Zurek, Habib and Paz [W. H. Zurek, S. Habib and J. P. Paz, Phys. Rev. Lett. {\bf 70} (1993)\ 1187] have characterized the set of states of maximal stability defined as the set of states having minimum entropy increase due to interaction with an environment, and shown that coherent states are maximal for the particular environment model examined. To generalize these results, I consider entropy production within the Lindblad theory of open systems, treating environment effects perturbatively. I characterize the maximally predicitive states which emerge from several forms of effective dynamics, including decoherence from spatially correlated noise. Under a variety of conditions, coherent states emerge as the maximal states.
We consider the claim that decoherence explains the emergence of classicality in quantum systems, and conclude that it does not. We show that, given a randomly chosen universe composed of a variety of subsystems, some of which are macroscopic and subject to decoherence-inducing interactions, and some of which are microscopic, the macroscopic subsystems will not display any distinctively classical behavior. Therefore, a universe in which macroscopic and microscopic do display distinct behavior must be in a very special, highly nongeneric quantum state.
We analyze seemingly contradictory claims in the literature about the role played by decoherence in ensuring classical behavior for the chaotically tumbling satellite Hyperion. We show that the controversy is resolved once the very different assumptions underlying these claims are recognized. In doing so, we emphasize the distinct notions of the problem of classicality in the ensemble interpretation of quantum mechanics and in decoherence-based approaches that are aimed at addressing the measurement problem.
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…
Choosing a specific way of dividing a closed system into parts is a starting point for the decoherence program and for the quantum thermalization program. It is shown that one can always chose such way of partitioning that decoherence-assisted classicality does not emerge and thermalization does not occur. Implications of this result are discussed.
It is shown how possible corrections to ordinary quantum mechanics described by the Lindblad equation might be detected by exploiting the great precision of atomic clocks.
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.
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.
The experimental observation of a clear quantum signature of gravity is believed to be out of the grasp of current technology. However, several recent promising proposals to test the possible existence of non-classical features of gravity seem to be accessible by the state-of-art table-top experiments. Among them, some aim at measuring the gravitationally induced entanglement between two masses which would be a distinct non-classical signature of gravity. We explicitly study, in two of these proposals, the effects of decoherence on the system's dynamics by monitoring the corresponding degree o…
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…
Inspired by an old idea of von Neumann, we seek a pair of commuting operators X,P which are, in a specific sense, "close" to the canonical non-commuting position and momentum operators, x,p. The construction of such operators is related to the problem of finding complete sets of orthonormal phase space localized states, a problem severely constrained by the Balian-Low theorem. Here these constraints are avoided by restricting attention to situations in which the density matrix is reasonably decohered (i.e., spread out in phase space). Commuting position and momentum operators are argued to be …
The high resilience to de-coherence shown by a recently discovered Macroscopic Quantum Superposition (MQS) generated by a quantum injected optical parametric amplifier (QI-OPA) and involving a number of photons in excess of 5x10^4 motivates the present theoretical and numerical investigation. The results are analyzed in comparison with the properties of the MQS based on coherent states and NOON states, in the perspective of the comprehensive theory of the subject by W.H.Zurek. In that perspective the concepts of "pointer state", "einselection" are applied to the new scheme.
The purpose of the present study is to derive the pointer states of a macroscopic system interacting with its environment, under the general assumptions, i.e., without assuming any form of the interaction Hamiltonian. The lowest order perturbation leads that the interaction energy shifts the phase factors of the state vectors. For a macroscopic system, these factors are the macroscopic quantities even for the very weak interaction. When we group the state vector of the total system by the view point of environmental side, the destructive interference occurs and the stationary phase approximati…
Maximally predictive states, as defined in recent work by Zurek, Habib and Paz, are studied for more elaborate environment models than a linear coupling. An environment model which includes spatial correlations in the noise is considered in the non-dissipative regime. The Caldeira-Leggett model is also reconsidered in the context of an averaging procedure which produces a completely positive form for the quantum master equation. In both cases, the maximally predictive states for the harmonic oscillator are the coherent states, which is the same result found by Zurek,Habib and Paz for the Calde…
Mixing and decoherence are both manifestations of classicality within quantum theory, each of which admit a very general category-theoretic construction. We show under which conditions these two 'roads to classicality' coincide. This is indeed the case for (finite-dimensional) quantum theory, where each construction yields the category of C*-algebras and completely positive maps. We present counterexamples where the property fails which includes relational and modal theories. Finally, we provide a new interpretation for our category-theoretic generalisation of decoherence in terms of 'leaking …
I consider the interaction of a superposition of mesoscopic coherent states and its approach to a mixed state as a result of a suitably controlled environment. I show how the presence of a gain medium in a cavity can lead to diagonalization in coherent state basis in contrast to the standard model of decoherence. I further show how the new model of decoherence can lead to the generation of $s$ ordered quasi distributions.
