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 observation in relation to recent experiments on quantum nonlinear systems in the quasi-classical region of parameters.
We study the exact decoherence dynamics of the entangled squeezed state of two single-mode optical fields interacting with two independent and uncorrelated environments. We analyze in detail the non-Markovian effects on the entanglement evolution of the initially entangled squeezed state for different environmental correlation time scales. We find that the environments have dual actions on the system: backaction and dissipation. In mparticular, when the environmental correlation time scale is comparable to the time scale for significant change in the system, the backaction would counteract the…
We study the dissipative dynamics of deformed coherent states superposition. We find that such kind of superposition can be more robust against decoherence than the usual Schrodinger cat states.
We address the dynamics of a two-qubit system interacting with a classical dephasing environment driven by a Gaussian stochastic process. Upon introducing the concept of entanglement-preserving time, we compare the degrading effects of different environments, e.g. those described by Ornstein-Uhlenbeck or fractional noise. In particular, we consider pure Bell states and mixtures of Bell states and study the typical values of the entanglement-preserving time for both independent and common environments. We found that engineering environments towards fractional Gaussian noise is useful to preserv…
The theory of decoherence attempts to explain the emergent classical behaviour of a quantum system interacting with its quantum environment. In order to formalize this mechanism we introduce the idea that the information preserved in an open quantum evolution (or channel) can be characterized in terms of observables of the initial system. We use this approach to show that information which is broadcast into many parts of the environment can be encoded in a single observable. This supports a model of decoherence where the pointer observable can be an arbitrary positive operator-valued measure (…
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.
We present a decoherence-based interpretation for the quantum Zeno effect (QZE) where measurements are dynamically treated as dispersive couplings of the measured system to the apparatus, rather than the von Neumann's projections. It is found that the explicit dependence of the survival probability on the decoherence time quantitatively distinguishes this dynamic QZE from the usual one based on projection measurements. By revisiting the cavity-QED experiment of the QZE [J. Bernu, et al., Phys. Rev. Lett, 101, 180402 (2008)], we suggest an alternative scheme to verify our theoretical considerat…
We analyze the effect of local decoherence of two qubits on their entanglement and the Bell inequality violation. Decoherence is described by Kraus operators, which take into account dephasing and energy relaxation at an arbitrary temperature. We show that in the experiments with superconducting phase qubits the survival time for entanglement should be much longer than for the Bell inequality violation.
We study the problem of driving an unknown initial mixed quantum state onto a known pure state without using unitary transformations. This can be achieved, in an efficient manner, with the help of sequential measurements on at least two unbiased bases. However here we found that, when the system is affected by a decoherence mechanism, only one observable is required in order to achieve the same goal. In this way the decoherence can assist the process. We show that, depending on the sort of decoherence, the process can converge faster or slower than the method implemented by means of two comple…
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).
According to the eigenstate thermalization ansatz, matrices representing generic few body observables take on a specific form when displayed in the eigenbasis of a chaotic Hamiltonian. We examine the effect of environmental induced decoherence on the dynamics of observables that conform with said eigenstate thermalization ansatz. The obtained result refers to a description of the dynamics in terms of an integro-differential equation of motion of the Nakajima-Zwanzig form. We find that environmental decoherence is equivalent to an exponential damping of the respective memory kernel. This statem…
Conditional expectation values of quantum mechanical observables reflect unique non-classical correlations, and are generally sensitive to decoherence. We consider the circumstances under which such sensitivity to decoherence is removed, namely, when the measurement process is subjected to conservation laws. Specifically, we address systems with additive conserved quantities and identify sufficient conditions for the system state such that its coherence plays no role in the conditional expectation values of observables that commute with the conserved quantity. We discuss our findings for a spe…
