Random quantum channels II: Entanglement of random subspaces, Renyi entropy estimates and additivity problems

Abstract

In this paper we obtain new bounds for the minimum output entropies of random quantum channels. These bounds rely on random matrix techniques arising from free probability theory. We then revisit the counterexamples developed by Hayden and Winter to get violations of the additivity equalities for minimum output Rényi entropies. We show that random channels obtained by randomly coupling the input to a qubit violate the additivity of the $p$-Rényi entropy. For some sequences of random quantum channels, we compute almost surely the limit of their Schatten $S_1\to S_p$ norms.

3 figures added, minor typos corrected

References in corpus (7)

• Aspects of generic entanglement
• Random quantum channels I: graphical calculus and the Bell state phenomenon
• Product of random projections, Jacobi ensembles and universality problems arising from free probability
• On Hastings' counterexamples to the minimum output entropy additivity conjecture
• Asymptotics of random density matrices
• Comments on Hastings' Additivity Counterexamples
• Entanglement of random subspaces via the Hastings bound

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• Laws of large numbers for eigenvectors and eigenvalues associated to random subspaces in a tensor product
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• Entanglement of random subspaces via the Hastings bound
• Weak multiplicativity for random quantum channels
• The difference between two random mixed quantum states: exact and asymptotic spectral analysis
• Almost one bit violation for the additivity of the minimum output entropy
• Towards a state minimizing the output entropy of a tensor product of random quantum channels
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• CB-norm estimates for maps between noncommutative $L_p$-spaces and quantum channel theory