Public Quantum Communication and Superactivation

Abstract

Is there a meaningful quantum counterpart to public communication? We argue that the symmetric-side channel -- which distributes quantum information symmetrically between the receiver and the environment -- is a good candidate for a notion of public quantum communication in entanglement distillation and quantum error correction. This connection is partially motivated by [Brandão and Oppenheim, arXiv:1004.3328], where it was found that if a sender would like to communicate a secret message to a receiver through an insecure quantum channel using a shared quantum state as a key, then the insecure quantum channel is only ever used to simulate a symmetric-side channel, and can always be replaced by it without altering the optimal rate. Here we further show, in complete analogy to the role of public classical communication, that assistance by a symmetric-side channel makes equal the distillable entanglement, the recently-introduced mutual independence, and a generalization of the latter, which quantifies the extent to which one of the parties can perform quantum privacy amplification. Symmetric-side channels, and the closely related erasure channel, have been recently harnessed to provide examples of superactivation of the quantum channel capacity. Our findings give new insight into this non-additivity of the channel capacity and its relation to quantum privacy. In particular, we show that single-copy superactivation protocols with the erasure channel, which encompasses all examples of non-additivity of the quantum capacity found to date, can be understood as a conversion of mutual independence into distillable entanglement.

10 pages

References in corpus (11)

• Quantum entanglement
• Distillation of secret key and entanglement from quantum states
• On the quantum, classical and total amount of correlations in a quantum state
• Quantum Communication With Zero-Capacity Channels
• Quantum mutual information and the one-time pad
• The private capacity of quantum channels is not additive
• The quantum capacity with symmetric side channels
• Uncertainty, Monogamy, and Locking of Quantum Correlations
• Extensive nonadditivity of privacy
• For quantum information, two wrongs can make a right
• Can non-private channels transmit quantum information?

Cited by in corpus (5)

• A Survey on Quantum Channel Capacities
• Correlation measures and distillable entanglement in AdS/CFT
• Game-theoretic characterization of antidegradable channels
• Uncertainty Relation for Mutual Information
• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation