Second-order coding rates for pure-loss bosonic channels

Mark M. Wilde, Joseph M. Renes, Saikat Guha

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


A pure-loss bosonic channel is a simple model for communication over free-space or fiber-optic links. More generally, phase-insensitive bosonic channels model other kinds of noise, such as thermalizing or amplifying processes. Recent work has established the classical capacity of all of these channels, and furthermore, it is now known that a strong converse theorem holds for the classical capacity of these channels under a particular photon-number constraint. The goal of the present paper is to initiate the study of second-order coding rates for these channels, by beginning with the simplest one, the pure-loss bosonic channel. In a second-order analysis of communication, one fixes the tolerable error probability and seeks to understand the back-off from capacity for a sufficiently large yet finite number of channel uses. We find a lower bound on the maximum achievable code size for the pure-loss bosonic channel, in terms of the known expression for its capacity and a quantity called channel dispersion. We accomplish this by proving a general “one-shot” coding theorem for channels with classical inputs and pure-state quantum outputs which reside in a separable Hilbert space. The theorem leads to an optimal second-order characterization when the channel output is finite-dimensional, and it remains an open question to determine whether the characterization is optimal for the pure-loss bosonic channel.

Original languageEnglish (US)
Pages (from-to)1289-1308
Number of pages20
JournalQuantum Information Processing
Issue number3
StatePublished - Mar 1 2016


  • Optical communication
  • Pure-loss bosonic channel
  • Second-order coding rates
  • Spectral entropy

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Statistical and Nonlinear Physics
  • Theoretical Computer Science
  • Signal Processing
  • Modeling and Simulation
  • Electrical and Electronic Engineering


Dive into the research topics of 'Second-order coding rates for pure-loss bosonic channels'. Together they form a unique fingerprint.

Cite this