Sequential decoding of a general classical-quantum channel

Abstract

Since a quantum measurement generally disturbs the state of a quantum system, one might think that it should not be possible for a sender and receiver to communicate reliably when the receiver performs a large number of sequential measurements to determine the message of the sender. We show here that this intuition is not true, by demonstrating that a sequential decoding strategy works well even in the most general "one-shot" regime, where we are given a single instance of a channel and wish to determine the maximal number of bits that can be communicated up to a small failure probability. This result follows by generalizing a non-commutative union bound to apply for a sequence of general measurements. We also demonstrate two ways in which a receiver can recover a state close to the original state after it has been decoded by a sequence of measurements that each succeed with high probability. The second of these methods will be useful in realizing an efficient decoder for fully quantum polar codes, should a method ever be found to realize an efficient decoder for classical-quantum polar codes.

12 pages; accepted for publication in the Proceedings of the Royal Society A

References in corpus (7)

• Coding Theorem and Strong Converse for Quantum Channels
• The information-theoretic costs of simulating quantum measurements
• Generalized relative entropies and the capacity of classical-quantum channels
• Physical Underpinnings of Privacy
• Generalized Entropies
• Sequential projective measurements for channel decoding
• Quantum polar codes for arbitrary channels

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• Achieving the Holevo bound via a bisection decoding protocol
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• Union bound for quantum information processing
• On the near-optimality of one-shot classical communication over quantum channels
• Simple and Tighter Derivation of Achievability for Classical Communication over Quantum Channels
• Post-processing of quantum instruments
• Polar Codes for Arbitrary Classical-Quantum Channels and Arbitrary cq-MACs
• Variational Quantum Algorithms for Trace Distance and Fidelity Estimation
• A hypothesis testing approach for communication over entanglement assisted compound quantum channel
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