a quantum mechanical system in interaction with a reservoir when the initial state is not factorized. In the weak-coupling (van Hove) limit, the dynamics can be properly described in terms of a master equation, but a consistent application of Nakajima-Zwanzig's projection method requires that the reference (not necessarily equilibrium) state of the reservoir be endowed with the mixing property. (c) 2006 Elsevier Inc. All rights reserved.

As a promising physical realization of a quantum computer, we discuss a system with stacked quantum dots buried in adjacent to the channel of a spin field-effect transistor. In this scheme, one can measure only the edge qubit (nearest to the channel) via the spin-blockade measurement, but still it is possible to know the state of the whole qubits.

Generation of entanglement between two qubits by scattering an entanglement mediator is discussed. The mediator bounces between the two qubits and exhibits a resonant scattering. It is clarified how the degree of the entanglement is enhanced by the constructive interference of such bouncing processes. Maximally entangled states are available via adjusting the incident momentum of the mediator or the distance between the two qubits, but their fine tunings are not necessarily required to gain highly entangled states and a robust generation of entanglement is possible.

The so-called Lindblad equation, a typical master equation describing the dissipative quantum dynamics, is shown to be solvable for finite-level systems in a compact form without resort to writing it down as a set of equations among matrix elements. The solution is then naturally given in an operator form, known as the Kraus representation. Following a few simple examples, the general applicability of the method is clarified.

We propose and analyze a scheme for the generation of multipartite entangled states in a system of inductively coupled Josephson flux qubits. The qubits have fixed eigenfrequencies during the whole process in order to minimize decoherence effects and their inductive coupling can be turned on and off at will by tuning an external control flux. Within this framework, we will show that a W state in a system of three or more qubits can be generated by exploiting the sequential one by one coupling of the qubits with one of them playing the role of an entanglement mediator.

We discuss three control strategies, whose objective is to counter the effects of decoherence: the first strategy hinges upon the quantum Zeno effect, the second makes use of frequent unitary interruptions ("bang-bang" pulses), and the third of a strong, continuous coupling. Decoherence can be suppressed only if the frequency tau(-1) of the measurements/pulses is large enough or if the coupling K is sufficiently strong. Otherwise, if tau(-1) or K are large, but not sufficiently large, all these control procedures accelerate decoherence.

We present a novel method for preparing pure quantum states, i.e., purification through Zeno-like measurements, and its possible applications and extensions. © 2006 IOP Publishing Ltd.

We propose and analyze a scheme for the generation of multipartite entangled states in a system of inductively coupled Josephson flux qubits. The qubits have fixed eigenfrequencies during the whole process in order to minimize decoherence effects and their inductive coupling can be turned on and off at will by tuning an external control flux. Within this framework, we will show that a W state in a system of three or more qubits can be generated by exploiting the sequential one by one coupling of the qubits with one of them playing the role of an entanglement mediator. © 2006 The American Physical Society.

We propose a method of operating a quantum state machine made of stacked quantum dots buried in adjacent to the channel of a spin field-effect transistor (FET) [S. Datta, B. Das, Appl. Phys. Lett. 56 (1990) 665; K. Yoh, et al., Proceedings of the 23rd International Conference oil Physics of Semiconductors (ICPS) 2004; H. Ohno, K. Yoh et al., Jpn. J. Appl. Phys. 42 (2003) L87; K. Yoh, J. Konda, S. Shiina, N. Nishiguchi, Jpn. J. Appl. Phys. 36 (1997) 4134]. In this method, a spin blockade measurement extracts the quantum state of a nearest quantum dot through Coulomb blockade [K. Yoh, J. Konda, S. Shiina, N. Nishiguchi, Jpn. J. Appl. Phys. 36 (1997) 4134; K. Yoh, H. Kazama, Physica E 7 (2000) 440] of the adjacent channel conductance. Repeated quantum Zeno-like (QZ) measurements [H. Nakazato, et al., Phys. Rev. Lett. 90 (2003) 060401] of the spin blockade is shown to purify the quantum dot states within several repetitions. The growth constraints of the stacked InAs quantum dots are shown to provide an exchange interaction energy in the range of 0.01-1 meV [S. Itoh, et al., Jpn. J. Appl. Phys. 38 (1999) L917; A. Tackeuchi, et al., Jpn. J. Appl. Phys. 42 (2003) 4278]. We have verified that one can reach the fidelity of 90% by repeating the measurement twice, and that of 99.9% by repeating only eleven QZ measurements. Entangled states with two and three vertically stacked dots are achieved with the sampling frequency of the order of 100 MHz. (c) 2005 Elsevier B.V. All rights reserved.

