Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State

Details Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State

2007-11-05

arxiv.org/abs/0711.0677v2

J. Stat. Phys. 131, 33 (2008)

Physics

Condensed Matter

Statistical Mechanics

13 pages, 2 figures included; typos corrected; to appear in J. Stat. Phys

Scientific paper

10.1007/s10955-008-9491-5

A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a random real and a random complex state. Our results are relevant to the entanglement properties of eigenvectors of the orthogonal and unitary ensembles of random matrix theory and quantum chaotic systems. They also provide a rare exactly solvable case for the distribution of the minimum of a set of N {\em strongly correlated} random variables for all values of N (and not just for large N).

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