Unifying typical entanglement and coin tossing: on randomization in probabilistic theories

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• Oscar Dahlsten (University of Oxford/National University of Singapore)
• Thursday 17 November 2011, 14:15-15:15
• MR4, Centre for Mathematical Sciences.

If you have a question about this talk, please contact Paul Skrzypczyk.

It is well-known that pure quantum states are typically almost maximally entangled, and thus have close to maximally mixed subsystems. We consider whether this is true for probabilistic theories more generally, and not just for quantum theory. We derive a formula for the expected purity of a subsystem in any probabilistic theory for which this quantity is well-defined. It applies to typical entanglement in pure quantum states, coin tossing in classical probability theory, and randomization in post-quantum theories; a simple generalization yields the typical entanglement in (anti)symmetric quantum subspaces. The formula is exact and simple, only containing the number of degrees of freedom and the information capacity of the respective systems. It allows us to generalize statistical physics arguments in a way which depends only on coarse properties of the underlying theory. The proof of the formula generalizes several randomization notions to general probabilistic theories. This includes a generalization of purity.

This talk is part of the CQIF Seminar series.

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