A hierarchy of efficient bounds on quantum capacities exploiting symmetry

Abstract

Optimal rates for achieving an information processing task are often characterized in terms of regularized information measures. In many cases of quantum tasks, we do not know how to compute such quantities. Here, we exploit the symmetries in the recently introduced $D^{\#}$ in order to obtain a hierarchy of semidefinite programming bounds on various regularized quantities. As applications, we give a general procedure to give efficient bounds on the regularized Umegaki channel divergence as well as the classical capacity and two-way assisted quantum capacity of quantum channels. In particular, we obtain slight improvements for the capacity of the amplitude damping channel. We also prove that for fixed input and output dimensions, the regularized sandwiched Rényi divergence between any two quantum channels can be approximated up to an $\epsilon$ accuracy in time that is polynomial in $1/\epsilon$.

References in corpus (4)

• Fundamental bound on the reliability of quantum information transmission
• On the strong converses for the quantum channel capacity theorems
• Matrix Algebras and Semidefinite Programming Techniques for Codes
• Block diagonalization for algebra's associated with block codes

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• Computable entanglement cost under positive partial transpose operations
• Extendible quantum measurements and limitations on classical communication
• Unextendible entanglement of quantum channels