A simple scheme to prepare an entanglement between two separated qubits from a given mixed state is proposed. A single qubit (entanglement mediator) is repeatedly made to interact locally and consecutively with the two qubits through rotating-wave couplings and is then measured. It is shown that we need to repeat this kind of process only three times to establish a maximally entangled state directly from an arbitrary initial mixed state, with no need to prepare the state of the qubits in advance or to rearrange the setup step by step. Furthermore, the maximum yield realizable with this scheme is compatible with the maximum entanglement, provided that the coupling constants are properly tuned.

A quantum system interacting with a repeatedly measured one undergoes a nonunitary time evolution pushing it into some specific subspaces. We deeply investigate the origin of the relevant selection rule, bringing to the light its connection with the survival probability related with the two-system interaction. The possibility of inducing an effective dynamics in the distilled subspace just during the distillation process is demonstrated. (c) 2005 Pleiades Publishing, Inc.

A quantum system in interaction with a repeatedly measured one undergoes a nonunitary time evolution and is pushed into a subspace substantially determined by the two-system coupling. The possibility of suitably modifying such an evolution through quantum Zeno dynamics (i.e., the generalized quantum Zeno effect) addressing the system toward an a priori decided target subspace is illustrated. Applications and their possible realizations in the context of trapped ions are also discussed.

We analyze and compare three different strategies, all aimed at controlling and eventually halting decoherence. The first strategy hinges upon the quantum Zeno effect, the second makes use of frequent unitary interruptions ("bang-bang" pulses and their generalization, quantum dynamical decoupling), and the third uses a strong, continuous coupling. Decoherence is shown to be suppressed only if the frequency N of the measurements or pulses is large enough or if the coupling K is sufficiently strong. Otherwise, if N or K is large, but not extremely large, all these control procedures accelerate decoherence. We investigate the problem in a general setting and then consider some practical examples, relevant for quantum computation.

A recently proposed purification method, in which Zeno-like measurements of a subsystem can bring about a distillation of another subsystem in interaction with the former, is utilized to yield entangled states between distant systems. It is shown that measurements of a two-level system, locally interacting with two other spatially separated uncoupled subsystems, can distill entangled states from the latter irrespective of the initial states of the two subsystems.

We present a novel method for purifying quantum states, i.e. purification through Zeno-like measurements, and show an application to entanglement purification.

A mechanism to purify quantum states by Zeno-like measurements was discussed and was applied to simple qubit systems. A pure state was extracted in a quantum system by a series of measurements on another quantum system in interaction with the former. Entanglement purification was one of the application in the purification method. An extension of this method was in the entanglement between two spatially separated qubits which was necessary for quantum communication and quantum teleportation.

We present a novel procedure to purify quantum states, i.e., purification through Zeno-like measurements. By simply repeating one and the same measurement on a quantum system, one can purify another system in interaction with the former. The conditions for the (efficient) purification are specified on a rather general setting, and the framework of the method possesses wide applicability. It is explicitly demonstrated on a specific setup that the purification becomes very efficient by tuning relevant parameters.

