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Threshold phenomena for quantum marginals

Tuesday 15th October 2013 - 15:30 to 16:30
INI Seminar Room 1
Co-authors: Guillaume Aubrun (U. Lyon 1), Deping Ye (Memorial U. of Newfoundland)

Consider a quantum system consisting of N identical particles and assume that it is in a random pure state (i.e., uniformly distributed over the sphere of the corresponding Hilbert space). Next, let A and B be two subsystems consisting of k particles each. Are A and B likely to share entanglement? Is the AB-marginal typically PPT?

As it turns out, for many natural properties there is a sharp "phase transition" at some threshold depending on the property in question. For example, there is a threshold K asymptotically equivalent to N/5 such that - if k > K then A and B typically share entanglement - if k The first statement was (essentially) shown in the talk by G. Aubrun. Here we present a general scheme for handling such questions and sketch the analysis specific to entanglement.

The talk is based on arxiv:1106.2264v3; a less-technical overview is in arxiv:1112.4582v2.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons