Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement

Quntao Zhuang, Elton Yechao Zhu, Peter W. Shor

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We give a capacity formula for the classical information transmission over a noisy quantum channel, with separable encoding by the sender and limited resources provided by the receiver's preshared ancilla. Instead of a pure state, we consider the signal-ancilla pair in a mixed state, purified by a "witness." Thus, the signal-witness correlation limits the resource available from the signal-ancilla correlation. Our formula characterizes the utility of different forms of resources, including noisy or limited entanglement assistance, for classical communication. With separable encoding, the sender's signals across multiple channel uses are still allowed to be entangled, yet our capacity formula is additive. In particular, for generalized covariant channels, our capacity formula has a simple closed form. Moreover, our additive capacity formula upper bounds the general coherent attack's information gain in various two-way quantum key distribution protocols. For Gaussian protocols, the additivity of the formula indicates that the collective Gaussian attack is the most powerful.

Original languageEnglish (US)
Article number200503
JournalPhysical review letters
Issue number20
StatePublished - May 19 2017
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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