Comments on Hastings' Additivity Counterexamples

Abstract

Hastings recently provided a proof of the existence of channels which violate the additivity conjecture for minimal output entropy. In this paper we present an expanded version of Hastings' proof. In addition to a careful elucidation of the details of the proof, we also present bounds for the minimal dimensions needed to obtain a counterexample.

38 pages

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• Gaussian optimizers and the additivity problem 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)
• Entanglement of random subspaces via the Hastings bound
• Generic nonadditivity of quantum capacity in simple channels
• Towards a state minimizing the output entropy of a tensor product of random quantum channels
• Almost one bit violation for the additivity of the minimum output entropy
• Algorithmic Superactivation of Asymptotic Quantum Capacity of Zero-Capacity Quantum Channels
• Revisiting additivity violation of quantum channels
• The minimum entropy output of a quantum channel is locally additive
• Asymptotically well-behaved input states do not violate additivity for conjugate pairs of random quantum channels
• Capacities of the covariant Pauli channel
• Low entropy output states for products of random unitary channels
• Purification of Gaussian maximally mixed states
• On the convergence of output sets of quantum channels
• Haagerup's inequality and additivity violation of the Minimum Output Entropy
• Geometry of generalized Pauli channels
• Black hole microstates vs. the additivity conjectures
• Estimates for compression norms and additivity violation in quantum information
• On the minimum output entropy of random orthogonal quantum channels
• Additive bounds of minimum output entropies for unital channels and an exact qubit formula
• The minimum Renyi entropy output of a quantum channel is locally additive
• Gelfand-Tsetlin polytopes and random contractions away from the limiting shapes
• Additivity violation of quantum channels via strong convergence to semi-circular and circular elements
• On the additivity of the minimum output entropy