Quantum correlations typically decrease with increasing noise, although classical correlators (CCors) may rise for a particular class of states with noise. To analyse the behavior of classical correlation (CC) in the presence of local noise, we scrutinize the set of classical correlators, axiomatic CC measures like classical discord, and local work for Haar uniformly generated states. Like quantum correlation measures, we illustrate that when noise levels rise, the average value of the CC measures for noisy output states obtained from random input states decreases for most of the channels. We also demonstrate a connection between the CCors of the noise-affected multipartite states that are produced and the CCors of the initial states that exhibit exponential, polynomial, and constant behavior as the noise level changes. Moreover, based on CCors of the generalised N-qubit W state as input, we determine a method to discriminate between the quantum channels, namely phase damping, depolarizing, and amplitude damping channels. We also relate classical, quantum, and total correlation measures that exhibit a comparable reaction to decoherence for generic states.
The destruction of entanglement of open quantum systems by decoherence is investigated in the asymptotic long-time limit. Starting from a general and analytically solvable decoherence model which does not involve any weak-coupling or Markovian assumption it is shown that two fundamentally different classes of entangled states can be distinguished. Quantum states of the first class are fragile against decoherence so that they can be disentangled asymptotically even if coherences between pointer states are still present. Quantum states of the second type are robust against decoherence. Asymptoti…
We study the robustness and fragility of entanglement of open quantum systems in some exactly solvable models in which the decoherence is caused by a pure dephasing process. In particular, for the toy models presented in this paper, we identify two different time scales, one is responsible for local dephasing, while the other is for entanglement decay. For a class of fragile entangled states defined in this paper, we find that the entanglement of two qubits, as measured by concurrence, decays faster asymptotically than the quantum dephasing of an individual qubit.
We study the effect of local decoherence on arbitrary quantum states. Adapting techniques developed in quantum metrology, we show that the action of generic local noise processes -- though arbitrarily small -- always yields a state whose Quantum Fisher Information (QFI) with respect to local observables is linear in system size N, independent of the initial state. This implies that all macroscopic quantum states, which are characterized by a QFI that is quadratic in N, are fragile under decoherence, and cannot be maintained if the system is not perfectly isolated. We also provide analytical bo…
Decoherence-free subsystems have been successfully developed as a tool to preserve fragile quantum information against noises. In this letter, we develop a structure theory for decoherence-free subsystems. Based on it, we present an effective algorithm to construct a set of maximal decoherence-free subsystems in the sense that any other such subsystem is a subspace of one of them. As an application of these techniques in quantum many body systems, we propose a simple and numerically robust method to determine if two irreducible tensors are repeated, a key step in deciding if they are equivalen…
A quantum version of the Minority game for an arbitrary number of agents is considered. It is known that when the number of agents is odd, quantizing the game produces no advantage to the players, but for an even number of agents new Nash equilibria appear that have no classical analogue and have improved payoffs. We study the effect on the Nash equilibrium payoff of various forms of decoherence. As the number of players increases the multipartite GHZ state becomes increasingly fragile, as indicated by the smaller error probability required to reduce the Nash equilibrium payoff to the classica…
Certain quantum states are well-known to be particularly fragile in the presence of decoherence, as illustrated by Schrodinger's famous gedanken cat experiment. It has been better appreciated more recently that quantum states can be characterized in a hierarchy of quantum quantities such entanglement, quantum correlations, and quantum coherence. It has been conjectured that each of these quantities have various degrees of fragility in the presence of decoherence. Here we experimentally confirm this conjecture by preparing tripartite photonic states and subjecting them to controlled amounts of …
We introduce, for each state of a bosonic quantum field, its quadrature coherence scale (QCS), a measure of the range of its quadrature coherences. Under coupling to a thermal bath, the purity and QCS are shown to decrease on a time scale inversely proportional to the QCS squared. The states most fragile to decoherence are therefore those with quadrature coherences far from the diagonal. We further show a large QCS is difficult to measure since it induces small scale variations in the state's Wigner function. These two observations imply a large QCS constitutes a mark of "macroscopic coherence…
By using quantum mechanical effects, quantum computers promise significant speedups in solving problems intractable for conventional computers. However, despite recent progress they remain limited in scaling and availability-making quantum software and hardware development heavily reliant on quantum simulators running on conventional hardware. However, most of those simulators mimic perfect quantum computers and, hence, ignore the fragile nature of quantum mechanical effects which frequently yield to decoherence errors in real quantum devices. Considering those errors during the simulation is …