We consider the classical algebra of observables that are diagonal in a given orthonormal basis, and define a complete decoherence process as a completely positive map that asymptotically converts any quantum observable into a diagonal one, while preserving the elements of the classical algebra. For quantum systems in dimension two and three any decoherence process can be undone by collecting classical information from the environment and using such an information to restore the initial system state. As a relevant example, we illustrate the quantum eraser of Scully et al. [Nature 351, 111 (199…
It is difficult to evaluate the precision of quantum measurements because it is not possible to conduct a second reference measurement on the same physical system to compare the measurement outcome with a more accurate value of the measured quantity. Here, I show that a direct evaluation of measurement uncertainties is possible when the measurement outcomes are used to compensate the small amount of decoherence induced in a probe qubit by carefully controlled interactions with the system. Since the original uncertainty of the target observable causes fluctuating phase shifts in the probe qubit…
The "self-induced decoherence" (SID) approach suggests that (1) the expectation value of any observable becomes diagonal in the eigenstates of the total Hamiltonian for systems endowed with a continuous energy spectrum, and (2), that this process can be interpreted as decoherence. We evaluate the first claim in the context of a simple spin bath model. We find that even for large environments, corresponding to an approximately continuous energy spectrum, diagonalization of the expectation value of random observables does in general not occur. We explain this result and conjecture that SID is li…
The coupled-channels density-matrix technique for nuclear reaction dynamics, which is based on the Liouville-von Neumann equation with Lindblad dissipative terms, is developed with the inclusion of full angular momentum couplings. It allows a quantitative study of the role and importance of quantum decoherence in nuclear scattering. Formulae of asymptotic observables that can reveal effects of quantum decoherence are given. A method for extracting energy-resolved scattering information from the time-dependent density matrix is introduced. As an example, model calculations are carried out for t…
In an ensemble of two-level atoms that can be described in terms of a collective spin, entangled states can be used to enhance the sensitivity of interferometric precision measurements. While non-Gaussian spin states can produce larger quantum enhancements than spin-squeezed Gaussian states, their use requires the measurement of observables that are nonlinear functions of the three components of the collective spin. In this paper we develop strategies that achieve the optimal quantum enhancements using non-Gaussian states produced by a nonlinear one-axis-twisting Hamiltonian, and show that mea…
According to our modal-Hamiltonian interpretation (MHI) of quantum mechanics, the Hamiltonian of the closed system defines the set of its definite-valued observables. This definition seems to be incompatible with the pointer basis selected by the environment-induced decoherence (EID) of the open system. In this paper we argue that decoherence can be understood from a closed system perspective which (i) shows that the incompatibility between MHI and EID is only apparent, and (ii) solves certain conceptual challenges that the EID program still has to face.
The evolution of observable quantities of finite quantum systems is analyzed when the latter are subject to nondestructive measurements. The type and number of measurements characterize the level of decoherence produced in the system. A finite number of instantaneous measurements leads to only a partial decoherence. But infinite number of such measurements yields complete decoherence and equilibration. Continuous measurements result in partial decoherence in finite time, but produce complete decoherence and equilibration as time tends to infinity. Resulting equilibrium states are characterized…
The so-called classical limit of quantum mechanics is generally studied in terms of the decoherence of the state operator that characterizes a system. This is not the only possible approach to decoherence. In previous works we have presented the possibility of studying the classical limit in terms of the decoherence of relevant observables of the system. On the basis of this approach, in this paper we introduce the classical limit from a logical perspective, by studying the way in which the logical structure of quantum properties corresponding to relevant observables acquires Boolean character…
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.
