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arXiv:0809.4445 · Journal of Physics A Mathematical and Theoretical

Asymptotic entanglement dynamics and geometry of quantum states

Raphael C. Drumond, Marcelo Terra Cunha

Published Jun 24, 2009• 18 citations
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Abstract

A given dynamics for a composite quantum system can exhibit several distinct properties for the asymptotic entanglement behavior, such as entanglement sudden death, asymptotic death of entanglement, sudden birth of entanglement, etc. A classification of the possible situations was given by Terra Cunha (2007 New J. Phys. 9 237) but for some classes there were no known examples. In this work, we give a better classification for the possible relaxing dynamics in light of the geometry of their set of asymptotic states and give explicit examples for all the classes. Although the classification is completely general, in the search for examples it is sufficient to use two qubits with dynamics given by differential equations in the Lindblad form (some of them are non-autonomous). We also investigate, in each case, the probabilities of finding each possible behavior for random initial states.

DOI
10.1088/1751-8113/42/28/285308

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A given dynamics for a composite quantum system can exhibit several distinct properties for the asymptotic entanglement behavior, such as entanglement sudden death, asymptotic death of entanglement, sudden birth of entanglement, etc. A classification of the possible situations was given by Terra Cunha (2007 New J. Phys. 9 237) but for some classes there were no known examples. In this work, we give a better classification for the possible relaxing dynamics in light of the geometry of their set of asymptotic states and give explicit examples for all the classes. Although the classification is completely general, in the search for examples it is sufficient to use two qubits with dynamics given by differential equations in the Lindblad form (some of them are non-autonomous). We also investigate, in each case, the probabilities of finding each possible behavior for random initial states.
Abstract. In open quantum systems, entanglement can vanish faster than coherence. This phenomenon is usually called sudden death of entanglement. In [M. O. Terra Cunha, New J. Phys. 9, 237 (2007)] a geometrical explanation was offered and a classification of all possible scenarios was given. Some classes were exemplified, but it was still an open question whether there were examples for the other ones. This was solved in [R. C. Drumond and M. O. Terra Cunha, arXiv:0809.4445v1]. Here we briefly review the problem, state our results in a precise way, discuss the generality of the approach, and add some speculative desirable generalizations.
In open quantum systems, entanglement can vanish faster than coherence. This phenomenon is usually called sudden death of entanglement. In [M. O. Terra Cunha, New J. Phys. 9, 237 (2007)] a geometrical explanation was offered and a classification of all possible scenarios was given. Some classes were examplified, but it was still an open question whether there were examples for the other ones. This was solved in [R. C. Drumond and M. O. Terra Cunha, arXiv:0809.4445v1]. Here we briefly review the problem, state our results in a precise way, discuss the generality of the approach, and add some speculative desirable generalizations.
In this paper, the origin of disentanglement for two specific sub-classes of [Formula: see text]-states namely maximally nonlocal mixed states (MNMSs) and maximally entangled mixed states (MEMSs) is investigated analytically for a physical system consisting of two spatially separated qubits interacting with a common vacuum bath. The phenomena of entanglement sudden death (ESD) and the entanglement sudden birth (ESB) are observed, but the characteristics of ESD and ESB are found to be different for the case of two-photon coherence and single photon coherence states. The role played by initial coherence for the underlying entanglement dynamics is investigated. Further, the entanglement dynamics of MNMSs and MEMSs under different environmental noises namely phase damping, amplitude damping and random telegraph noise (RTN) noise with respect to the decay and revival of entanglement is analyzed. It is observed that the single photon coherence states are more robust against the sudden death of entanglement, indicating the usability of such states in the development of technologies for the practical implementation of quantum information processing tasks.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuousvariable entanglement for a system consisting of two independent harmonic oscillators interacting with a general environment.Using Peres-Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we describe the generation and evolution of entanglement in terms of the covariance matrix for an arbitrary Gaussian input state.For some values of diffusion and dissipation coefficients describing the environment, the state keeps for all times its initial type: separable or entangled.In other cases, entanglement generation or entanglement collapse (entanglement sudden death) take place or even a periodic collapse and revival of entanglement.We show that for certain classes of environments the initial state evolves asymptotically to an entangled equilibrium bipartite state, while for other values of the coefficients describing the environment, the asymptotic state is separable.We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.