Quantum contextuality is a nonintuitive property of quantum mechanics, that distinguishes it from any classical theory. A complementary quantum property is quantum nonlocality, which is an essential resource for many quantum information tasks. Here we experimentally study the contextual and nonlocal properties of polarization biphotons. First, we investigate the ability of the biphotons to exhibit contextuality by testing the violation of the KCBS inequality. In order to do so, we used the original protocol suggested in the KCBS paper, and adjusted it to the real scenario, where some of the bi…
A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences between the classical and quantum decoherence dynamics of an initial quantum state are exposed using both analytical and computational results. In particular, the classicality of early-time intrinsic decoherence dynamics is explored analytically using a second-order perturbative treatment, and an interesting connection between decoherence rates and the stabil…
A direct classical analog of quantum decoherence is introduced. Similarities and differences between decoherence dynamics examined quantum mechanically and classically are exposed via a second-order perturbative treatment and via a strong decoherence theory, showing a strong dependence on the nature of the system-environment coupling. For example, for the traditionally assumed linear coupling, the classical and quantum results are shown to be in exact agreement.
I give a pedagogical overview of decoherence and its role in providing a dynamical account of the quantum-to-classical transition. The formalism and concepts of decoherence theory are reviewed, followed by a survey of master equations and decoherence models. I also discuss methods for mitigating decoherence in quantum information processing and describe selected experimental investigations of decoherence processes.
The observation of the non-local properties of multipartite entangled states is of great importance for quantum information protocols. Such properties, however, are fragile and may not be observed in the presence of decoherence exhibited by practical physical systems. In this work, we investigate the robustness of the non-locality of symmetric states experiencing phase and amplitude damping, using suitable Bell inequalities based on an extended version of Hardy's paradox. We derive thresholds for observing non-locality in terms of experimental noise parameters, and demonstrate the importance o…
Niels Bohr famously insisted on the indispensability of what he termed "classical concepts." In the context of the decoherence program, on the other hand, it has become fashionable to talk about the "dynamical emergence of classicality" from the quantum formalism alone. Does this mean that decoherence challenges Bohr's dictum -- for example, that classical concepts do not need to be assumed but can be derived? In this paper, we'll try to shed some light down the murky waters where formalism and philosophy mingle. To begin, we'll clarify the notion of classicality in the decoherence description…
We address decoherence and classicalization of continuous-time quantum walks (CTQWs) on graphs. In particular, we investigate three different models of decoherence, and employ the quantum-classical (QC) dynamical distance as a figure of merit to assess whether, and to which extent, decoherence classicalizes the CTQW, i.e. turns it into the analogue classical process. We show that the dynamics arising from intrinsic decoherence, i.e. dephasing in the energy basis, do not fully classicalize the walker and partially preserves quantum features. On the other hand, dephasing in the position basis, a…
The diverging responses to parameter variations of systems at quantum critical points motivate schemes of quantum metrology that feature sub-Heisenberg scaling of the sensitivity with the system size (e.g., the number of particles). This sensitivity enhancement is fundamentally rooted in the formation of Schrödinger cat states, or macroscopic superposition states at the quantum critical points. The cat states, however, are fragile to decoherence caused by local noises on individual particles or coupling to local environments, since the local decoherence of any particle would cause the collapse…
We study the dynamics of quantum and classical correlations in the presence of nondissipative decoherence. We discover a class of initial states for which the quantum correlations, quantified by the quantum discord, are not destroyed by decoherence for times t < \bar{t}. In this initial time interval classical correlations decay. For t > \bar{t}, on the other hand, classical correlations do not change in time and only quantum correlations are lost due to the interaction with the environment. Therefore, at the transition time \bar{t} the open system dynamics exhibits a sudden transition from cl…
It is now widely accepted that environmental entanglement and the resulting decoherence processes play a crucial role in the quantum-to-classical transition and the emergence of "classicality" from quantum mechanics. To this extent, decoherence is often understood as signifying a break with the Copenhagen interpretation, and in particular with Bohr's view of the indispensability of classical concepts. This paper analyzes the relationship between Bohr's understanding of the quantum-classical divide and his doctrine of classical concepts and the decoherence-based program of emergent classicality…
For a wide set of quantum systems it is demonstrated that the quantum regime can be considered as the transient phase while the final classical statistical regime is a permanent state. A basis where exact matrix decoherence appears for these final states is found. The relation with the decoherence of histories formalism is studied. A set of final intrinsically consistent histories is found.
