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arXiv · 0711.0677

Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State

Satya N. Majumdar·Oriol Bohigas·Arul Lakshminarayan
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Abstract

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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BibTeXRIS

Satya N. Majumdar, Oriol Bohigas, Arul Lakshminarayan. 2008-01-14. Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State. https://doi.org/10.1007/s10955-008-9491-5

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