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.
Nuclei are rather classical systems in a sense. In the old days, their phenomena were roughly explained in classical rules such as the liquid drop model. This fact may be understood that when we see an finite quantum many body system like nucleus, though which is a group of quantum mechanical particles, its any collective degree of freedom has any classicality. Getting a classicality does not depend on spatial scales of objects. It is made by a phenomenon called Quantum Decoherence. We have studied about Quantum Decoherence in a finite system as nucleus. In this paper, at the harmonic three bo…
A recent debate has ensued over the claim by Pikovski et al. [Nat. Phys. 11, 668 (2015)] that systems with internal degrees of freedom undergo a universal, gravity-induced, type of decoherence that explains their quantum-to-classical transition. This decoherence is supposed to arise from the different gravitational redshifts experienced by such systems when placed in a superposition of two wave packets at different heights in a gravitational field. Here we investigate some aspects of the discussion with the aid of simple examples. In particular, we first resolve an apparent conflict between th…
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.
We give a pedagogical introduction to the process of decoherence - the irreversible emergence of classical properties through interaction with the environment. After discussing the general concepts, we present the following examples: Localisation of objects, quantum Zeno effect, classicality of fields and charges in QED, and decoherence in gravity theory. We finally emphasise the important interpretational features of decoherence.
Emergence of classicality from quantum mechanics, a hotly debated topic, has had no satisfactory resolution so far. Various approaches including decoherence and gravitational interactions have been suggested. In the present work, the Schrödinger-Newton model is used to study the role of semi-classical self-gravity in the evolution of massive spin-1/2 particles in a Stern-Gerlach experiment. For small mass, evolution of the initial wavepacket in a spin superposition shows a splitting in the magnetic field gradient into two trajectories as in the standard Stern-Gerlach experiment. For larger mas…
In a series of comments, Bonder et al. criticized our work on decoherence due to time dilation [Nature Physics 11, 668-672 (2015)]. First the authors erroneously claimed that our results contradict the equivalence principle, only to "resolve" the alleged conflict in a second note. The resolution - relativity of simultaneity - was already explained in our reply [arXiv:1508.03296], which Bonder et al. now essentially reiterate. The newly raised points were also already extensively clarified in our note. The physical prediction of our work remains valid: systems with internal dynamics decohere if…
Can the computational complexity theory of computer science and mathematics say something new about unresolved problems in quantum physics? Particularly, can the P versus NP question in the computational complexity theory be a factor in the elucidation of the emergency of classicality in quantum mechanics? The paper compares two different ways of deriving classicality from the quantum formalism resulted from two differing hypotheses regarding the P versus NP question -- the approach of the quantum decoherence theory implying that P = NP and the computational complexity approach which assumes t…
In the framework of the Lindblad theory for open quantum systems, expressions for the density operator, von Neumann entropy and effective temperature of the damped harmonic oscillator are obtained. The entropy for a state characterized by a Wigner distribution function which is Gaussian in form is found to depend only on the variance of the distribution function. We give a series of inequalities, relating uncertainty to von Neumann entropy and linear entropy. We analyze the conditions for purity of states and show that for a special choice of the diffusion coefficients, the correlated coherent…
It has been claimed that decoherence of open quantum systems explains the tendency of macroscopic systems to exhibit quasiclassical behavior. We show that quasiclassicality is in fact an unremarkable property, characterizing generic subsystems of environments even in the absence of dynamical decoherence. It is suggested that decoherence is best regarded as explaining the persistence of true classicality, rather than the emergence, rather than the emergence of quasiclassicality.
