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Title: Highly entangled states with almost no secrecy
Authors: Christandl, M.
Schuch, N.
Winter, A. 
Issue Date: 17-Jun-2010
Citation: Christandl, M., Schuch, N., Winter, A. (2010-06-17). Highly entangled states with almost no secrecy. Physical Review Letters 104 (24) : -. ScholarBank@NUS Repository.
Abstract: In this Letter we illuminate the relation between entanglement and secrecy by providing the first example of a quantum state that is highly entangled, but from which, nevertheless, almost no secrecy can be extracted. More precisely, we provide two bounds on the bipartite entanglement of the totally antisymmetric state in dimension d×d. First, we show that the amount of secrecy that can be extracted from the state is low; to be precise it is bounded by O(1/d). Second, we show that the state is highly entangled in the sense that we need a large amount of singlets to create the state: entanglement cost is larger than a constant, independent of d. In order to obtain our results we use representation theory, linear programming, and the entanglement measure known as squashed entanglement. Our findings also clarify the relation between the squashed entanglement and the relative entropy of entanglement. © 2010 The American Physical Society.
Source Title: Physical Review Letters
ISSN: 00319007
DOI: 10.1103/PhysRevLett.104.240405
Appears in Collections:Staff Publications

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