Hastings' additivity counterexample via Dvoretzky's theorem

Abstract

The goal of this note is to show that Hastings' counterexample to the additivity of minimal output von Neumann entropy can be readily deduced from a sharp version of Dvoretzky's theorem on almost spherical sections of convex bodies.

12 pages; v.2: added references, Appendix A expanded to make the paper essentially self-contained

References in corpus (6)

• Superadditivity of communication capacity using entangled inputs
• Aspects of generic entanglement
• Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1
• On Hastings' counterexamples to the minimum output entropy additivity conjecture
• Comments on Hastings' Additivity Counterexamples
• Non-additivity of Renyi entropy and Dvoretzky's Theorem

Cited by in corpus (34)

• Quantum channels and memory effects
• A Survey on Quantum Channel Capacities
• Random matrix techniques in quantum information theory
• Should Entanglement Measures be Monogamous or Faithful?
• Entanglement thresholds for random induced states
• From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking
• Eigenvalue Distributions of Reduced Density Matrices
• Gaussian optimizers and the additivity problem in quantum information theory
• Correlation length in random MPS and PEPS
• Weak multiplicativity for random quantum channels
• Capacity Estimates via comparison with TRO channels
• The absolute positive partial transpose property for random induced states
• Almost one bit violation for the additivity of the minimum output entropy
• Random positive operator valued measures
• Highly entangled, non-random subspaces of tensor products from quantum groups
• Partial transpose of random quantum states: exact formulas and meanders
• The PPT square conjecture holds generically for some classes of independent states
• Identification Via Quantum Channels
• Revisiting additivity violation of quantum channels
• Typical local measurements in generalised probabilistic theories: emergence of quantum bipartite correlations
• Asymptotically well-behaved input states do not violate additivity for conjugate pairs of random quantum channels
• Quantum channels with polytopic images and image additivity
• $k$-extendibility of high-dimensional bipartite quantum states
• Capacity Bounds via Operator Space Methods
• Approximation, Gelfand, and Kolmogorov numbers of Schatten class embeddings
• Estimates for compression norms and additivity violation in quantum information
• Optimal input states for quantifying the performance of continuous-variable unidirectional and bidirectional teleportation
• Concentration estimates for random subspaces of a tensor product, and application to Quantum Information Theory
• On the minimum output entropy of random orthogonal quantum channels
• Metric and classical fidelity uncertainty relations for random unitary matrices
• The Partial Transpose and Asymptotic Free Independence for Wishart Random Matrices: Part II
• Potential output purity of completely positive maps
• Gelfand-Tsetlin polytopes and random contractions away from the limiting shapes
• New constructive counterexamples to additivity of minimum output Rényi p-entropy of quantum channels