Non-additivity of Renyi entropy and Dvoretzky's Theorem

Abstract

The goal of this note is to show that the analysis of the minimum output p-Renyi entropy of a typical quantum channel essentially amounts to applying Milman's version of Dvoretzky's Theorem about almost Euclidean sections of high-dimensional convex bodies. This conceptually simplifies the (nonconstructive) argument by Hayden-Winter disproving the additivity conjecture for the minimal output p-Renyi entropy (for p>1).

8 pages, LaTeX; v2: added and updated references, minor editorial changes, no content changes

References in corpus (4)

• The volume of separable states is super-doubly-exponentially small
• Counterexamples to additivity of minimum output p-Renyi entropy for p close to 0
• Random quantum channels II: Entanglement of random subspaces, Renyi entropy estimates and additivity problems
• Entanglement of random subspaces via the Hastings bound

Cited by in corpus (12)

• Random matrix techniques in quantum information theory
• Hastings' additivity counterexample via Dvoretzky's theorem
• From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking
• Weak multiplicativity for random quantum channels
• Limitations on quantum dimensionality reduction
• Revisiting additivity violation of quantum channels
• Quantum channels with polytopic images and image additivity
• Estimates for compression norms and additivity violation in quantum information
• Approximation, Gelfand, and Kolmogorov numbers of Schatten class embeddings
• Metric and classical fidelity uncertainty relations for random unitary matrices
• Additive bounds of minimum output entropies for unital channels and an exact qubit formula
• Average output entropy for quantum channels