Superadditivity in Trade-Off Capacities of Quantum Channels

Elton Yechao Zhu, Quntao Zhuang, Min Hsiu Hsieh, Peter W. Shor

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


In this paper, we investigate the additivity phenomenon in the quantum dynamic capacity region of a quantum channel for trading the resources of classical communication, quantum communication, and entanglement. Understanding such an additivity property is important if we want to optimally use a quantum channel for general communication purposes. However, in a lot of cases, the channel one will be using only has an additive single or double resource capacity region, and it is largely unknown if this could lead to a strictly superadditive double or triple resource capacity region, respectively. For example, if a channel has additive classical and quantum capacities, can the classical-quantum capacity region be strictly superadditive? In this paper, we answer such questions affirmatively. We give proof-of-principle requirements for these channels to exist. In most cases, we can provide an explicit construction of these quantum channels. The existence of these superadditive phenomena is surprising in contrast to the result that the additivity of both classical-entanglement and classical-quantum capacity regions imply the additivity of the triple resource capacity region for a given channel.

Original languageEnglish (US)
Article number8585118
Pages (from-to)3973-3989
Number of pages17
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - Jun 2019
Externally publishedYes


  • Additivity
  • quantum channel capacity
  • quantum shannon theory
  • trade-off capacity regions

ASJC Scopus subject areas

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


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