Dynamics of the entanglement between two oscillators in the same environment

We provide a complete characterization of the evolution of entanglement between two oscillators coupled to a common environment. For initial Gaussian states we identify three phases with different qualitative long time behavior: There is a phase where entanglement undergoes a sudden death (SD). Another phase (SDR) is characterized by an infinite sequence of events of sudden death and revival of entanglement. In the third phase (NSD) there is no sudden death of entanglement, which persist for long time. The phase diagram is described and analytic expressions for the boundary between phases are obtained. Numerical simulations show the accuracy of the analytic expressions. These results are applicable to a large variety of non--Markovian environments. The case of non--resonant oscillators is also numerically investigated.Comment: 4 pages, 5 figure

Entanglement dynamics during decoherence

The evolution of the entanglement between oscillators that interact with the same environment displays highly non-trivial behavior in the long time regime. When the oscillators only interact through the environment, three dynamical phases were identified and a simple phase diagram characterizing them was presented. Here we generalize those results to the cases where the oscillators are directly coupled and we show how a degree of mixidness can affect the final entanglement. In both cases, entanglement dynamics is fully characterized by three phases (SD: sudden death, NSD: no-sudden death and SDR: sudden death and revivals) which cover a phase diagram that is a simple variant of the previously introduced one. We present results when the oscillators are coupled to the environment through their position and also for the case where the coupling is symmetric in position and momentum (as obtained in the RWA). As a bonus, in the last case we present a very simple derivation of an exact master equation valid for arbitrary temperatures of the environment.Comment: to appear in QIP special issue on Quantum Decoherence and Entanglemen

Dynamical phases for the evolution of the entanglement between two oscillators coupled to the same environment

We study the dynamics of the entanglement between two oscillators that are initially prepared in a general two-mode Gaussian state and evolve while coupled to the same environment. In a previous paper we showed that there are three qualitatively different dynamical phases for the entanglement in the long time limit: sudden death, sudden death and revival and no-sudden death [Paz & Roncaglia, Phys. Rev. Lett. 100, 220401 (2008)]. Here we generalize and extend those results along several directions: We analyze the fate of entanglement for an environment with a general spectral density providing a complete characterization of the corresponding phase diagrams for ohmic and sub--ohmic environments (we also analyze the super-ohmic case showing that for such environment the expected behavior is rather different). We also generalize previous studies by considering two different models for the interaction between the system and the environment (first we analyze the case when the coupling is through position and then we examine the case where the coupling is symmetric in position and momentum). Finally, we analyze (both numerically and analytically) the case of non-resonant oscillators. In that case we show that the final entanglement is independent of the initial state and may be non-zero at very low temperatures. We provide a natural interpretation of our results in terms of a simple quantum optics model.Comment: 18 pages, 13 figure

Work measurement as a generalized quantum measurement

We present a new method to measure the work $w$ performed on a driven quantum system and to sample its probability distribution $P(w)$. The method is based on a simple fact that remained unnoticed until now: Work on a quantum system can be measured by performing a generalized quantum measurement at a single time. Such measurement, which technically speaking is denoted as a POVM (positive operator valued measure) reduces to an ordinary projective measurement on an enlarged system. This observation not only demystifies work measurement but also suggests a new quantum algorithm to efficiently sample the distribution $P(w)$. This can be used, in combination with fluctuation theorems, to estimate free energies of quantum states on a quantum computer.Comment: 4 page

Gapped Two-Body Hamiltonian for continuous-variable quantum computation

We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv) possess a constant energy gap proportional to the squared inverse of the squeezing. Their ground states are the celebrated Gaussian graph states, which are universal resources for quantum computation in the limit of infinite squeezing. These Hamiltonians constitute the basic ingredient for the adiabatic preparation of graph states and thus open new venues for the physical realization of continuous-variable quantum computing beyond the standard optical approaches. We characterize the correlations in these systems at thermal equilibrium. In particular, we prove that the correlations across any multipartition are contained exactly in its boundary, automatically yielding a correlation area law.Comment: 4 pages, one figure. New version: typos corrected, one reference added. To appear in PR

Lyapunov decay in quantum irreversibility

The Loschmidt echo -- also known as fidelity -- is a very useful tool to study irreversibility in quantum mechanics due to perturbations or imperfections. Many different regimes, as a function of time and strength of the perturbation, have been identified. For chaotic systems, there is a range of perturbation strengths where the decay of the Loschmidt echo is perturbation independent, and given by the classical Lyapunov exponent. But observation of the Lyapunov decay depends strongly on the type of initial state upon which an average is done. This dependence can be removed by averaging the fidelity over the Haar measure, and the Lyapunov regime is recovered, as it was shown for quantum maps. In this work we introduce an analogous quantity for systems with infinite dimensional Hilbert space, in particular the quantum stadium billiard, and we show clearly the universality of the Lyapunov regime.Comment: 8 pages, 6 figures. Accepted in Phil. Trans. R. Soc.

Relaxation of isolated quantum systems beyond chaos

In classical statistical mechanics there is a clear correlation between relaxation to equilibrium and chaos. In contrast, for isolated quantum systems this relation is -- to say the least -- fuzzy. In this work we try to unveil the intricate relation between the relaxation process and the transition from integrability to chaos. We study the approach to equilibrium in two different many body quantum systems that can be parametrically tuned from regular to chaotic. We show that a universal relation between relaxation and delocalization of the initial state in the perturbed basis can be established regardless of the chaotic nature of system.Comment: 4+ pages, 4 figs. Closest to published versio

Comment on "General Non-Markovian Dynamics of Open Quantum Systems"

The existence of a "non-Markovian dissipationless" regime, characterized by long lived oscillations, was recently reported for a class of quantum open systems (Zhang et al, PRL, 109, 170402, (2012)). It is claimed this could happen in the strong coupling regime, a surprising result which has attracted some attention. We show that this regime exists if and only if the total Hamiltonian is unbounded from below, casting serious doubts on the usefulness of this result

Redundancy of classical and quantum correlations during decoherence

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.Comment: 6 pages, 4 figure

A Wigner quasiprobability distribution of work

In this article we introduce a quasiprobability distribution of work that is based on the Wigner function. This construction rests on the idea that the work done on an isolated system can be coherently measured by coupling the system to a quantum measurement apparatus. In this way, a quasiprobability distribution of work can be defined in terms of the Wigner function of the apparatus. This quasidistribution contains the information of the work statistics and also holds a clear operational definition. Moreover, it is shown that the presence of quantum coherence in the energy eigenbasis is related with the appearance of characteristics related to non-classicality in the Wigner function such as negativity and interference fringes. On the other hand, from this quasiprobability distribution it is straightforward to obtain the standard two-point measurement probability distribution of work and also the difference in average energy for initial states with coherences.Comment: 11 pages, 3 figure