The Quantum Capacity of Channels With Arbitrarily Correlated Noise

• Published in: IEEE transactions on information theory Vol. 56; no. 3; pp. 1447 - 1460
• Main Authors: Buscemi, F., Datta, N.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Asymptotic properties; Capacity planning; Channel capacity; Channels; Communication channels; Correlation; Correlation analysis; Electric noise; entanglement transmission; Entropy; Exact sciences and technology; Hilbert space; information spectrum; Information theory; Information, signal and communications theory; Mathematical analysis; Noise; one-shot capacity; Optimization; Protocols; Quantum capacity; Quantum computing; Quantum entanglement; Quantum mechanics; Quantum theory; quasi-entropies; smooth Rényi entropies; Studies; Telecommunications and information theory; Teleportation; Quantum channel; one-shot capacity; Correlated noise; quasi-entropies; Entropy; entanglement transmission; information spectrum; Renyi theory; smooth Rényi entropies; Quantum capacity; Quantum communication
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2009.2039166

We study optimal rates for quantum communication over a single use of a channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. The corresponding capacity is often referred to as the one-shot quantum capacity. In this paper, we prove bounds on the one-shot quantum capacity of an arbitrary channel. This allows us to compute the quantum capacity of a channel with arbitrarily correlated noise, in the limit of asymptotically many uses of the channel. In the memoryless case, we explicitly show that our results reduce to known expressions for the quantum capacity.