Potential capacities of quantum channels

Abstract

We introduce potential capacities of quantum channels in an operational way and provide upper bounds for these quantities, which quantify the ultimate limit of usefulness of a channel for a given task in the best possible context. Unfortunately, except for a few isolated cases, potential capacities seem to be as hard to compute as their "plain" analogues. We thus study upper bounds on some potential capacities: For the classical capacity, we give an upper bound in terms of the entanglement of formation. To establish a bound for the quantum and private capacity, we first "lift" the channel to a Hadamard channel and then prove that the quantum and private capacity of a Hadamard channel is strongly additive, implying that for these channels, potential and plain capacity are equal. Employing these upper bounds we show that if a channel is noisy, however close it is to the noiseless channel, then it cannot be activated into the noiseless channel by any other contextual channel; this conclusion holds for all the three capacities. We also discuss the so-called environment-assisted quantum capacity, because we are able to characterize its "potential" version.

10 pages, IEEE style; minor changes, references added; accepted for publication in EEE Trans Inf. Theory

References in corpus (9)

• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Quantum Communication With Zero-Capacity Channels
• Entanglement of assistance and multipartite state distillation
• Unbounded number of channel uses are required to see quantum capacity
• The quantum capacity with symmetric side channels
• The private classical capacity with a symmetric side channel and its application to quantum cryptography
• Extensive nonadditivity of privacy
• Additive Extensions of a Quantum Channel
• Superadditivity of private information for any number of uses of the channel

Cited by in corpus (19)

• Operational Resource Theory of Coherence
• Amortized entanglement of a quantum channel and approximately teleportation-simulable channels
• On converse bounds for classical communication over quantum channels
• Generic nonadditivity of quantum capacity in simple channels
• A semidefinite programming upper bound of quantum capacity
• Holevo Capacity of Discrete Weyl Channels
• Capacity Estimates via comparison with TRO channels
• Deterministic identification over channels with finite output: a dimensional perspective on superlinear rates
• A new property of the Lovász number and duality relations between graph parameters
• Non-convexity of private capacity and classical environment-assisted capacity of a quantum channel
• Capacity Bounds via Operator Space Methods
• Heralded Channel Holevo Superadditivity Bounds from Entanglement Monogamy
• On decomposable correlation matrices
• Bounding the quantum capacity with flagged extensions
• Additivity of quantum capacities in simple non-degradable quantum channels
• Noise is resource-contextual in quantum communication
• Potential output purity of completely positive maps
• Information storage and transmission under Markovian noise
• Activation of zero-error classical capacity in low-dimensional quantum systems