A neutron-spin experimental test of the quantum Zeno effect (QZE) is discussed from a practical point of view, where the nonideal efficiency of the magnetic mirrors, used for filtering the spin state, is taken into account. In the idealized case, the number N of (ideal) mirrors can be indefinitely increased, yielding an increasingly better QZE. In contrast, in a practical situation with imperfect mirrors, there is an optimal number of mirrors, N-opt, at which the QZE becomes maximum: more frequent measurements would deteriorate the performance. However, a quantitative analysis shows that a good experimental test of the QZE is still feasible. These conclusions are of general validity: in a realistic experiment, the presence of losses and imperfections leads to an optimal frequency N-opt, which is in general finite. One should not increase N beyond N-opt. A convenient formula for N-opt, valid in a broad framework, is derived as a function of the parameters characterizing the experimental setup.

A series of frequent measurements on a quantum system (Zeno-like measurements) is shown to result in the "purification" of another quantum system in interaction with the former. Even though the measurements are performed on the former system, their effect drives the latter into a pure state, irrespectively of its initial (mixed) state, provided certain conditions are satisfied.

The exact expression of the survival amplitude of a model system, which may describe photodetachment of a negative ion, is derived and analyzed in detail with an attention on its behavior as a function of time. The latter is governed by the location of poles of the amplitude in the complex energy plane. Poles located on the real energy axis can prevent the system from decay (known as plasmon poles), while other poles on the second Riemannian sheet give rise to exponentially decaying terms. The solvability of the model enables us to see explicitly the analytic structure of the amplitude, e.g., the movement of the poles in the complex energy plane as functions of parameters of the model. The behavior both at short and long times is also derived exactly and its peculiarity is pointed out and discussed.

The temporal evolution of an unstable quantum mechanical system undergoing repeated measurements is investigated. In general, by changing the time interval between successive measurements, the decay can be accelerated (inverse quantum Zeno effect) or slowed down (quantum Zeno effect), depending on the features of the interaction Hamiltonian. A geometric criterion is proposed for a transition to occur between these two regimes.

A quantum mechanical version of a classical inverted pendulum is analyzed. The stabilization of the classical motion is reflected in the bounded evolution of the quantum mechanical operators in the Heisenberg picture. Interesting links with the quantum Zeno effect are discussed. (C) 2001 Elsevier Science B.V. All rights reserved.

We study the dynamical properties of a two-level system in interaction with its environment, whose action on the system is modeled by means of a noise term in the Hamiltonian. We solve the Schrodinger equation, obtain an evolution equation of the Lindblad type for the noise average of the density matrix, and: discuss the results in terms of a "decoherence parameter." Finally, we concentrate our attention on the possibility of hindering the transitions between the two levels in two (apparently unrelated) ways: (a) by increasing the strength of the noise; (b) by a series of frequent measurements. There is an interesting relation between these two situations.

The dynamics of a quantum system undergoing frequent "measurements," leading to the so-called quantum Zeno effect, is examined on the basis of a neutron-spin experiment recently proposed for its demonstration. Unlike in all previous studies, the spatial degrees of freedom of the neutron are duly taken into account. Their inclusion in the analysis is important for two reasons: first, neutron-reflection effects are shown to be very important; second, the evolution may rum out to be totally different from the ideal case. Our results can be interpreted in terms of a rigorous theorem due to Misra and Sudarshan: indeed we clarify that, in contrast with a widespread belief, a quantum Zeno effect does not halt the evolution of a quantum system; it rather modifies it, by forcing the system to remain in a certain subspace, defined by the very measurement performed. [S1050-2947(99)00811-2].

By making use of the Langevin equation with a kernel, it was shown that the Feynman measure e(-S) can be realized in a restricted sense in a diffusive stochastic process, which diverges and has no equilibrium, for bottomless systems. In this paper, the dependence on the initial conditions and the temporal behavior are analyzed for 0-dim bottomless systems. Furthermore, it is shown that it is possible to find stationary quantities.

The limit of infinitely many measurements is critically analyzed within the quantum mechanical framework, in connection with the quantum Zeno effect. It is shown that such a limit is unphysical and that quantum losses are unavoidable. A specific example involving neutron spin is considered. (C) 1998 Elsevier Science B.V.

