Capacity Bounds via Operator Space Methods

Abstract

Quantum capacity, as the ultimate transmission rate of quantum communication, is characterized by regularized coherent information. In this work, we reformulate approximations of the quantum capacity by operator space norms and give both upper and lower bounds on quantum capacity, and potential quantum capacity using interpolation techniques. We identify a situation in which nice classes of channels satisfy a "comparison property" on entropy, coherent information and capacities. The paradigms for our estimates are so-called conditional expectations. These generally non-degradable channels admit a strongly additive expression for $Q^{(1)}$. We also identify conditions on channels showing that the "hashing bound" is optimal for the cb-entropy. These two estimates combined give upper and lower bounds on quantum capacity on our "nice" classes of channels, which differ only up to a factor 2, independent of the dimension. The estimates are discussed for certain classes of channels, including group channels, Pauli channels and other high-dimensional channels.

Added two figures, typos corrected

References in corpus (10)

• Converse bounds for private communication over quantum channels
• Unbounded number of channel uses are required to see quantum capacity
• The quantum capacity with symmetric side channels
• Approximate Degradable Quantum Channels
• Simplifying additivity problems using direct sum constructions
• Hastings' additivity counterexample via Dvoretzky's theorem
• Potential capacities of quantum channels
• A semidefinite programming upper bound of quantum capacity
• Distributed Private Randomness Distillation
• Capacity Estimates via comparison with TRO channels

Cited by in corpus (6)

• Entropic singularities give rise to quantum transmission
• Pursuing the fundamental limits for quantum communication
• Distributed Private Randomness Distillation
• Partially Coherent Direct Sum Channels
• Geometric Rényi Divergence and its Applications in Quantum Channel Capacities
• Estimate distillable entanglement and quantum capacity by squeezing useless entanglement