Quantum decoherence arises due to uncontrollable entanglement between a system with its environment. However the effects of decoherence are often thought of and modeled through a simpler picture in which the role of the environment is to introduce classical noise in the system's degrees of freedom. Here we establish necessary conditions that the classical noise models need to satisfy to quantitatively model the decoherence. Specifically, for pure-dephasing processes we identify well-defined statistical properties for the noise that are determined by the quantum many-point time correlation func…
Recently some authors have pointed out that there exist nonclassical correlations which are more general, and possibly more fundamental, than entanglement. For these general quantum correlations and their classical counterparts, under the action of decoherence, we identify three general types of dynamics that include a peculiar sudden change in their decay rates. We show that, under suitable conditions, the classical correlation is unaffected by decoherence. Such dynamic behavior suggests an operational measure of both classical and quantum correlations that can be computed without any extremi…
In the framework of the Lindblad theory for open quantum systems we determine the degree of quantum decoherence and classical correlations of a harmonic oscillator interacting with a thermal bath. The transition from quantum to classical behaviour of the considered system is analyzed and it is shown that the classicality takes place during a finite interval of time. We calculate also the decoherence time and show that it has the same scale as the time after which thermal fluctuations become comparable with quantum fluctuations.
In the framework of the Lindblad theory for open quantum systems we determine the degree of quantum decoherence and classical correlations of a harmonic oscillator interacting with a thermal bath. The transition from quantum to classical behaviour of the considered system is analyzed and it is shown that the classicality takes place during a finite interval of time. We calculate also the decoherence time and show that it has the same scale as the time after which statistical fluctuations become comparable with quantum fluctuations.
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…
A most simple theoretical argument is given in order to explain the quantitative estimate of the effect of collisional decoherence in matter-wave interferometry. The argument highlights the relevance of quantum and classical features in the description of the phenomenon, showing in particular the connection between the formula used for the experimental fit and the loss term in the classical linear Boltzmann equation.
Decoherence across phase-space scales: From compass states to general quantum states
School of Physics, Anhui University（安徽大学物理学院）；School of Physics and Technology, Nantong University（南通大学物理与信息技术学院）；Department of Physics, Zhejiang Normal University（浙江师范大学物理系）；Department of Physics, Jiangsu University（江苏大学物理系）
Our account of the problem of the classical limit of quantum mechanics involves two elements. The first one is self-induced decoherence, conceived as a process that depends on the own dynamics of a closed quantum system governed by a Hamiltonian with continuous spectrum; the study of decoherence is addressed by means of a formalism used to give meaning to the van Hove states with diagonal singularities. The second element is macroscopicity: when the macroscopic limit is applied to the Wigner transformation of the diagonal state resulting from decoherence, the description of the quantum system …
The environment surrounding a quantum system can, in effect, monitor some of the systems observables. As a result, the eigenstates of these observables continuously decohere and can behave like classical states.