A one-dimensional scattering problem off a delta-shaped potential is solved analytically and the time development of a wave packet is derived from the time-dependent Schrodinger equation. The exact and explicit expression of the scattered wave packet supplies us with interesting information about the "time delay" by potential scattering in the asymptotic region. It is demonstrated that a wave packet scattered by a spin-flipping potential can give us quite a different value for the delay times from that obtained without spin-degrees of freedom.

We first stress that the time symmetry in quantum mechanics manifests itself in the analytical properties of the Fourier transform of the evolution operator in the complex E-plane (E being the variable conjugate to time), in such a way that all singularities are distributed only on the real axis in the first Riemannian sheet, and new poles appear, in the N infinite limit (N standing for the number of degrees of freedom of detector or instrument concerned), on the second Riemannian sheet in a symmetric way with respect to the real axis. We then examine the symmetry-breaking phenomenon, such as decay or dissipation, by setting up the initial value problem: The temporal evolution of the transition probability is divided into three parts, the first being Gaussian for very short times, the second exponential for intermediate times and the third of the power type for very long times. We know that the Gaussian decay is directly connected to the so-called quantum Zeno effect, the exponential decay corresponds to a sort of dephasing process, because the time rate of the total transition probability becomes a sum of time rates of partial probabilities, and both the Gaussian-like and power-like decay will disappear, leaving only the exponential one, in the van Hove limit. The dominance of the exponential decay is equivalent to the appearance of a master equation, which tells us that we have no phase-correlation but decoherence or dephasing. All temporal behaviors of quantum-mechanical transition probability and related physics are reflected in the analytical property of the Fourier transform of the evolution operator.

The temporal behavior of an unstable system is analyzed quantum mechanically and compared to the exponential decay law. The general mathematical features of the quantum evolution, yielding a quadratic region at short times and a power law at long times, are briefly reviewed.
The consequences of the short-time quadratic evolution are curious: By performing many measurements in rapid succession on a quantum system, in order to check whether it is still in its initial state, one can hinder its evolution. This phenomenon is known as the quantum Zeno effect and is discussed in detail. In this respect, a specific example involving neutron spin is considered. Finally, we focus our attention on some interesting features of the evolution law.

A one-dimensional scattering problem off a delta-shaped potential is solved analytically and the time development of a wave packet is derived from the time-dependent Schrodinger equation. The exact and explicit expression of the scattered wave packet supplies us with interesting information about the 'time delay' by potential scattering in the asymptotic region. It is demonstrated that a wave packet scattered by a spin-flipping potential can give us quite a different value for the delay times from that obtained without spin-degrees of freedom.

We analyze a modified version of the Coleman-Hepp model, which is able to take into account energy-exchange processes between the incoming particle and the linear array made up of N spin-1/2 systems. We bring to light the presence of a Wiener dissipative process in the weak-coupling, macroscopic (N --> infinity) limit. In such a limit and a restricted portion of the total Hilbert space, the particle undergoes a sort of Brownian motion, while the flee Hamiltonian of the spin array serves as a Wiener process. No partial trace is computed over the states of the spin system (which plays the role of ''reservoir''). The mechanism of appearance of the stochastic process is discussed and contrasted to other noteworthy examples in the literature. The links with van Hove's ''lambda(2)T'' limits are emphasized.

We study the Coleman-Hepp or AgBr Hamiltonian, concentrating our attention on a weak-coupling, macroscopic Limit that yields dissipative effects. We analyze the role played by Van Hove's "lambda(2)T" limit.

The modified Coleman-Hepp (AgBr) model describes the interaction between an ultrarelativistic quantum mechanical particle Q and an N-spin array D (a macroscopic medium in the N --> infinity limit). We prove that the energy operator for D essentially behaves as a Wiener process in the weak-coupling, macroscopic limit, in a restricted state space. No assumptions are made on the spectrum of the Hamiltonian of the macroscopic system D. The mechanism of appearance of such a stochastic process and its relevance to issues like dissipation and irreversibility are briefly discussed.

