Minimizing the loss of entanglement under dimensional reduction |
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Authors: | Email author" target="_blank">V?PetersenEmail author L?B?Madsen K?M?lmer |
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Institution: | (1) QUANTOP, Danish National Research Foundation Center for Quantum Optics, Denmark;(2) Department of Physics and Astronomy, University of Aarhus, 8000 Århus C, Denmark |
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Abstract: | We investigate the possibility of transforming, under local operations and classical communication, a general bipartite quantum state on a dA x dB tensor-product space into a final state in 2 x 2 dimensions, while maintaining as much entanglement as possible. For pure states, we prove that Nielsens theorem provides the optimal protocol, and we present quantitative results on the degree of entanglement before and after the dimensional reduction. For mixed states, we identify a protocol that we argue is optimal for isotropic and Werner states. In the literature, it has been conjectured that some Werner states are bound entangled and in support of this conjecture our protocol gives final states without entanglement for this class of states. For all other entangled Werner states and for all entangled isotropic states some degree of free entanglement is maintained. In this sense, our protocol may be used to discriminate between bound and free entanglement.Received: 21 January 2004, Published online: 2 March 2004PACS:
03.67.Mn Entanglement production, characterization, and manipulation - 42.50.Dv Nonclassical states of the electromagnetic field, including entangled photon states; quantum state engineering and measurements - 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bells inequalities, GHZ states, etc.) |
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