In this work we investigate the relation between quantum measurements and decoherence, in order to formally express the necessity of the latter for obtaining an informative output from the former. To this aim, referring to the Von Neumann scheme for ideal quantum measurements, we first look for the minimal structure that the interaction between principal system and measurement apparatus must have for properly describing the process, beyond the quantum measurement limit, and then analyze the dynamical evolution induced by one such interaction. The analysis is developed by means of a recently in…
The population decay due to a small opening in an otherwise closed cavity supporting chaotic classical dynamics displays a quantum correction on top of the classical exponential form, a pure manifestation of quantum coherence that acquires a universal form and can be explained by path interference. Being coherent, such enhancement is prone to decoherence effects due to the coupling of the system to an external environment. We study this interplay between incoherent and coherent quantum corrections to decay by evaluating, within a Caldeira-Legget scenario, off-diagonal contributions to the deco…
We consider time-dependent relaxation of observables in quantum systems of chaotic and regular type. We show that the spread of the wave function in the Hilbert space is determined by the survival probability which is known to have pre-exponential, exponential, and long-term power-law limiting behaviors. This result relies on complexity of the wave functions and thus is generic to many systems. In the chaotic limit modeled by the Gaussian Orthogonal Ensemble we show that the survival probability obtained analytically also fully defines the relaxation timescale of observables. This is not the c…
The problem investigated in this paper is einselection, i. e. the selection of mutually exclusive quantum states with definite probabilities through decoherence. Its study is based on a theory of decoherence resulting from the projection method in the quantum theory of irreversible processes, which is general enough for giving reliable predictions. This approach leads to a definition (or redefinition) of the coupling with the environment involving only fluctuations. The range of application of perturbation calculus is then wide, resulting in a rather general master equation. Two distinct cases…
We address the witnessing of quantum correlations beyond the limits imposed by an ensemble statistical average. By relying upon the continuous observation of a single quantum open system under the action of classical or quantum noise, we show how the statistical distribution of outcomes of physically measurable quantities provides enough information to detect entanglement in situations where a simple averaging procedure yields to a vanishing value. In this way, we are able to specify the meaning of decoherence when single read-out measurements are available, to demonstrate that these distribut…
We study a class of quantum measurement models. A microscopic object is entangled with a macroscopic pointer such that a distinct pointer position is tied to each eigenvalue of the measured object observable. Those different pointer positions mutually decohere under the influence of an environment. Overcoming limitations of previous approaches we (i) cope with initial correlations between pointer and environment by considering them initially in a metastable local thermal equilibrium, (ii) allow for object-pointer entanglement and environment-induced decoherence of distinct pointer readouts to …
Superselection rules induced by the interaction with the environment are a basis to understand the emergence of classical observables within quantum theory. The aim of this article is to investigate the decoherence effects, which lead to superselection sectors, with the help of exactly soluble Hamiltonian models. Starting from the examples of Araki and of Zurek more general models with scattering are presented for which the projection operators onto the induced superselection sectors do no longer commute with the Hamiltonian. The example of an environment given by a free quantum field indicate…
The aim of this paper is to review a new perspective about decoherence, according to which formalisms originally devised to deal just with closed or open systems can be subsumed under a closed-system approach that generalizes the traditional account of the phenomenon. This new viewpoint dissolves certain conceptual difficulties of the orthodox open-system approach but, at the same time, shows that the openness of the quantum system is not the essential ingredient for decoherence, as commonly claimed. Moreover, when the behavior of a decoherent system is described from a closed-system perspecti…
The use of d-state systems, or qudits, in quantum information processing is discussed. Three-state and higher dimensional quantum systems are known to have very different properties from two-state systems, i.e., qubits. In particular there exist qudit states which are not equivalent under local unitary transformations unless a selection rule is violated. This observation is shown to be an important factor in the theory of decoherence-free, or noiseless, subsystems. Experimentally observable consequences and methods for distinguishing these states are also provided, including the explicit const…
We examine the adiabatic dynamics of a quantum system coupled to a noisy classical control field. A stochastic phase shift is shown to arise in the off-diagonal elements of the system's density matrix which can cause decoherence. We derive the condition for onset of decoherence, and identify the noise properties that drive decoherence. We show how this decoherence mechansim causes: (1) a dephasing of the observable consequences of the adiabatic geometric phase; and (2) the loss of computational efficiency of the Shor algorithm when run on a sufficiently noisy geometric quantum computer.
We extend the results on decoherence in the thermodynamic limit [M. Frasca, Phys. Lett. A {\bf 283}, 271 (2001)] to general Hamiltonians. It is shown that N independent particles, initially properly prepared, have a set of observables behaving classically in the thermodynamic limit. This particular set of observables is then coupled to a quantum system that in this way decoheres so to have the density matrix in a mixed form. This gives a proof of the generality of this effect.
I consider a thought experiment measuring the decoherence for quasiclassical superpositions of gravitational field. A version of the hole argument allows to prove that a covariant (background-free) theory is completely unable to define the outcome of this experiment and is therefore not viable. Instead, the results of experiments of this type allow to reconstruct a common background shared by all superposed gravitational fields.
