The present letter finds the complete set of exact solutions of the time-dependent generalized Cini model by making use of the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation and, based on this, the general explicit expression for the decoherence factor is therefore obtained. This study provides us with a useful method to consider the geometric phase and topological properties in the time-dependent quantum decoherence process.
By making the second quantization for the Cini Model of quantum measurement without wave function collapse [M. Cini, Nuovo Cimento, B73 27(1983)], the second order quantum decoherence (SOQD) is studied with a two mode boson system interacting with an idealized apparatus composed by two quantum oscillators. In the classical limit that the apparatus is prepared in a Fock state with a very large quantum number, or in a coherent state with average quantum numbers large enough, the SOQD phenomenon appears similar to the first order case of quantum decoherence.
Distribution functions defined in accord with the quantum theory of measurement are combined with results obtained from the quantum Langevin equation to discuss decoherence in quantum Brownian motion. Closed form expressions for wave packet spreading and the attenuation of coherence of a pair of wave packets are obtained. The results are exact within the context of linear passive dissipation. It is shown that, contrary to widely accepted current belief, decoherence can occur at high temperature in the absence of dissipation. Expressions for the decoherence time with and without dissipation are…
We study the nonclassicality of photon-added squeezed vacuum (PASV) and its decoherence in thermal environment in terms of the sub-Poissonian statistics and the negativity of Wigner function (WF). By converting the PASV to a squeezed Hermite polynomial excitation state, we derive a compact expression for the normalization factor of m-PASV, which is an m-order Legendre polynomial of squeezing parameter r. We also derive the explicit expression of WF of m-PASV and find the negative region of WF in phase space. We show that there is an upper bound value of r for this state to exhibit sub-Poissoni…
In this work we investigate the dynamical Casimir effect in a nonideal cavity by deriving an effective Hamiltonian. We first compute a general expression for the average number of particle creation, applicable for any law of motion of the cavity boundary. We also compute a general expression for the linear entropy of an arbitrary state prepared in a selected mode, also applicable for any law of motion of the cavity boundary. As an application of our results we have analyzed both the average number of particle creation and linear entropy within a particular oscillatory motion of the cavity boun…
In this work, we investigate the dynamics of quantum correlations captured by entropic and geometric measures of discord under the influence of dissipative channels for widely used two qubit X state with maximally mixed marginals. Identifying the phenomena of the preservation, sudden change and revival of quantum correlation quantifiers, we determine their hierarchy of robustness under memory-less decoherence channels. We find the analytical expressions of decoherence probabilities at which sudden change occur when the first qubit is subjected to the decoherence channels for multiple times. We…
While agreeing with our exact expression for the time dependence of the motion of a free particle in an initial superposition state, corresponding to two identical Gaussians separated by a distance $d$, at temperature $T$, Gobert et al., in the preceding Comment [Phys. Rev. A xxx], dispute our conclusions on decoherence time scales. However, the parameters they used to generate their figures are outside the regime of validity of our interpretation of the results and, moreover, are not of physical interest in that they correspond to $T\approx 0$. The point is that in their figures they have cho…
The dynamics of a quantum anharmonic oscillator whose position is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double well potential is studied. The (non-exponential) decoherence induced on the oscillator by the measuring device is analysed. A detailed quasiclassical and quantum analysis is presented. In the first case, for an arbitrary initial coherent state, two different decoherence regimes are observed: An initial Gaussian decay followed by a power law decay for longer times. The characteristic time scales of both regimes are reported. Analytical approximated expres…
The present paper finds the complete set of exact solutions of the general time-dependent dynamical models for quantum decoherence, by making use of the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation. Based on this, the general explicit expression for the decoherence factor is then obtained and the adiabatic classical limit of an illustrative example is discussed. The result (i.e., the adiabatic classical limit) obtained in this paper is consistent with what obtained by other authors, and futhermore we obtain the more general results concerning t…
