Superadditivity of Quantum Channel Coding Rate with Finite Blocklength Joint Measurements

Hye Won Chung, Saikat Guha, Lizhong Zheng

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The maximum rate at which classical information can be reliably transmitted per use of a quantum channel strictly increases in general with N, the number of channel outputs that are detected jointly by the quantum joint-detection receiver (JDR). This phenomenon is known as superadditivity of the maximum achievable information rate over a quantum channel. We study this phenomenon for a pure-state classical-quantum channel and provide a lower bound on CN/N, the maximum information rate when the JDR is restricted to making joint measurements over no more than N quantum channel outputs, while allowing arbitrary classical error correction. We also show the appearance of a superadditivity phenomenon-of mathematical resemblance to the aforesaid problem-in the channel capacity of a classical discrete memoryless channel when a concatenated coding scheme is employed, and the inner decoder is forced to make hard decisions on N-length inner codewords. Using this correspondence, we develop a unifying framework for the above two notions of superadditivity, and show that for our lower bound to CN/N to be equal to a given fraction of the asymptotic capacity C of the respective channel, N must be proportional to V/C2, where V is the respective channel dispersion quantity.

Original languageEnglish (US)
Article number7529100
Pages (from-to)5938-5959
Number of pages22
JournalIEEE Transactions on Information Theory
Issue number10
StatePublished - Oct 2016


  • Concatenated codes
  • Holevo capacity
  • Pure-state classical input-quantum output (cq) channel
  • joint measurement
  • superadditivity of capacity

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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