Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels

Abstract

Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models of relevance for the recent counterexamples to the minimum output entropy additivity problems. Our main result is a classification of regimes for which the von Neumann entropy is lower on average than the elementary bounds that can be obtained with linear algebra techniques.

References in corpus (4)

• Random quantum channels I: graphical calculus and the Bell state phenomenon
• Product of random projections, Jacobi ensembles and universality problems arising from free probability
• Asymptotics of random density matrices
• Random graph states, maximal flow and Fuss-Catalan distributions

Cited by in corpus (10)

• Random matrix techniques in quantum information theory
• Gaussianization and eigenvalue statistics for random quantum channels (III)
• Weak multiplicativity for random quantum 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
• 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
• On the convergence of output sets of quantum channels
• Additivity rates and PPT property for random quantum channels
• Estimates for compression norms and additivity violation in quantum information