Families of complex tensor trace-invariants with tree-like dominant pairings factorize at large N, allowing computation of typical multipartite Rényi entropies for uniform random states.
Average Entropy of a Subsystem
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abstract
It was recently conjectured by D. Page that if a quantum system of Hilbert space dimension $nm$ is in a random pure state then the average entropy of a subsystem of dimension $m$ where $m \leq n$ is $ S_{mn} = \sum^{mn}_{k=n+1}(1/k) - (m-1)/2n$. In this letter this conjecture is proved.
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Derives closed expressions for power moments of entanglement entropy of random states via Schur-Weyl duality and S_N character theory.
Quantum systems reach a Maximal Entanglement Limit where entanglement geometry produces thermal reduced density matrices and probabilistic behavior in statistical and high-energy physics.
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Large $N$ factorization of families of tensor trace-invariants
Families of complex tensor trace-invariants with tree-like dominant pairings factorize at large N, allowing computation of typical multipartite Rényi entropies for uniform random states.
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The Maximal Entanglement Limit in Statistical and High Energy Physics
Quantum systems reach a Maximal Entanglement Limit where entanglement geometry produces thermal reduced density matrices and probabilistic behavior in statistical and high-energy physics.