CVChannel.jl

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

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

1. Install Julia: https://julialang.org/downloads/
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.

This project optimizes the communication value of quantum channels using semidefinite programming via Convex.jl.

By default, CVChannel.jl uses SCS to solve semidefinite programs. SCS is an open-source numerical solver easily accessible through Julia.

If desired, MOSEK can be used instead. However, a MOSEK license is required and can be downloaded at https://www.mosek.com/products/academic-licenses/. The license is free for personal and institutional academic use and once downloaded, should be saved at $HOME/mosek/mosek.lic.

To cite this software please see CITATION.bib or .

It is recommended that you use Revise.jl so that your saved changes are reflected in the working codebase used by Julia. Please refer to the Revise.jl documentation for more details.

To open the CVChannel.jl package for development,

• Enter package mode from the Julia REPL by entering ].
• Run (@vx.x) pkg> develop --local .

This tells Julia to run code from the local version of the CVChannel.jl module rather than from the github repository. Thus, using CVChannel will load the local version that you are modifying.

To run a script:

• $ julia --proj=./script ./script/path/to/script.jl

Jupyter notebooks are found in the ./notebook directory and are written either with Python or Julia. If you are committing changes to a notebook, make sure you restart the kernel and run all cells before committing. To run or develop notebooks, perform the following steps:

1. Navigate to the ./notebook directory $ cd ./notebook
2. Run $ julia --project=. -e "using IJulia; notebook(dir=pwd())"

At this point, the Jupyter Notebook interface will launch in your default web browser and you can then edit, create, or run the project notebooks.

1. Create the CVChannel.jl-notebook Conda environment with $ conda env create -f python_environment.yml.
2. Activate the CVChannel.jl-notebook environment with $ conda activate CVChannel.jl-notebook.
3. Launch the Jupyter notebook server with $ jupyter-notebook.

At this point, the Jupyter Notebook interface will launch in your default web browser and you can then edit, create, or run the project notebooks.

All tests can be run in two ways:

• From the command prompt run $ julia --proj=./test --color=yes test/runtests.jl.
• From package mode run (@vx.x) pkg> test CVChannel.

To run a single test, you can either run the test from the command line like a script, or you can run it within your text editor.

Please refer to the Documenter.jl documentation for details on how to write and build Julia documentation.

To verify that content renders properly, you'll need to build the documentation locally by running the ./docs/make.jl script.

• $ julia --color=yes ./docs/make.jl

This will build the HTML for the docs webpage. To view the webpage, spawn a local http server: the constructed website in your browser by spawning a local http server.

1. Navigate to the ./docs/build/ directory.
2. Run $ python -m http.server --bind localhost
3. Then copy/paste the returned url into your web browser.

For this to work properly, the python command should run python version 3 or greater.

Project dependencies are listed in Project.toml. To load the project environment in the julia> REPL type ] to enter Pkg mode. Then run

• pkg> activate .

Each directory ./docs, ./test, ./script, and ./notebook has its own Project.toml which specifies the dependencies for the code in that directory These dependencies are independent from the CVChannel dependencies specified in ./Project.toml file in the root directory.

See Pkg.jl for details about how to add or update packages.