Achieving the Holevo capacity of a pure state classical-quantum channel via unambiguous state discrimination

Masahiro Takeoka, Hari Krovi, Saikat Guha

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)


We prove that the ultimate channel capacity, the Holevo bound, for sending classical data on a quantum channel (the so-called classical-quantum, or cq channel) can be achieved for a pure-state cq channel by decoding codewords via a collective quantum measurement based on unambiguous state discrimination (USD). In cq communication theory, the channel decoder acts directly on the modulated codeword waveform in the quantum (viz., electromagnetic or optical) domain, and it is known that collective measurements on long codeword blocks are needed to attain the Holevo capacity, which is strictly larger than the Shannon capacity of the classical channel induced by any specific measurement choice on each channel use. The USD measurement based channel decoder we propose, can distinguish finite blocklength codeword quantum states unambiguously (i.e., an incorrect codeword is never chosen) provided one allows for a finite probability of obtaining an inconclusive (erasure) outcome. We show that the probability of the inconclusive outcome goes to zero for asymptotically long codewords whenever the code rate is below the Holevo bound. The USD channel decoder is an addition to a small list of other collective measurements known to achieve the Holevo capacity (such as, the square root measurement, the minimum probability of error measurement, the sequential decoding measurement, and the quantum successive cancellation decoder for the cq polar code). A structured optical receiver design is not known yet for any of these decoders. What makes the USD decoder special is that there is no classical analogue to truly unambiguous discrimination (say, of samples drawn from a set of probability distributions). Secondly, the erasures-only decoding of USD is likely to result in a better channel reliability function. Finally, the USD measurement seems more likely to lead naturally to a structured optical receiver design and implementation.

Original languageEnglish
Title of host publication2013 IEEE International Symposium on Information Theory, ISIT 2013
Number of pages5
Publication statusPublished - 2013
Externally publishedYes
Event2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey
Duration: 2013 Jul 72013 Jul 12

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095


Conference2013 IEEE International Symposium on Information Theory, ISIT 2013

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modelling and Simulation
  • Applied Mathematics


Dive into the research topics of 'Achieving the Holevo capacity of a pure state classical-quantum channel via unambiguous state discrimination'. Together they form a unique fingerprint.

Cite this