We examine whether the chaotic behavior of classical systems with a limited number of degrees of freedom can produce quantum dephasing, against the conventional idea that dephasing takes place only in large systems with a huge number of constituents and complicated internal interactions. On the basis of this analysis, we briefly discuss the possibility of defining quantum chaos and of inventing a ''chaos detector''.

The quantum Zeno effect consists in the hindrance of the evolution of a quantum system that is very frequently monitored and found to be in its initial state at every single measurement. On the basis of the correct formula for the survival probability, i.e. the probability of finding the system in its initial state at every single measurement, we critically analyze a recent proposal and experimental test that make use of an oscillating system.

The temporal behavior of quantum mechanical systems is reviewed. We mainly focus our attention on the time development of the so-called ''survival'' probability of those systems that are initially prepared in eigenstates of the unperturbed Hamiltonian, by assuming that the latter has a continuous spectrum.
The exponential decay of the survival probability, familiar, for example, in radioactive decay phenomena, is representative of a purely probabilistic character of the system under consideration and is naturally expected to lead to a master equation. This behavior, however, can be found only at intermediate times, for deviations from it exist both at short and long times and can have significant consequences.
After a short introduction to the long history of the research on the temporal behavior of such quantum mechanical systems, the short-time behavior and its controversial consequences when it is combined with von Neumann's projection postulate in quantum measurement theory are critically overviewed from a dynamical point of view. We also discuss the so-called quantum Zeno effect from this standpoint.
The behavior of the survival amplitude is then scrutinized by investigating the analytic properties of its Fourier and Laplace transforms. The analytic property that there is no singularity except a branch cut running along the real energy axis in the first Riemannian sheet is an important reflection of the time-reversal invariance of the dynamics governing the whole process. It is shown that the exponential behavior is due to the presence of a simple pole in the second Riemannian sheet, while the contribution of the branch point yields a power behavior for the amplitude. The exponential decay form is cancelled at short times and dominated at very long times by the branch-point contributions, which give a Gaussian behavior for the former and a power behavior for the latter.
In order to realize the exponential law in quantum theory, it is essential to take into account a certain kind of macroscopic nature of the total system, since the exponential behavior is regarded as a manifestation of a complete loss of coherence of the quantum subsystem under consideration. In this respect, a few attempts at extracting the exponential decay form on the basis of quantum theory, aiming at the master equation, are briefly reviewed, including van Hove's pioneering work and his well-known ''lambda(2)T'' limit.
In the attempt to further clarify the mechanism of the appearance of a purely probabilistic behavior without resort to any approximation, a solvable dynamical model is presented and extensively studied. The model describes an ultrarelativistic particle interacting with N two-level systems (called ''spins'') and is shown to exhibit an exponential behavior at all times in the weak-coupling, macroscopic limit. Furthermore, it is shown that the model can even reproduce the short-time Gaussian behavior followed by the exponential law when an appropriate initial state is chosen. The analysis is exact and no approximation is involved. An interpretation for the change of the temporal behavior in quantum systems is drawn from the results obtained. Some implications for the quantum measurement problem are also discussed, in particular in connection with dissipation.

The conditions that yield deviations from a purely exponential behavior of a quantum mechanical system at short times are analyzed with special emphasis on the boundedness of the Hamiltonian. A few practical examples are considered. The problem of dissipation in quantum mechanics and quantum field theory is also briefly discussed.

The limit of infinitely frequent measurements (continuous observation), yielding the quantum Zeno paradox, is critically analyzed and shown to be unphysical. A specific example involving neutron spin is considered and some practical estimates are given.

By making use of Schwinger's oscillator model of angular momentum, we put forward an interesting connection among three solvable Hamiltonians, widely used for discussions on the quantum measurement problem. This connection implies that a particular macroscopic limit has to be taken for these models to be physically sensible.

An exponential behavior at all times is derived for a solvable dynamical model in the weak-coupling macroscopic limit. Some implications for the quantum measurement problems are discussed, in particular in connection with dissipation.

