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.Comment: Updated version: new title and contents. 22 pages, 8 figure

Quantum Darwinism requires an extra-theoretical assumption of encoding redundancy

Observers restricted to the observation of pointer states of apparatus cannot conclusively demonstrate that the pointer of an apparatus A registers the state of a system of interest S without perturbing S. Observers cannot, therefore, conclusively demonstrate that the states of a system S are redundantly encoded by pointer states of multiple independent apparatus without destroying the redundancy of encoding. The redundancy of encoding required by quantum Darwinism must, therefore, be assumed from outside the quantum-mechanical formalism and without the possibility of experimental demonstration.Comment: 5 pages, 1 figure. Comments on foundational assumptions of W. Zurek (2009) Nat Phys 5 181 (arXiv 0903.5082). v2 significant revision to improve clarit

Decoherence, Re-coherence, and the Black Hole Information Paradox

We analyze a system consisting of an oscillator coupled to a field. With the field traced out as an environment, the oscillator loses coherence on a very short {\it decoherence timescale}; but, on a much longer {\it relaxation timescale}, predictably evolves into a unique, pure (ground) state. This example of {\it re-coherence} has interesting implications both for the interpretation of quantum theory and for the loss of information during black hole evaporation. We examine these implications by investigating the intermediate and final states of the quantum field, treated as an open system coupled to an unobserved oscillator.Comment: 23 pages, 2 figures included, figures 3.1 - 3.3 available at http://qso.lanl.gov/papers/Papers.htm

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.Comment: 21 pages, 6 figures, RevTex 4. Submitted to Foundations of Physics (Asher Peres Festschrift

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.Comment: RevTeX, 29 pages, 5 EPS figures. Substantially rewritten analysis, improved figures, additional references, and errors fixed. Final version (to appear in PRA

Fragility of a class of highly entangled states of many quantum-bits

We consider a Quantum Computer with n quantum-bits (`qubits'), where each qubit is coupled independently to an environment affecting the state in a dephasing or depolarizing way. For mixed states we suggest a quantification for the property of showing {\it quantum} uncertainty on the macroscopic level. We illustrate in which sense a large parameter can be seen as an indicator for large entanglement and give hypersurfaces enclosing the set of separable states. Using methods of the classical theory of maximum likelihood estimation we prove that this parameter is decreasing with 1/\sqrt{n} for all those states which have been exposed to the environment. Furthermore we consider a Quantum Computer with perfect 1-qubit gates and 2-qubit gates with depolarizing error and show that any state which can be obtained from a separable initial state lies inbetween a family of pairs of certain hypersurfaces parallel to those enclosing the separable ones.Comment: 9 Pages, RevTe

Entropy and Wigner Functions

The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive definite probability distributions which are also admissible Wigner functionsComment: 18 page

Environment-Induced Decoherence and the Transition From Quantum to Classical

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 equations we study einselection employing the general strategy of the predictability sieve. Assumptions that are usually made in the discussion of decoherence are critically reexamined along with the ``standard lore'' to which they lead. Restoration of quantum-classical correspondence in systems that are classically chaotic is discussed. The dynamical second law -it is shown- can be traced to the same phenomena that allow for the restoration of the correspondence principle in decohering chaotic systems (where it is otherwise lost on a very short time-scale). Quantum error correction is discussed as an example of an anti-decoherence strategy. Implications of decoherence and einselection for the interpretation of quantum theory are briefly pointed out.Comment: 80 pages, 7 figures included, Lectures given by both authors at the 72nd Les Houches Summer School on "Coherent Matter Waves", July-August 199

What is "system": the information-theoretic arguments

The problem of "what is 'system'?" is in the very foundations of modern quantum mechanics. Here, we point out the interest in this topic in the information-theoretic context. E.g., we point out the possibility to manipulate a pair of mutually non-interacting, non-entangled systems to employ entanglement of the newly defined '(sub)systems' consisting the one and the same composite system. Given the different divisions of a composite system into "subsystems", the Hamiltonian of the system may perform in general non-equivalent quantum computations. Redefinition of "subsystems" of a composite system may be regarded as a method for avoiding decoherence in the quantum hardware. In principle, all the notions refer to a composite system as simple as the hydrogen atom.Comment: 13 pages, no figure

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.Comment: 12 pages in RevTex; improved presentation; a new comment on decoherence-free pointer subspaces in BEC; accepted in Phys.Rev.