In this paper, we study the reduction criterion for detecting entanglement of large dimensional bipartite quantum systems. We first obtain an explicit formula for the moments of a random quantum state to which the reduction criterion has been applied. We show that the empirical eigenvalue distribution of this random matrix converges strongly to a limit that we compute, in three different asymptotic regimes. We then employ tools from free probability theory to study the asymptotic positivity of the reduction operators. Finally, we compare the reduction criterion with other entanglement criteria, via thresholds.
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Research Article| November 18 2014
On the reduction criterion for random quantum states
Maria Anastasia Jivulescu;
Nicolae Lupa ;
Maria Anastasia Jivulescu, Nicolae Lupa, Ion Nechita; On the reduction criterion for random quantum states. J. Math. Phys. 1 November 2014; 55 (11): 112203. https://doi.org/10.1063/1.4901548
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