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 strongly correlated random variables for all values of N (and not just for large N).
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Majumdar, S.N., Bohigas, O. & Lakshminarayan, A. Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State. J Stat Phys 131, 33–49 (2008). https://doi.org/10.1007/s10955-008-9491-5
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DOI: https://doi.org/10.1007/s10955-008-9491-5