It is argued that the partition of a quantum system into subsystems is dictated by the set of operationally accessible interactions and measurements. The emergence of a multi-partite tensor product structure of the state-space and the associated notion of quantum entanglement are then relative and observable-induced. We develop a general algebraic framework aimed to formalize this concept. We discuss several cases relevant to quantum information processing and decoherence control.
We consider departures from hamiltonian dynamics in the evolution of neutral kaons due to their interactions with environment that generate entanglement among them. We propose a phenomenological model of stochastic re-scattering and estimate the coefficients of the effective hamiltonian and decoherence terms. Finally we analyze the interplay between the weak interaction and matter effects and propose the observables suitable to measure the matter characteristics of CPT violation and decoherence.
We provide an alternative approach to the decoherence-by-environment paradigm in the field of the quantum measurement process and the appearance of a classical world. In contrast to the decoherence approach we argue that the transition from pure states to mixtures and the appearance of macro objects (and macroscopic properties) can be understood without invoking the measurement-like influence of the environment on the pointer-states of the measuring instrument. We show that every generic many-body system contains within the class of microscopic quantum observables a subalgebra of macro observa…
In the view of the quantum dynamic theory of measurement developed from the Hepp-Colemen (HC) model (K. Hepp, Hev.Phys.Acta, {\bf 45}, 237 (1972)), the quantum decoherence in neutrino flavor oscillation caused by an environment surrounding neutrinos is generally considered in this paper. The Ellis, Hagelin, Nanopoulos and Srednicki (EHNS) mechanism for solving the solar neutrino problem can be comprehended in a framework of the ordinary quantum mechanics. In the weak- coupling limit, a microscopic model is proposed to describe the transition of two neutrino system from a pure state to a mixed …
We study the role of the information deposited in the environment of an open quantum system in course of the decoherence process. Redundant spreading of information -- the fact that some observables of the system can be independently ``read-off'' from many distinct fragments of the environment -- is investigated as the key to effective objectivity, the essential ingredient of ``classical reality''. This focus on the environment as a communication channel through which observers learn about physical systems underscores importance of quantum Darwinism -- selective proliferation of information ab…
In Everett's many worlds interpretation, where quantum measurements are seen as decoherence events, inexact decoherence may let large worlds mangle the memories of observers in small worlds, creating a cutoff in observable world size. I solve a growth-drift-diffusion-absorption model of such a mangled worlds scenario, and show that it reproduces the Born probability rule closely, though not exactly. Thus deviations from exact decoherence can allow the Born rule to be derived in a many worlds approach via world counting, using a finite number of worlds and no new fundamental physics.
The exact reduced dynamics for the independent oscillator model in the RWA approximation at zero and finite temperatures is derived. It is shown that the information about the interaction and the environment is encapsulated into three time dependent coefficients of the master equation, one of which vanishes in the zero temperature case. In currently used optical cavities all the information about the field dynamics is contained into {\it two} (or three) experimentally accesible and physically meaningful real functions of time. From the phenomenological point of view it suffices then to careful…
When subjected to a classical fluctuating field characterized by a Gaussian process, we examine the {purity} and coherence protection in a three-level quantum system. This symmetry of the three-level system is examined when the local random field is investigated further in the noiseless and noisy regimes. In~particular, we consider fractional Gaussian, Gaussian, Ornstein--Uhlenbeck, and~power law noisy regimes. We show that the destructive nature of the Ornstein--Uhlenbeck noise toward the symmetry of the qutrit to preserve encoded {purity and coherence} remains large. Our findings suggest tha…
It is known that a macroscopic quantum superposition (MQS), when it is exposed to environment, decoheres at a rate scaling with the separation of its component states in phase space. This is more or less consistent with the well known proposition that a more macroscopic quantum state is reduced more quickly to a classical state in general. Effects of initial mixedness, however, on the subsequent decoherence of MQSs have been less known. In this paper, we study the evolution of a highly mixed MQS interacting with an environment, and compare it with that of a pure MQS having the same size of the…
In this contribution, we have investigated the bidirectional quantum teleportation (BQT) of single-qubit states using a Bell state influenced by decoherence channels with memory, dephasing and amplitude damping channels. The expressions of the negativity, as a measure of the entanglement remaining in the BQT quantum channel, the teleportation fidelities and the quantum Fisher information are also evaluated. We find that both these last quantities depend on the survival amount of entanglement in the BQT quantum channel, on the decoherence factor and on the correlation degree of the decoherence …
Introduction to the theory of decoherence. Contents: 1. The phenomenon of decoherence: superpositions, superselection rules, decoherence by "measurements". 2. Observables as a derivable concept. 3. The measurement problem. 4. Density matrix, coarse graining, and "events". 5. Conclusions.
