Entanglement of random subspaces via the Hastings bound

Abstract

Recently Hastings proved the existence of random unitary channels which violate the additivity conjecture. In this paper we use Hastings' method to derive new bounds for the entanglement of random subspaces of bipartite systems. As an application we use these bounds to prove the existence of non-unital channels which violate additivity of minimal output entropy.

25 pages

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Cited by in corpus (16)

• A Survey on Quantum Channel Capacities
• Random matrix techniques in quantum information theory
• Random quantum channels II: Entanglement of random subspaces, Renyi entropy estimates and additivity problems
• Gaussianization and eigenvalue statistics for random quantum channels (III)
• Non-additivity of Renyi entropy and Dvoretzky's Theorem
• The difference between two random mixed quantum states: exact and asymptotic spectral analysis
• Random positive operator valued measures
• 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
• Highly entangled, non-random subspaces of tensor products from quantum groups
• Revisiting additivity violation of quantum channels
• Asymptotically well-behaved input states do not violate additivity for conjugate pairs of random quantum channels
• Low entropy output states for products of random unitary channels
• Quantum channels with polytopic images and image additivity
• On the minimum output entropy of random orthogonal quantum channels
• Additive bounds of minimum output entropies for unital channels and an exact qubit formula