We derive the analytical expression of local quantum uncertainty for three-qubit X-states. We give also the expressions of quantum discord and the negativity. A comparison of these three quantum correlations quantifiers is discussed in the special cases of mixed GHZ states and Bell-type states. We find that local quantum uncertainty gives the same amount of non-classical correlations as are measured by entropic quantum discord and goes beyond negativity. We also discuss the dynamics of non-classical correlations under the effect of phase damping, depolarizing and phase reversal channels. We fi…
We study a model of dephasing (decoherence) in a two-state quantum system (qubit) coupled to a bath of harmonic oscillators. An exact analytic solution for the reduced dynamics of a two-state system in this model has been obtained previously for factorizing initial states of the combined system. We show that the model admits exact solutions for a large class of correlated initial states which are typical in the theory of quantum measurements. We derive exact expressions for the off-diagonal elements of the qubit density matrix, which hold for an arbitrary strength of coupling between the qubit…
This paper describes the dynamics of a quantum two-level system (qubit) under the influence of an environment modeled by an ensemble of random matrices. In distinction to earlier work, we consider here separable couplings and focus on a regime where the decoherence time is of the same order of magnitude than the environmental Heisenberg time. We derive an analytical expression in the linear response approximation, and study its accuracy by comparison with numerical simulations. We discuss a series of unusual properties, such as purity oscillations, strong signatures of spectral correlations (i…
We consider environment induced decoherence of quantum superpositions to mixtures in the limit in which that process is much faster than any competing one generated by the Hamiltonian $H_{\rm sys}$ of the isolated system. This interaction dominated decoherence limit has previously not found much attention even though it is of importance for the emergence of classical behavior in the macroworld, since it will always be the relevant regime for large enough separations between superposed wave packets. The usual golden-rule treatment then does not apply but we can employ a short-time expansion for…
We discuss a few mathematical aspects of random dynamical decoupling, a key tool procedure in quantum information theory. In particular, we place it in the context of discrete stochastic processes, limit theorems and CPT semigroups on matrix algebras. We obtain precise analytical expressions for expectation and variance of the density matrix and fidelity over time in the continuum-time limit depending on the system Lindbladian, which then lead to rough short-time estimates depending only on certain coupling strengths. We prove that dynamical decoupling does not work in the case of intrinsic (i…
We address the problem of two interacting atoms of different species inside a cavity and find the explicit solutions of the corresponding eigenvalues and eigenfunctions using a new invariant. This model encompasses various commonly used models. By way of example we obtain closed expressions for concurrence and purity as a function of time for the case where the cavity is prepared in a number state. We discuss the behaviour of these quantities and and their relative behaviour in the concurrence-purity plane.
The no-knowledge quantum feedback was proposed by Szigeti et al., Phys. Rev. Lett. 113, 020407 (2014), as a measurement-based feedback protocol for decoherence suppression for an open quantum system. By continuously measuring environmental noises and feeding back controls on the system, the protocol can completely reverse the measurement backaction and therefore suppress the system's decoherence. However, the complete decoherence cancellation was shown only for the instantaneous feedback, which is impractical in real experiments. Therefore, in this work, we generalize the original work and inv…
Markovian regime decoherence effects in quantum computers are studied in terms of the fidelity for the situation where the number of qubits N becomes large. A general expression giving the decoherence time scale in terms of Markovian relaxation elements and expectation values of products of system fluctuation operators is obtained, which could also be applied to study decoherence in other macroscopic systems such as Bose condensates and superconductors. A standard circuit model quantum computer involving three-state lambda system ionic qubits is considered, with qubits localised around well-se…
We study the stability of the coherence of a state of a quantum system under the effect of an interaction with another quantum system at short time. We find an expression for evaluating the order of magnitude of the time scale for the onset of instability as a function of the initial state of both involved systems and of the sort of interaction between them. As an application we study the spin-boson interaction in the dispersive interaction regime, driven by a classical field. We find, for this model, that the behavior of the time scale for the onset of instability, with respect to the boson b…