The Born-Markov master equation analysis of the vibrating mirror and photon experiment proposed by Marshall, Simon, Penrose and Bouwmeester is completed by including the important issues of temperature and friction. We find that at the level of cooling available to date, visibility revivals are purely classical, and no quantum effect can be detected by the setup, no matter how strong the photon-mirror coupling is. Checking proposals of universal nonenvironmental decoherence is ruled out by dominating thermal decoherence; a conjectured coordinate-diffusion contribution to decoherence may become…
In Everett's many worlds interpretation, quantum measurements are considered to be decoherence events. If so, then inexact decoherence may allow large worlds to mangle the memory of observers in small worlds, creating a cutoff in observable world size. Smaller world are mangled and so not observed. If this cutoff is much closer to the median measure size than to the median world size, the distribution of outcomes seen in unmangled worlds follows the Born rule. Thus deviations from exact decoherence can allow the Born rule to be derived via world counting, with a finite number of worlds and no …
Electron transport through disordered quasi one-dimensional quantum systems is studied. Decoherence is taken into account by a spatial distribution of virtual reservoirs, which represent local interactions of the conduction electrons with their environment. We show that the decoherence distribution has observable effects on the transport. If the decoherence reservoirs are distributed randomly without spatial correlations, a minimal degree of decoherence is necessary to obtain Ohmic conduction. Below this threshold the system is localized and thus, a decoherence driven metal-insulator transitio…
It has been experimentally demonstrated that quantum coherence can persist in macroscopic phenomena [J.R. Friedman et al.,Nature, 406 (2000) 43]. To face the challenge of this new fact, in this article QM in its standard form is assumed to be extended by one beable (hidden variable), i. e., a quantum observable with always definite values in nature (but usually only statistically given in the quantum state). Localization is taken as the most plausible beable. The paradoxical aspects of conventional QM take now a different form. Suitably defining the notion of "subject" fully within the QM form…
Heisenberg's uncertainty principle, exemplified by the gamma ray thought experiment, suggests that any finite precision measurement disturbs any observables noncommuting with the measured observable. Here, it is shown that this statement contradicts the limit of the accuracy of measurements under conservation laws originally found by Wigner in 1950s, and should be modified to correctly derive the unavoidable noise caused by the conservation law induced decoherence. The obtained accuracy limit leads to an interesting conclusion that a widely accepted, but rather naive, physical encoding of qubi…
It is shown that many dissipative phenomena of "old" quantum mechanics which appeared 100 years ago in the form of the statistics of quantum thermal noise and quantum spontaneous jumps, have never been explained by the "new" conservative quantum mechanics discovered 75 years ago by Heisenberg and Schroedinger. This led to numerous quantum paradoxes which are reconsidered in this paper. The development of quantum measurement theory, initiated by von Neumann, indicated a possibility for resolution of this interpretational crisis by divorcing the algebra of the dynamical generators from the algeb…
In quantum Darwinism, the pointer observable of a system leaves redundant imprints in its environment after decoherence. Each imprint is recorded in a fraction of the environment, which identifies a particular partition of the environment. An ambiguity situation may occur when another observable noncommuting to the pointer observable also leaves redundant imprints with respect to another partition of the environment. We study this problem based on a uniqueness theorem we proved. We find that within a particular subset of all possible partitions of the environment, the observable of the system …
