Searcharxiv⌕ Search

arXiv subjects

Wojciech H. Zurek

Publications and source records attributed to Wojciech H. Zurek.

At least 91 records · Page 5Linked to original sources
arXiv2004

Conditional quantum dynamics with several observers

We consider several observers who monitor different parts of the environment of a single quantum system and use their data to deduce its state. We derive a set of conditional stochastic master equations that describe the evolution of the density matrices each observer ascribes to the system under the Markov approximation, and show that this problem can be reduced to the case of a single "super-observer", who has access to all the acquired data. The key problem - consistency of the sets of data acquired by different observers - is then reduced to the probability that a given combination of data sets will be ever detected by the "super-observer". The resulting conditional master equations are applied to several physical examples: homodyne detection of phonons in quantum Brownian motion, photo-detection and homodyne detection of resonance fluorescence from a two-level atom. We introduce {\it relative purity} to quantify the correlations between the information about the system gathered by different observers from their measurements of the environment. We find that observers gain the most information about the state of the system and they agree the most about it when they measure the environment observables with eigenstates most closely correlated with the optimally predictable {\it pointer basis} of the system.

quant-ph↗
arXiv2004

A simple example of "Quantum Darwinism": Redundant information storage in many-spin environments

As quantum information science approaches the goal of constructing quantum computers, understanding loss of information through decoherence becomes increasingly important. The information about a system that can be obtained from its environment can facilitate quantum control and error correction. Moreover, observers gain most of their information indirectly, by monitoring (primarily photon) environments of the "objects of interest." Exactly how this information is inscribed in the environment is essential for the emergence of "the classical" from the quantum substrate. In this paper, we examine how many-qubit (or many-spin) environments can store information about a single system. The information lost to the environment can be stored redundantly, or it can be encoded in entangled modes of the environment. We go on to show that randomly chosen states of the environment almost always encode the information so that an observer must capture a majority of the environment to deduce the system's state. Conversely, in the states produced by a typical decoherence process, information about a particular observable of the system is stored redundantly. This selective proliferation of "the fittest information" (known as Quantum Darwinism) plays a key role in choosing the preferred, effectively classical observables of macroscopic systems. The developing appreciation that the environment functions not just as a garbage dump, but as a communication channel, is extending our understanding of the environment's role in the quantum-classical transition beyond the traditional paradigm of decoherence.

quant-ph↗
arXiv2004

Objective properties from subjective quantum states: Environment as a witness

We study the emergence of objective properties in open quantum systems. In our analysis, the environment is promoted from a passive role of reservoir selectively destroying quantum coherence, to an active role of amplifier selectively proliferating information about the system. We show that only preferred pointer states of the system can leave a redundant and therefore easily detectable imprint on the environment. Observers who--as it is almost always the case--discover the state of the system indirectly (by probing a fraction of its environment) will find out only about the corresponding pointer observable. Many observers can act in this fashion independently and without perturbing the system: they will agree about the state of the system. In this operational sense, preferred pointer states exist objectively.

quant-ph↗
arXiv2003

Decoherence, einselection, and the quantum origins of the classical

Decoherence is caused by the interaction with the environment. Environment monitors certain observables of the system, destroying interference between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the Universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly non-local "Schrödinger cat" states. Classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit: Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation.

quant-ph↗
arXiv2003

Decoherence from a Chaotic Environment: An Upside Down "Oscillator" as a Model

Chaotic evolutions exhibit exponential sensitivity to initial conditions. This suggests that even very small perturbations resulting from weak coupling of a quantum chaotic environment to the position of a system whose state is a non-local superposition will lead to rapid decoherence. However, it is also known that quantum counterparts of classically chaotic systems lose exponential sensitivity to initial conditions, so this expectation of enhanced decoherence is by no means obvious. We analyze decoherence due to a "toy" quantum environment that is analytically solvable, yet displays the crucial phenomenon of exponential sensitivity to perturbations. We show that such an environment, with a single degree of freedom, can be far more effective at destroying quantum coherence than a heat bath with infinitely many degrees of freedom. This also means that the standard "quantum Brownian motion" model for a decohering environment may not be as universally applicable as it once was conjectured to be.

quant-ph↗
arXiv2003

Reduction of the Wavepacket: How Long Does it Take?

We show that the ``reduction of the wavepacket'' caused by the interaction with the environment occurs on a timescale which is typically many orders of magnitude shorter than the relaxation timescale $τ$. In particular, we show that in a system interacting with a ``canonical'' heat bath of harmonic oscillators decorrelation timescale of two pieces of the wave-packet separated by $N$ thermal de Broglie wavelengths is approximately $τ/N^2$. Therefore, in the classical limit $\hbar \to 0$ dynamical reversibility $(τ\to \infty)$ is compatible with ``instantaneous'' coherence loss.

quant-ph↗
arXiv2001

Information transfer in quantum measurements: irreversibility and amplification

The aim of these lectures is to investigate the transfer of information occurring in course of quantum interactions. In particular, I shall explore circumstances in which such an information transfer with the quantum environment of the considered quantum system leads to the destruction of the phase coherence between the states of the privileged basis in the system Hilbert space. This basis shall be called the pointer basis. I shall argue that states of this pointer basis correspond to the ``classical'' states of the observables of the quantum system in question.