The interaction between an ultrarelativistic particle and a linear array made up of N two-level systems (AgBr molecules) is studied by making use of a modified version of the Coleman-Hepp Hamiltonian. Energy-exchange processes between the particle and the molecules axe properly taken into account, and the evolution of the total system is calculated exactly both when the array is initially in the ground state and in a thermal state. In the weak-coupling, macroscopic (N --> infinity) limit, the system remains solvable and leads to interesting connections with the Jaynes-Cummings model, which describes the interaction of a particle with a maser. The visibility of the interference pattern produced by the two branch waves of the particle is computed, and the conditions under which the spin array behaves as a ''detector'' are investigated. The behavior of the visibility yields good insights into the issue of quantum measurements: It is found that, in the N --> infinity limit, a superselection-rule space appears in the description of the (macroscopic) apparatus. In general, an initial thermal state of the ''detector'' provokes a more substantial loss of quantum coherence than an initial ground state. It is argued that a system increasingly loses coherence as the temperature of the detector increases. The problem of ''imperfect measurements'' is also briefly discussed.

The stochastic quantization method is formulated in Minkowski space. Owing to a complex drift which appears in the Langevin equation (one of the basic equations of this quantization method), it is not manifest whether the system has a definite equilibrium state. To guarantee the system will reach equilibrium, the so-called ie-prescription is adopted. It is shown that in the Fokker-Planck formalism there naturally appears an effective Fokker-Planck distribution, which is complex-valued and is to be expected to become the Feynman amplitude e^<iS> in the equilibrium limit. The dynamics which governs the hypothetical thermal process can be clarified by investigating the spectrum of the Fokker-Planck Hamiltonian. Here the spectrum is studied by means of the δ-expansion technique of Bender et al. and the ordinary perturbation theory to show its important role.

A model Hamiltonian describing an energy-exchange process between an ultrarelativistic particle and a one-dimensional spin array is proposed and solved exactly. Interesting relations with the quantum measurement problem are discussed.

A quantum-mechanical measurement process is analyzed in terms of a model Hamiltonian describing the interaction between a quantum system (a "particle") and a macroscopic apparatus (a "detector"), which is assumed to be made up of N two-level elementary constituents ("molecules"). The description of the molecule locations introduces an effective fluctuating coupling constant, and this provokes a loss of quantum-mechanical coherence in the limit of large N. It is argued that coherence is lost statistically, as a result of the interaction: The collapse of the wave function is indeed obtained when the same experiment is performed many times, as a result of the microscopic differences among macroscopically identical initial states of the detector. In this way, insight is obtained into the mechanism engendering the loss of coherence suffered by a quantum-mechanical system when interacting with a macroscopic apparatus, and the concept of "wave-function collapse" is replaced by that of a statistically defined dephasing process. No classical behavior of the detection system is postulated and the presence of no external observer is required.

Two different approaches to the problem of measurement in quantum mechanics are combined. In this way, new insights are obtained into the mechanism engendering the loss of coherence suffered by a quantum mechanical system when interacting with a macroscopic apparatus.

Einstein's version of the double-slit interferometer is reexamined by taking into account possible degrees of freedom of the detector. This can be considered as a natural generalization of an earlier attempt by Wooters and Zurek, however, it is found that in this approach a new element which is directly related to the uncertainties of physical variables appears and that it affects considerably the visibility of the interference pattern. This fact turns out to be a quantitative realization of the complementarity principle in quantum mechanics.

On the basis of the renormalization scheme of the stochastic quantization method, two β-functions in φ^4 theory, β_λ and β_γ which govern the scaling behaviors of the coupling constant λ and the fictitious time, respectively, are calculated up to the two-loop order.

Thermal equilibrium state in Minkowski stochastic quantization based on the complex Langevin equation is discussed by introducing an effective Fokker-Planck distribution for physical quantities. It is shown that this effective Fokker-Planck distribution becomes the usual Feynman measure exp(iS) in the thermal limit.

From phenomenological and field-theoretical considerations on photon mass, we first show that photon is not limited to being massless at the present stage. Next we illustrate a possibility of formulating a local field theory for massive photons coupled with nonconserved currents, while we cannot formulate it for massless photons.