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arXiv:0811.3344 · AIP conference proceedings

Geometry of Entanglement Sudden Death: Explicit Examples

Raphael C. Drumond, Marcelo O. Terra Cunha, Luigi Accardi, Guillaume Adenier, Christopher A. Fuchs, Gregg S. Jaeger, Andrei Yu. Khrennikov, Jan-Åke Larsson, Stig Stenholm

Published Jan 1, 2009• 1 citation
arXivHTMLPDF

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 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.

DOI
10.1063/1.3109968

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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.
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.
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.
Sudden death of entanglement is a well-known effect resulting from the finite volume of separable states. We study the case when the observer has a limited measurement capability and analyze the effective entanglement (i.e., entanglement minimized over the output data). We show that in the well-defined system of two quantum dots monitored by single-electron transistors, one may observe a sudden death of effective entanglement when real, physical entanglement is still alive. For certain measurement setups, this occurs even for initial states for which sudden death of physical entanglement is not possible at all. The principles of the analysis may be applied to other analogous scenarios, such as estimation of the parameters arising from quantum process tomography.
A new development in the dynamical behavior of elementary quantum systems is the surprising discovery that correlation between two quantum units of information called qubits can be degraded by environmental noise in a way not seen previously in studies of dissipation. This new route for dissipation attacks quantum entanglement, the essential resource for quantum information as well as the central feature in the Einstein-Podolsky-Rosen so-called paradox and in discussions of the fate of Schrödinger's cat. The effect has been labeled ESD, which stands for early-stage disentanglement or, more frequently, entanglement sudden death. We review recent progress in studies focused on this phenomenon.