Can non-private channels transmit quantum information?

Abstract

We study the power of quantum channels with little or no capacity for private communication. Because privacy is a necessary condition for quantum communication, one might expect that such channels would be of little use for transmitting quantum states. Nevertheless, we find strong evidence that there are pairs of such channels that, when used together, can transmit far more quantum information than the sum of their individual private capacities. Because quantum transmissions are necessarily private, this would imply a large violation of additivity for the private capacity. Specifically, we present channels which display either (1) A large joint quantum capacity but very small individual private capacities or (2) a severe violation of additivity for the Holevo information.

We both think so. 4 pages and 3 figures explain why

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Cited by in corpus (11)

• A Survey on Quantum Channel Capacities
• The private capacity of quantum channels is not additive
• Nonadditivity of quantum and classical capacities for entanglement breaking multiple-access channels and butterfly network
• Extensive nonadditivity of privacy
• Generic nonadditivity of quantum capacity in simple channels
• Public and private communication with a quantum channel and a secret key
• Maximal Privacy Without Coherence
• Public Quantum Communication and Superactivation
• Quantum superadditivity in linear optics networks: sending bits via multiple access Gaussian channels
• Non-convexity of private capacity and classical environment-assisted capacity of a quantum channel
• Activation of zero-error classical capacity in low-dimensional quantum systems