Gaussianization and eigenvalue statistics for random quantum channels (III)

Abstract

In this paper, we present applications of the calculus developed in Collins and Nechita [Comm. Math. Phys. 297 (2010) 345-370] and obtain an exact formula for the moments of random quantum channels whose input is a pure state thanks to Gaussianization methods. Our main application is an in-depth study of the random matrix model introduced by Hayden and Winter [Comm. Math. Phys. 284 (2008) 263-280] and used recently by Brandao and Horodecki [Open Syst. Inf. Dyn. 17 (2010) 31-52] and Fukuda and King [J. Math. Phys. 51 (2010) 042201] to refine the Hastings counterexample to the additivity conjecture in quantum information theory. This model is exotic from the point of view of random matrix theory as its eigenvalues obey two different scalings simultaneously. We study its asymptotic behavior and obtain an asymptotic expansion for its von Neumann entropy.

Published in at http://dx.doi.org/10.1214/10-AAP722 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (8)

• Random quantum channels I: graphical calculus and the Bell state phenomenon
• On Hastings' counterexamples to the minimum output entropy additivity conjecture
• Asymptotics of random density matrices
• Comments on Hastings' Additivity Counterexamples
• Random graph states, maximal flow and Fuss-Catalan distributions
• Random quantum channels II: Entanglement of random subspaces, Renyi entropy estimates and additivity problems
• Entanglement of random subspaces via the Hastings bound
• Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels

Cited by in corpus (30)

• A Survey on Quantum Channel Capacities
• Random matrix techniques in quantum information theory
• Random quantum channels I: graphical calculus and the Bell state phenomenon
• Entanglement, quantum randomness, and complexity beyond scrambling
• Generalized Entanglement Entropies of Quantum Designs
• Relative Entropy of Random States and Black Holes
• Weingarten calculus for matrix ensembles associated with compact symmetric spaces
• Distinguishing Random and Black Hole Microstates
• Weak multiplicativity for random quantum channels
• Realigning random states
• Designs via Free Probability
• The absolute positive partial transpose property for random induced states
• 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
• The PPT square conjecture holds generically for some classes of independent states
• A graphical calculus for integration over random diagonal unitary matrices
• Low entropy output states for products of random unitary channels
• On the reduction criterion for random quantum states
• Asymptotically well-behaved input states do not violate additivity for conjugate pairs of random quantum channels
• On the convergence of output sets of quantum channels
• $k$-extendibility of high-dimensional bipartite quantum states
• Strong asymptotic freeness for independent uniform variables on compact groups associated to non-trivial representations
• Estimates for compression norms and additivity violation in quantum information
• On the joint distribution of the marginals of multipartite random quantum states
• Block-modified Wishart matrices and free Poisson laws
• On the minimum output entropy of random orthogonal quantum channels
• Moment Methods on compact groups: Weingarten calculus and its applications
• Entanglement criteria for the bosonic and fermionic induced ensembles
• Linear algebra and group theory
• Generating series and matrix models for meandric systems with one shallow side