Capacity Estimates via comparison with TRO channels

Abstract

A ternary ring of operators (TRO) in finite dimensions is a diagonal sum of spaces of rectangular matrices. TRO as operator space corresponds to quantum channels that are diagonal sums of partial traces, which we call TRO channels. TRO channels admits simple, single-letter capacity formula. Using operator space and complex interpolation techniques, we give perturbative capacities estimates for a wider class of quantum channels by comparison to TRO channels. Our estimates applies mainly for quantum and private capacity and also strong converse rates. The examples includes random unitary from group representations which in general are non-degradable channels.

arXiv commentv2, 35 pages

References in corpus (37)

• General Benchmarks for Quantum Repeaters
• Fundamental Limits of Repeaterless Quantum Communications
• The capacity of the noisy quantum channel
• On quantum Renyi entropies: a new generalization and some properties
• Entanglement-Assisted Classical Capacity of Noisy Quantum Channels
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Capacities of Quantum Erasure Channels
• Quantum Communication With Zero-Capacity Channels
• An improved bound on distillable entanglement
• The mother of all protocols: Restructuring quantum information's family tree
• Converse bounds for private communication over quantum channels
• Degenerate Quantum Codes for Pauli Channels
• The squashed entanglement of a quantum channel
• Reverse Coherent Information
• Unbounded number of channel uses are required to see quantum capacity
• The private capacity of quantum channels is not additive
• The private classical capacity with a symmetric side channel and its application to quantum cryptography
• The quantum capacity with symmetric side channels
• A classical analogue of entanglement
• Multiplicativity of completely bounded $p$-norms implies a strong converse for entanglement-assisted capacity
• Asymptotic Relative Entropy of Entanglement for Orthogonally Invariant States
• Multiplicativity of completely bounded p-norms implies a new additivity result
• Relative Entropy Bounds on Quantum, Private and Repeater Capacities
• Entanglement Cost of Quantum Channels
• Approximate Degradable Quantum Channels
• Simplifying additivity problems using direct sum constructions
• Strong converse rates for quantum communication
• Hastings' additivity counterexample via Dvoretzky's theorem
• The quantum dynamic capacity formula of a quantum channel
• Positivity of linear maps under tensor powers
• Superadditivity of private information for any number of uses of the channel
• Potential capacities of quantum channels
• Public and private resource trade-offs for a quantum channel
• Squashed entanglement and approximate private states
• Amortization does not enhance the max-Rains information of a quantum channel
• A semidefinite programming upper bound of quantum capacity
• Quantum channels arising from abstract harmonic analysis

Cited by in corpus (13)

• Entropic singularities give rise to quantum transmission
• Distributed Private Randomness Distillation
• Magic Resource Can Enhance the Quantum Capacity of Channels
• The platypus of the quantum channel zoo
• Temperley-Lieb quantum channels
• Partially Coherent Direct Sum Channels
• Quasi-factorization and Multiplicative Comparison of Subalgebra-Relative Entropy
• Multivariate Trace Inequalities, p-Fidelity, and Universal Recovery Beyond Tracial Settings
• Operator-valued Schatten spaces and quantum entropies
• Capacity Bounds via Operator Space Methods
• Information-theoretic aspects of the generalized amplitude damping channel
• Additivity of quantum capacities in simple non-degradable quantum channels
• Information storage and transmission under Markovian noise