Highly Entangled States With Almost No Secrecy

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• Matthias Christandl, LMU Munich
• Thursday 22 October 2009, 14:00-15:00
• MR15, Centre for Mathematical Sciences.

If you have a question about this talk, please contact Dr Alastair Kay.

In this talk, we will 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. 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 (plethysms!!!), linear programming and the entanglement measure known as squashed entanglement. This is joint work with Andreas Winter and Norbert Schuch.

This talk is part of the CQIF Seminar series.

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