This Julia package and numerical analysis support the findings in The Communication Value of a Quantum Channel.


A numerics library for evaluating the communication value of a quantum channel.

The communication value (CV) quantifies the performance of single-copy classical communication.


  • Convex optimization methods for certifying the communication value of a quantum channel.
  • Tools for certifying the non-multiplicativity of the communication value for quantum channels.


  • A formal introduction to the communication value is found in the CV Background section.
  • Documentation for our optimization methods is found in the CV Optimizations section.
  • Documentation for our multiplicativity analysis tools are found in the CV Multiplicativity section.
  • Supporting methods are found in the Utilities section.

Quick Start

  1. Install Julia:
  2. Add the CVChannel.jl package from the Julia command prompt:
julia> using Pkg; Pkg.add("CVChannel")

To import the CVChannel.jl, run using CVChannel in the desired Julia file or workspace.

Numerical Analysis

The numerical analysis in this work investigates (non-)multiplicativity of the communication value over a wide range of quantum channels.


This project uses scripts to verify and investigate the (non-)multiplicativity of different quantum channels. Scripts are found in the ./script directory and are categorized into two directories as:

Instructions for running scripts can be found in the


Our analysis uses Jupyter notebooks for figures and demonstrations. Jupyter notebooks are found in the ./notebook directory. Notebooks are most conveniently viewed on github, however, instructions for running notebooks are found in


To cite this software please see CITATION.bib or Zenodo.


If you are interested in contributing to this software, please reach out to the authors. Development instructions are found in the


CVChannel.jl is released under the MIT License.


Development of CVChannel.jl was made possible by the advisory of Eric Chitambar and support from the Electrical and Computer Engineering and Physics departments at the University of Illinois at Urbana-Champaign.


This project is funded by NSF Award # 2016136.