Control of quantum dissipative systems can be challenging because control variables are typically part of the system Hamiltonian, which can only generate motion along unitary orbits of the system. To transit between orbits, one must harness the dissipation super-operator. To separate the inter-orbit dynamics from the Hamiltonian dynamics for a generic two-dimensional system, we project the Lindblad master equation onto the set of spectra of the density matrix, and we interpret the location along the orbit to be a new control variable. The resulting differential equation allows us to analyze th…
Within the framework of the Lindblad master equation, we propose a general methodology to describe the effects of the environment on a system in dilute gas phase. The phenomenological parameters characterizing the transitions between rovibrational states of the system induced by collisions can be extracted from experimental transition kinetic constants, relying on Energy Gap fitting laws. As the availability of this kind of experimental data can be limited, the present work relied on experimental line broadening coefficients, however still using Energy Gap fitting laws. The 3 $μ$m infrared spe…
A single quantum dissipative oscillator described by the Lindblad equation serves as a model for a nanosystem. This model is solved exactly by using the ambiguity function. The solution shows the features of decoherence (spatial extent of quantum behavior), correlation (spatial scale over which the system localizes to its physical dimensions), and mixing (mixed- state spatial correlation). A new relation between these length scales is obtained here. By varying the parameters contained in the Lindblad equation, it is shown that decoherence and correlation can be controlled. We indicate possible…
It is accepted that among the ways through which a quantum phenomenon decoheres and becomes a classical one is what is termed in the literature the Zeno effect. This effect, named after the ancient Greek philosopher Zeno of Elea (born about 485 B.C), were used in 1977 to analytically predict that an initial quantum state may be preserved in time by merely repeating a large number of times, in a finite total time, the experiment of checking its state. Since then this effect has been experimentally validated and has become an established physical fact. It has been argued by Simonius that the Zen…
A pair of coupled quantum dissipative oscillators, serving as a model for a nanosystem, is here described by the Lindblad equation. Its dynamic evolution is shown to exhibit the features of decoherence (spatial extent of quantum behavior), correlation (spatial scale over which the system localizes to its physical dimensions), and entanglement (a special quantum feature making its appearance first in such bipartite systems) as a function of the coupling constants of the Lindblad equation. One interesting feature emerging out of this calculation is that the entanglement may exhibit revivals in t…
We lay a comprehensive foundation for the study of redundant information storage in decoherence processes. Redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects. We consider two ensembles of states for a model universe consisting of one system and many environments: the first consisting of arbitrary states, and the second consisting of ``singly-branching'' states consistent with a simple decoherence model. Typical states from the random ensemble do not store information about the system redundantly, but information stored in branching states…
We clarify the way in which cosmological perturbations of quantum origin, produced during inflation, assume classical properties. Two features play an important role in this process: First, the dynamics of fluctuations which are presently on large cosmological scales leads to a very peculiar state (highly squeezed) that is indistinguishable, in a precise sense, from a classical stochastic process. This holds for almost all initial quantum states. Second, the process of decoherence by interaction with the environment distinguishes the field amplitude basis as a robust pointer basis. We discuss …
We use the Bloch-Redfield-Wangsness theory to calculate the effects of acoustic phonons in coherent control experiments, where quantum-dot excitons are driven by shaped laser pulses. This theory yields a generalized Lindblad equation for the density operator of the dot, with time-dependent damping and decoherence due to phonon transitions between the instantaneous dressed states. It captures similar physics to the form recently applied to Rabi oscillation experiments [A. J. Ramsay et al., Phys. Rev. Lett. 104, 017402 (2010)], but guarantees positivity of the density operator. At sufficiently l…
We study various measures of classicality of the states of open quantum systems subject to decoherence. Classical states are expected to be stable in spite of decoherence, and are thought to leave conspicuous imprints on the environment. Here these expected features of environment-induced superselection (einselection) are quantified using four different criteria: predictability sieve (which selects states that produce least entropy), purification time (which looks for states that are the easiest to find out from the imprint they leave on the environment), efficiency threshold (which finds stat…
We prove a generalization of the classic Groenewold-Lindblad entropy inequality, combining decoherence and the quantum Bayes theorem into a simple unified picture where decoherence increases entropy while observation decreases it. This provides a rigorous quantum-mechanical version of the second law of thermodynamics, governing how the entropy of a system (the entropy of its density matrix, partial-traced over the environment and conditioned on what is known) evolves under general decoherence and observation. The powerful tool of spectral majorization enables both simple alternative proofs of …
Phase-space features of the Wigner flow are examined so to provide a set of continuity equations that describe the flux of quantum information in the phase-space. The reported results suggest that the non-classicality profile of anharmonic (periodic) quantum systems can be consistently obtained in terms of the fluxes of probability, purity and von Neumann entropy. Extensions of the such phase-space quantifiers are also investigated in the context of the so-called Rényi entropy.
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）
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.