quant-ph↗
arXiv2001

Quantum Chaotic Environments, The Butterfly Effect, And Decoherence

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.

quant-ph↗
arXiv2001

Introducing Quantum Discord

Two classically identical expressions for the mutual information generally differ when the two systems involved are quantum. We investigate this difference -- quantum discord -- and show that it can be used as a criterion for the classicality of the correlations. We also show that quantum discord can be used for describing the selection of the preferred, effectively classical, pointer states.

quant-ph↗
arXiv2001

Breakdown of correspondence in chaotic systems: Ehrenfest versus localization times

Breakdown of quantum-classical correspondence is studied on an experimentally realizable example of one-dimensional periodically driven system. Two relevant time scales are identified in this system: the short Ehrenfest time t_h and the typically much longer localization time scale T_L. It is shown that surprisingly weak modification of the Hamiltonian may eliminate the more dramatic symptoms of localization without effecting the more subtle but ubiquitous and rapid loss of correspondence at t_h.

nlin.CD↗
arXiv2000

Decoherence and long-lived Schroedinger cats in BEC

We consider quantum superposition states in Bose-Einstein condensates. A decoherence rate for the Schrödinger cat is calculated and shown to be a significant threat to this macroscopic quantum superposition of BEC's. An experimental scenario is outlined where the decoherence rate due to the thermal cloud is dramatically reduced thanks to trap engineering and "symmetrization" of the environment. We show that under the proposed scenario the Schroedinger cat belongs to an approximate decoherence-free pointer subspace. This paper is a simplified and more pedagogical version of our previous work, Phys.Rev. A62, 13607 (2000).

cond-mat↗
arXiv2000

Decoherence in Bose-Einstein Condensates: towards Bigger and Better Schroedinger Cats

We consider a quantum superposition of Bose-Einstein condensates in two immiscible internal states. A decoherence rate for the resulting Schroedinger cat is calculated and shown to be a significant threat to this macroscopic quantum superposition of BEC's. An experimental scenario is outlined where the decoherence rate due to the thermal cloud is dramatically reduced thanks to trap engineering and "symmetrization" of the environment which allow for the Schroedinger cat to be an approximate pointer states.

cond-mat↗
arXiv1999

Symmetry Breaking with a Slant: Topological Defects after an Inhomogeneous Quench

We show that, in second-order phase transformations induced by an inhomogeneous quench, the density of topological defects is drastically suppressed as the velocity with which the quench propagates becomes smaller than the speed at which the front of the broken symmetry phase spreads. The velocity of the broken symmetry phase front is approximately given by the ratio of the healing length to relaxation time at freeze-out, that is at the instant when the critical slowing down results in a transition from the adiabatic to the impulse behavior in the order parameter. Experimental implications are briefly discussed.

cond-mat↗
arXiv1998

Vortex String Formation in a 3D U(1) Temperature Quench

We report the first large scale numerical study of the dynamics of the second order phase transition of a U(1) $λϕ^4$ theory in three spatial dimensions. The transition is induced by a time-dependent temperature drop in the heat bath to which the fields are coupled. We present a detailed account of the dynamics of the fields and vortex string formation as a function of the quench rate. The results are found in good agreement to the theory of defect formation proposed by Kibble and Zurek.

hep-ph↗
arXiv1998

Decoherence, Einselection, and the Existential Interpretation (the Rough Guide)

The roles of decoherence and environment-induced superselection in the emergence of the classical from the quantum substrate are described. The stability of correlations between the einselected quantum pointer states and the environment allows them to exist almost as objectively as classical states were once thought to exist: There are ways of finding out what is the pointer state of the system which utilize redundancy of their correlations with the environment, and which leave einselected states essentially unperturbed. This relatively objective existence of certain quantum states facilitates operational definition of probabilities in the quantum setting. Moreover, once there are states that `exist' and can be `found out', a `collapse' in the traditional sense is no longer necessary --- in effect, it has already happened. The records of the observer will contain evidence of an effective collapse. The role of the preferred states in the processing and storage of information is emphasized. The existential interpretation based on the relatively objective existence of stable correlations between the einselected states of observers memory and in the outside Universe is formulated and discussed.

quant-ph↗
arXiv1998

Decoherence, chaos, quantum-classical correspondence, and the algorithmic arrow of time

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).

quant-ph↗
arXiv1998

Vortex formation in two dimensions: When symmetry breaks, how big are the pieces?

We investigate the dynamics of second order phase transitions in two dimensions, breaking a gauged U(1) symmetry. Using numerical simulations, we show that the density of topological defects formed scales with the quench timescale $τ_Q$ as $n \sim τ_Q^{-1/2}$ when the dynamics is overdamped at the instant when the freezeout of thermal fluctuations takes place, and $n \sim τ_Q^{-2/3}$ in the underdamped case. This is predicted by the scenario proposed by one of us [1].

hep-ph↗