The time evolution of low energy spin states of a single molecular magnet in a local electric field is investigated. The decoherence of the driven single molecular magnet weakly coupled to a thermal bosonic environment is analyzed by the second-order time-convolutionless non-Markovian master equation. If the characteristic time of the system is much smaller than the correlation time of the environment, the analytical expression of the reduced density matrix of the system is obtained. The non-Markovian dynamics of the spin states at low temperatures is induced by the memory effects in the decay…
The decoherence of mixed electron-nuclear spin qubits is a topic of great current importance, but understanding is still lacking: while important decoherence mechanisms for spin qubits arise from quantum spin bath environments with slow decay of correlations, the only analytical framework for explaining observed sharp variations of decoherence times with magnetic field is based on the suppression of classical noise. Here we obtain a general expression for decoherence times of the central spin system which exposes significant differences between quantum-bath decoherence and decoherence by class…
We investigate the quantum evolution of spin states of a single molecular magnet in a local electric field. The decoherence of a $\texttt{\{}\emph{Cu}_3\texttt{\}}$ single molecular magnet weakly coupled to a thermal bosonic environment can be analyzed by the spin-boson model. Using the finite-temperature time-convolutionless quantum master equation, we obtain the analytical expression of the reduced density matrix of the system in the secular approximation. The suppressed and revived dynamical behavior of the spin states are presented by the oscillation of the chirality spin polarization on t…
There exists the well known approximate expression describing the large time behaviour of matrix elements of the evolution operator in quantum theory: <U(t)>=exp(at)+... This expression plays the crucial role in considerations of problems of quantum decoherence, radiation, decay, scattering theory, stochastic limit, derivation of master and kinetic equations etc. This expression was obtained in the Weisskopf-Wigner approximation and in the van Hove (stochastic) limit. We derive the exact general formula which includes the higher order corrections to the above approximate expression: <U(t)>=exp…
In statistical estimation theory, it has been shown previously that the Wigner-Yanase skew information is bounded by the quantum Fisher information associated with the phase parameter. Besides, the quantum Cramér-Rao inequality is expressed in terms of skew information. Since these two fundamental quantities are based on the concept of quantum uncertainty, we derive here their analytical formulas for arbitrary two qubit $X$-states using the same analytical procedures. A comparison of these two informational quantifiers for two quasi-Werner states composed of two bipartite superposed coherent s…
Using the path integral representation of the density matrix propagator of quantum Brownian motion, we derive its asymptotic form for times greater than the localization time, $ (\hbar / γk T )^{\half}$, where $γ$ is the dissipation and $T$ the temperature of the thermal environment. The localization time is typically greater than the decoherence time, but much shorter than the relaxation time, $γ^{-1}$. We use this result to show that the reduced density operator rapidly evolves into a state which is approximately diagonal in a set of generalized coherent states. We thus reproduce, using a co…
For the generalized master equations derived by Karrlein and Grabert for the microscopic model of a damped harmonic oscillator, the conditions for purity of states are written, in particular for different initial conditions and different types of damping, including Ohmic, Drude and weak coupling cases, Agarwal and Weidlich-Haake models. It is shown that the states which remain pure are the squeezed states with constant in time variances. For pure states, the generalized nonlinear Schr\" odinger-type equations corresponding to these master equations are also obtained. Then the condition for pur…
Bounds of the minimum evolution time between two distinguishable states of a system can help to assess the maximal speed of quantum computers and communication channels. We study the quantum speed limit time of a composite quantum states in the presence of nondissipative decoherence. For the initial states with maximally mixed marginals, we obtain the exactly expressions of quantum speed limit time which mainly depend on the parameters of the initial states and the decoherence channels. Furthermore, by calculating quantum speed limit time for the time-dependent states started from a class of i…
A Mean-Field Lindblad Master Equation Framework for Interaction-Driven Decoherence in Solid-State Qubit Ensembles
Department of Chemistry, University of Colorado Boulder（科罗拉多大学博尔德分校化学系）；Ann and H.J. Smead Aerospace Engineering Sciences, University of Colorado Boulder（科罗拉多大学博尔德分校安恩和H.J.斯米德航空航天工程科学）