Decoherence of quantum systems from entanglement with an unmonitored environment is to date the most compelling explanation of the emergence of a classical picture from a quantum world. While it is well understood for a single Lindblad operator, the role in the einselection process of a complex system-environment interaction remains to be clarified. In this paper, we analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators modeling decoherence in the number basis and dissipative decoherence in the coherent state basis. We study and solve exactly t…
This study was started to know mysterious classicality of nuclei. Using three particles model without external environments, it is found that decisions of respective state of three particles by decoherence are not simultaneous. Furthermore, in this model, wave function of total three body system collapses spontaneously without any external environments. Therefore we may able to insist that a wavefunction of our universe has already collapsed spontaneously without any external observer, because of the same mechanism with this model.
Time-dependent density-matrix propagation is used to demonstrate, in a schematic model of an open quantum system, that the complex potential approach and the Lindblad dissipative dynamics are \emph{not} equivalent. While the former preserves coherence, it is destroyed in the Lindblad dissipative dynamics. Quantum decoherence is the key aspect that makes the difference between the two approaches, indicating that the complex potential model is inadequate for a consistent description of open quantum-system dynamics. It is suggested that quantum decoherence should always be explicitly included whe…
The Lindblad equation governs general markovian evolution of the density operator in an open quantum system. An expression for the rate of change of the Wigner function as a sum of integrals is one of the forms of the Weyl representation for this equation. The semiclassical description of the Wigner function in terms of chords, each with its classically defined amplitude and phase, is thus inserted in the integrals, which leads to an explicit differential equation for the Wigner function. All the Lindblad operators are assumed to be represented by smooth phase space functions corresponding to …
By using the complete solution of the Milburn equation (beyond the Lindblad form that it is generally used) that describes intrinsic decoherence, we study the decaying dynamics of a displaced harmonic oscillator. We calculate the expectation values of position quadrature, and the number operator in initial coherent and squeezed states.
We investigate the implications of quantum Darwinism in a composite quantum system with interacting constituents exhibiting a decoherence-free subspace. We consider a two-qubit system coupled to an $N$-qubit environment via a dephasing interaction. For excitation preserving interactions between the system qubits, an analytical expression for the dynamics is obtained. It demonstrates that part of the system Hilbert space redundantly proliferates its information to the environment, while the remaining subspace is decoupled and preserves clear non-classical signatures. For measurements performed …
Spontaneous collapse models aim to resolve the measurement problem in quantum mechanics by considering wave-function collapse as a physical process. We analyze how these models affect a decaying flavor-oscillating system whose evolution is governed by a phenomenological non-Hermitian Hamiltonian. In turn, we apply two popular collapse models, the Quantum Mechanics with Universal Position Localization and the Continuous Spontaneous Localization models, to a neutral meson system. By using the equivalence between the approaches to the time evolution of decaying systems with a non-Hermitian Hamilt…
The question of classicality is addressed in relation with the shape of the nuclear skeleton of molecular systems. As the most natural environment, the electrons of the molecule are considered as continuously monitoring agents for the nuclei. For this picture, an elementary formalism of decoherence theory is developed and numerical results are presented for few-particle systems. The numerical examples suggest that the electron-nucleus Coulomb interaction is sufficient for inducing a blurred shape with strong quantum coherences in compounds of the lightest elements, H$_2$, D$_2$, T$_2$, and HeH…
We introduce a condition for the strong decoherence of a set of alternative histories of a closed quantum-mechanical system such as the universe. The condition applies, for a pure initial state, to sets of homogeneous histories that are chains of projections, generally branch-dependent. Strong decoherence implies the consistency of probability sum rules but not every set of consistent or even medium decoherent histories is strongly decoherent. Two conditions characterize a strongly decoherent set of histories: (1) At any time the operators that effectively commute with generalized records of h…
We investigate departures from the Hamiltonian dynamics such as the quantum decoherence in a supersymmetric quantum system due to its interaction with the environment. The effective description is given by the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. The prescription for supersymmetrization of this equation is elaborated and pairs of related isospectral quantum systems are built. We present some instructive examples of such a construction.
It is shown how any Lindbladian evolution with selfadjoint Lindblad operators, either Markovian or nonMarkovian, can be understood as an averaged random unitary evolution. Both mathematical and physical consequences are analyzed. First a simple and fast method to solve this kind of master equations is suggested and particularly illustrated with the phase-damped master equation for the multiphoton resonant Jaynes-Cummings model in the rotating-wave approximation. A generalization to some intrinsic decoherence models present in the literature is included. Under the same philosophy a proposal to …
