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 (26)

• Mixed State Entanglement and Quantum Error Correction
• On quantum Renyi entropies: a new generalization and some properties
• Entanglement-Assisted Classical Capacity of Noisy Quantum Channels
• Superadditivity of communication capacity using entangled inputs
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Capacities of Quantum Erasure Channels
• Quantum Information Processing with Finite Resources -- Mathematical Foundations
• An improved bound on distillable entanglement
• Computing quantum discord is NP-complete
• Approaches for approximate additivity of the Holevo information of quantum channels
• On the strong converses for the quantum channel capacity theorems
• Fundamental bound on the reliability of quantum information transmission
• The squashed entanglement of a quantum channel
• Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
• Different quantum f-divergences and the reversibility of quantum operations
• Semidefinite approximations of the matrix logarithm
• Resource theory of asymmetric distinguishability for quantum channels
• A chain rule for the quantum relative entropy
• Matrix Algebras and Semidefinite Programming Techniques for Codes
• Semidefinite programming converse bounds for quantum communication
• Amortization does not enhance the max-Rains information of a quantum channel
• Defining quantum divergences via convex optimization
• On converse bounds for classical communication over quantum channels
• Semidefinite bounds for nonbinary codes based on quadruples
• A new quantum version of f-divergence
• Block diagonalization for algebra's associated with block codes

Cited by in corpus (8)

• Semidefinite programming relaxations for quantum correlations
• Quantum NETwork: from theory to practice
• Testing symmetry on quantum computers
• Parallelization of Adaptive Quantum Channel Discrimination in the Non-Asymptotic Regime
• An invitation to the sample complexity of quantum hypothesis testing
• Computable entanglement cost under positive partial transpose operations
• Extendible quantum measurements and limitations on classical communication
• Unextendible entanglement of quantum channels