In quantum metrology, quantum probe states are capable of estimating unknown physical parameters to precisions beyond classical limits. What qualities do such states possess? Here we relate the performance of a probe state at estimating a parameter $ϕ$ -- as quantified by the quantum Fisher information -- to the amount of purity it loses when $ϕ$ undergoes statistical fluctuation. This indicates that the better a state is for estimating $ϕ$, the more it decoheres when $ϕ$ is subject to noise.
We demonstrate that a classical emulation of quantum gate operations, here represented by an actual analog electronic device, can be modeled accurately as a quantum operation in terms of a universal set of Pauli operators. This observation raises the possibility that quantum error correction methods may be applied to classical systems to improve fault tolerance.
A quantum system with discrete and continuos evolution spectrum is studied. A final pointer basis is found, that can be defined in a presised mathematical way. This result is use to explain the quantum measurement in the system.
We find the conditions for one quantum system to function as a classical controller of another quantum system: the controller must be an open system and rapidly diagonalised in the basis of the controller variable that is coupled to the controlled system. This causes decoherence in the controlled system that can be made small if the rate of diagonalisation is fast. We give a detailed example based on the quantum optomechanical control of a mechanical resonator. The resulting equations are similar in structure to recently proposed models for consistently combining quantum and classical stochast…
The initial states which minimize the predictability loss for a damped harmonic oscillator are identified as quasi-free states with a symmetry dictated by the environment's diffusion coefficients. For an isotropic diffusion in phase space, coherent states (or mixtures of coherent states) are selected as the most stable ones.
We study the quantum kicked rotor in resonance subjected to an unitary noise defined through Kraus operators, we show that this type of decoherence does not, in general, lead to the classical diffusive behavior. We find exact analytical expressions for the density matrix and the variance in the primary resonances. The variance does not loose its ballistic behavior, however the coherence decays as a power law. The secondary resonances are treated numerically, obtaining a power-law decay for the variance and an exponential law decay for the coherence.
In the pursuit of speculative new particles, forces, and dimensions with vanishingly small influence on normal matter, understanding the ultimate physical limits of experimental sensitivity is essential. Here, I show that quantum decoherence offers a window into otherwise inaccessible realms. There is a standard quantum limit for diffusion that restricts some entanglement-generating phenomena, like soft collisions with new particle species, from having appreciable classical influence on normal matter. Such phenomena are classically undetectable but can be revealed by the anomalous decoherence …
Decoherence effects on quantum and classical dynamics in reactive scattering are examined using a Caldeira-Leggett type model. Through a study of dynamics of the collinear H+H2 reaction and the transmission over simple one-dimensional barrier potentials, we show that decoherence leads to improved agreement between quantum and classical reaction and transmission probabilities, primarily by increasing the energy dispersion in a well defined way. Increased potential nonlinearity is seen to require larger decoherence in order to attain comparable quantum-classical agreement.
We analyze the time dependence of entanglement and total correlations between a system and fractions of its environment in the course of decoherence. For the quantum Brownian motion model we show that the entanglement and total correlations have rather different dependence on the size of the environmental fraction. Redundancy manifests differently in both types of correlations and can be related with induced--classicality. To study this we introduce a new measure of redundancy and compare it with the existing one.
We present evidence that decoherence can produce a smooth quantum-to-classical transition in nonlinear dynamical systems. High-resolution tracking of quantum and classical evolutions reveals differences in expectation values of corresponding observables. Solutions of master equations demonstrate that decoherence destroys quantum interference in Wigner distributions and washes out fine structure in classical distributions bringing the two closer together. Correspondence between quantum and classical expectation values is also re-established.
