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

Masahiro Takeoka, Hari Krovi, Saikat Guha

研究成果: Conference contribution

2 被引用数 (Scopus)

抄録

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.

本文言語English
ホスト出版物のタイトル2013 IEEE International Symposium on Information Theory, ISIT 2013
ページ166-170
ページ数5
DOI
出版ステータスPublished - 2013
外部発表はい
イベント2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey
継続期間: 2013 7月 72013 7月 12

出版物シリーズ

名前IEEE International Symposium on Information Theory - Proceedings
ISSN(印刷版)2157-8095

Conference

Conference2013 IEEE International Symposium on Information Theory, ISIT 2013
国/地域Turkey
CityIstanbul
Period13/7/713/7/12

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 情報システム
  • モデリングとシミュレーション
  • 応用数学

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