QRLab

QRLab is a MATLAB toolbox for exploring quantum information processing and quantum resource theory.

Features

• Entanglement Theory:

  • Static Entanglement Measure: Tempered Logarithmic Negativity $E_{ \mathrm{\tau}}$, Rains Bound $R$, MaxRainsEntropy $R_{ \mathrm{max}}$, Logarithmic Negativity $E_\text{N}$, $E_{ \mathrm{PPT}}$, $E_ \mathrm{eta}$

  • Dynamic Entanglement Measure: Max Logarithmic Negativity, Max Rains information

  • Quantum Capacity

• Coherence Theory:

  • Static Coherence Measure: Robustness of Coherence

  • Channel Simulation: Simulating non-free operations via resource states

• Magic Theory:

  • Static Magic Measure: Robustness of Magic (qubit), Magic Mana (qudit), max/min Thuama (qudit)

  • Representative Magic State Generation

• Quasi-Theory:

  • Probabilistic error cancelation

  • Observable dependent probabilistic error cancellation

  • Observable dependent deterministic error cancelation

  • Circuit Knitting

  • Virtual Recovery

• Supermap:

  • Quantum Switch (both kraus and choi), Apply Quantum Switch
  • Link Product

• Seesaw Algorithms: Algorithms for providing sub-optimal solutions for non-linear optimization problems.

  • CHSH game

  • LOCC protocol

• Extra Functions:

  • Conditional quantum mutual information

• API Documents:

  • API documents can be found in this website https://quair.github.io/QRLab/api/.

Requirements

1. QETLAB == 0.9
2. CVX == 2.1

Installation

1. Clone QRLab to your local machine.
2. Download QETLAB 0.9. You could download it from https://qetlab.com/.
3. Add QRLab and QETLAB to MATLAB's path​, through command

addpath(genpath('...\QETLAB-0.9'));
addpath(genpath('...\QRlab'));

4. Download and install CVX 2.1. You could download it from https://cvxr.com/cvx/. Install CVX on Windows

cd yourpath\cvx;​
cvx_setup;

Install CVX on Linux or a Mac

cd ~/MATLAB/cvx;​
cvx_setup;

5. To fully unlock the magic qubit related functions, it is necessary to install channel_magic 2.0 in https://github.com/jamesrseddon/channel_magic.

Getting Started: Use Cases

To use the package, simply call the function you need with appropriate parameters. For example:

% To calculate the logarithmic negativity for a given state
rho = MaxEntangled(2) * MaxEntangled(2)'; % Define a quantum state
LN = LogNeg(rho);
disp('Logarithmic Negativity:');
disp(LN);

More functions are coming.

Contributing

Contributions to expand and improve this package are welcome.

Acknowledgement

We acknowledge the use of the CVXQUAD package, a tool for MATLAB-based convex optimization. This package offers several essential functions, such as calculating the von Neumann entropy and quantum relative entropy, which have been invaluable to our research.