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic interaction with a quantum environment. Here we prove that, in the absence of de-phasing environmental interaction, the asymptotic spatial wave function of any quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to arbitrary deterministic fields, becomes proportional to the initial momentum wave func…
The environment -- external or internal degrees of freedom coupled to the system -- can, in effect, monitor some of its observables. As a result, the eigenstates of these observables decohere and behave like classical states: Continuous destruction of superpositions leads to environment-induced superselection (einselection). Here I investigate it in the context of quantum chaos (i. e., quantum dynamics of systems which are classically chaotic).
We study the decoherence process for an open quantum system which is classically chaotic (a quartic double well with harmonic driving coupled to a sea of harmonic oscillators). We analyze the time dependence of the rate of entropy production showing that it has two relevant regimes: For short times it is proportional to the diffusion coefficient (fixed by the system--environment coupling strength). For longer times (but before equilibration) it is fixed by dynamical properties of the system (and is related to the Lyapunov exponent). The nature of the transition time between both regimes is inv…
We re-analyse the optomechanical interferometer experiment proposed by Marshall, Simon, Penrose and Bouwmeester with the help of a recently developed quantum-classical hybrid theory. This leads to an alternative evaluation of the mirror induced decoherence. Surprisingly, we find that it behaves essentially in the same way for suitable initial conditions and experimentally relevant parameters, no matter whether the mirror is considered a classical or quantum mechanical object. We discuss the parameter ranges where this result holds and possible implications for a test of spontaneous collapse mo…
We show that for qubits and qutrits it is always possible to perfectly recover quantum coherence by performing a measurement only on the environment, whereas for dimension d>3 there are situations where recovery is impossible, even with complete access to the environment. For qubits, the minimal amount of classical information to be extracted from the environment equals the entropy exchange.
We study dynamics of quantum open systems, paying special attention to those aspects of their evolution which are relevant to the transition from quantum to classical. We begin with a discussion of the conditional dynamics of simple systems. The resulting models are straightforward but suffice to illustrate basic physical ideas behind quantum measurements and decoherence. To discuss decoherence and environment-induced superselection einselection in a more general setting, we sketch perturbative as well as exact derivations of several master equations valid for various systems. Using these equa…
We address the time evolution of the quantum correlations ($QCs$) such as entanglement, purity, and coherence for a model of two non-interacting qubits initially prepared as a maximally entangled bipartite state. We contrast the comparative potential of the classical fields to preserve these $QCs$ in the noisy and noiseless realms. We also disclose the characteristic dynamical behavior of the $QCs$ of the two-qubit state under the static noisy effects originating from the common and different configuration models. We show that there is a direct connection between the fluctuations allowed by an…
In this work we propose a novel strategy using techniques from systems theory to completely eliminate decoherence and also provide conditions under which it can be done so. A novel construction employing an auxiliary system, the bait, which is instrumental to decoupling the system from the environment is presented. Our approach to decoherence control in contrast to other approaches in the literature involves the bilinear input affine model of quantum control system which lends itself to various techniques from classical control theory, but with non-trivial modifications to the quantum regime. …
We have studied the emergence of classical states in the perturbative interaction model. The states which interact with many other degrees of freedom, such as the center of mass of a macro-object, play important role. Although the random phase mechanism is effective as same as Zurek's strong correlation model, there are enormous states, each of which independently developes due to the orthogonality of the environmental states. In these privileged states, the subsystem picture with the separability is stable.
Using the Gell-Mann and Hartle formalism of generalized quantum mechanics of closed systems, we study the classical limit of coarse-grained spacetime histories and their decoherence. The system under consideration is one-dimensional and consists of a particle coupled to a von Neumann apparatus that performs a measurement of the position of the particle during the finite time interval during which the histories of this system take place. We consider two cases: a free particle and a harmonic oscillator. The real line is divided into intervals of the same length, and coarse-grained histories are …
Within the decoherent histories formulation of quantum mechanics, we investigate necessary conditions for decoherence of arbitrarily long histories. We prove that fine-grained histories of arbitrary length decohere for all classical initial states if and only if the unitary evolution preserves classicality of states (using a natural formal definition of classicality). We give a counterexample showing that this equivalence does not hold for coarse-grained histories.