The mixing time of a discrete-time quantum walk on the hypercube is considered. The mean probability distribution of a Markov chain on a hypercube is known to mix to a uniform distribution in time O(n log n). We show that the mean probability distribution of a discrete-time quantum walk on a hypercube mixes to a (generally non-uniform) distribution pi(x) in time O(n) and the stationary distribution is determined by the initial state of the walk. An explicit expression for pi(x) is derived for the particular case of a symmetric walk. These results are consistent with those obtained previously f…
We analyze rigorously the dynamics of the entanglement between two qubits which interact only through collective and local environments. Our approach is based on the resonance perturbation theory which assumes a small interaction between the qubits and the environments. The main advantage of our approach is that the expressions for (i) characteristic time-scales, such as decoherence, disentanglement, and relaxation, and (ii) observables are not limited by finite times. We introduce a new classification of decoherence times based on clustering of the reduced density matrix elements. The charact…
The quantum random walk has been much studied recently, largely due to its highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum walk on the line: the presence of decoherence in the quantum ``coin'' which drives the walk. We find exact analytical expressions for the time dependence of the first two moments of position, and show that in the long-time limit the variance grows linearly with time, unlike the unitary walk. We compare this to the results of direct numerical simulation, and see how the form of the position distribution…
Developing quantum technologies requires the control and understanding of the non-equilibrium dynamics of quantum information in many-body systems. Local information propagates in the system by creating complex correlations known as information scrambling, as this process prevents extracting the information from local measurements. In this work, we develop a model adapted from solid-state NMR methods, to quantify the information scrambling. The scrambling is measured via time-reversal Loschmidt echoes (LE) and Multiple Quantum Coherences experiments that intrinsically contain imperfections. Co…
This paper presents an analysis of decoherence resulting from the physically real non-unitarity, or 'objective reduction,' that occurs in the Transactional Interpretation (TI). Two distinct aspects of the decoherence process are identified and disambiguated; specifically, (i) the resolution of the basic measurement interaction with respect to the observable under study, and (ii) the effect on the measured system of repetition of the measurement interaction. It is shown that the measurement interaction as described in TI leads naturally to the same quantitative expression for the decoherence fu…
Gravitationally Induced Quantum Decoherence of Macroscopic Objects
The Hakubi Center for Advanced Research, Kyoto University（京都大学白川中心）；Department of Physics, Kyoto University（京都大学物理系）；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）
We take a central spin model (CSM), consisting of a one dimensional environmental Ising spin chain and a single qubit connected globally to all the spins of the environment, to study numerically the excess energy (EE) of the environment and the logarithm of decoherence factor namely, dynamical fidelity susceptibility per site (DFSS), associated with the qubit under a periodic driving of the transverse field term of environment across its critical point using the Floquet technique. The coupling to the qubit, prepared in a pure state, with the transverse field of the spin chain yields two sets o…
Sachdev-Ye-Kitaev (SYK) or embedded random ensembles are models of $N$ fermions with random k-body interactions. They play an important role in understanding black hole dynamics, quantum chaos, and thermalization. We study out of equilibrium scenarios in these systems and show they display perfect decoherence at all times. This peculiar feature makes them very attractive in the context of the quantum-to-classical transition and the emergence of classical general relativity. Based on this feature and unitarity, we propose a rate/continuity equation for the dynamics of the $\mathcal{O}(e^N)$ mic…
We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point contact. We derive the analytical expression of the probability distribution along the cycle. Upper bound estimate to mixing time is shown.
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two-harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [Hu, Paz and Zhang, Phys. Rev. D \textbf{45}, 284…
This work considers the theory underlying a discrete-time quantum filter recently used in a quantum feedback experiment. It proves that this filter taking into account decoherence and measurement errors is optimal and stable. We present the general framework underlying this filter and show that it corresponds to a recursive expression of the least-square optimal estimation of the density operator in the presence of measurement imperfections. By measurement imperfections, we mean in a very general sense unread measurement performed by the environment (decoherence) and active measurement perform…
