Entanglement of random quantum states: phase transitions

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• Stanislaw Szarek, Case Western Reserve University & Sorbonne Université
• Thursday 06 March 2025, 14:15-15:15
• MR2.

If you have a question about this talk, please contact Laurens Lootens.

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) and two subsystems A and B, consisting of k particles each. Are A and B likely to share entanglement? For many natural properties, of which “being entangled” is one example, there is a sharp “phase transition.” In the current setting, there is a threshold K (which is roughly N/5) such that A and B typically share entanglement if k > K, and do not if k < K. We give precise statements of results of the above type and hint on the arguments, which involve random matrices and various concepts/techniques from geometric functional analysis.

This talk is part of the CQIF Seminar series.

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