The total correlations in a bipartite quantum system are measured by the quantum mutual information $\mathcal{I}$, which consists of quantum discord and classical correlation. However, recent results in quantum information shows that coherence, which is a part of total correlation, is more general and more fundamental than discord. The role of coherence in quantum resource theories is worthwhile to investigate. We first study the relation between quantum discord and coherence by reducing the difference between them. And then, we consider the dynamics of quantum discord, classical correlations …
We investigate the sensitivity of quantum systems that are chaotic in a classical limit, to small perturbations of their equations of motion. This sensitivity, originally studied in the context of defining quantum chaos, is relevant to decoherence in situations when the environment has a chaotic classical counterpart.
When a quantum nonlinear system is linearly coupled to an infinite bath of harmonic oscillators, quantum coherence of the system is lost on a decoherence time-scale $τ_D$. Nevertheless, quantum effects for observables may still survive environment-induced decoherence, and be observed for times much larger than the decoherence time-scale. In particular, we show that the Ehrenfest time, which characterizes a departure of quantum dynamics for observables from the corresponding classical dynamics, can be observed for a quasi-classical nonlinear oscillator for times $τ\ggτ_D$. We discuss this obser…
We show that some classically chaotic quantum systems uncoupled from noisy environments may generate intrinsic decoherence with all its associated effects. In particular, we have observed time irreversibility and high sensitivity to small perturbations in the initial conditions in a quasiperiodic version of the kicked rotor. The existence of simple quantum systems with intrinsic decoherence clarifies the quantum--classical correspondence in chaotic systems.
We study the physical implementation of the Photon Carnot engine (PCE) based on the cavity QED system [M. Scully et al, Science, \textbf{299}, 862 (2003)]. Here, we analyze two decoherence mechanisms for the more practical systems of PCE, the dissipation of photon field and the pure dephasing of the input atoms. As a result we find that (I) the PCE can work well to some extent even in the existence of the cavity loss (photon dissipation); and (II) the short-time atomic dephasing, which can destroy the PCE, is a fatal problem to be overcome.
Some hypothetical particles are considered essentially undetectable because they are far too light and slow-moving to transfer appreciable energy or momentum to the normal matter that composes a detector. I propose instead directly detecting such feeble particles, like sub-MeV dark matter or even gravitons, through their uniquely distinguishable decoherent effects on quantum devices like matter interferometers. More generally, decoherence can reveal phenomena that have arbitrarily little classical influence on normal matter, giving new motivation for the pursuit of macroscopic superpositions.
Standard semi-classical models of decoherence do not take explicit account of the classical information required to specify the system - environment boundary. I show that this information can be represented as a finite set of reference eigenvalues that must be encoded by any observer, including any apparatus, able to distinguish the system from its environment. When the information required for system identification is accounted for in this way, decoherence can be described as a sequence of entanglement swaps between reference and pointer components of the system and their respective environme…
Although various pieces of indirect evidence about the nature of dark matter have been collected, its direct detection has eluded experimental searches despite extensive effort. If the mass of dark matter is below 1 MeV, it is essentially imperceptible to conventional detection methods because negligible energy is transferred to nuclei during collisions. Here I propose directly detecting dark matter through the quantum decoherence it causes rather than its classical effects such as recoil or ionization. I show that quantum spatial superpositions are sensitive to low-mass dark matter that is in…
We study the behavior of an open quantum system, with an $N$--dimensional space of states, whose density matrix evolves according to a non--unitary map defined in two steps: A unitary step, where the system evolves with an evolution operator obtained by quantizing a classically chaotic map (baker's and Harper's map are the two examples we consider). A non--unitary step where the evolution operator for the density matrix mimics the effect of diffusion in the semiclassical (large $N$) limit. The process of decoherence and the transition from quantum to classical behavior are analyzed in detail b…
