Probabilistic Distillation of Quantum Coherence

August 15, 2018

Codes MATLAB

For any given quantum state $\rho$, target state dimension $m$ and error tolerance $\varepsilon$, the maximal success probability of distillation under MIO or DIO is given by the optimal value of the following SDP:

% package requirement: [CVX](http://cvxr.com/cvx/)
% input state rho with dimension d by d
% target state dimension m
% error tolerance epsilon, e
% the maximal sucess probability under MIO, pMIO
% the maximal sucess probability under DIO, pDIO

cvx_begin sdp quiet
    variable G(d,d)
    variable C(d,d)
    pMIO = trace(G*rho);
    maximize pMIO
    subject to
        diag(G) == m*diag(C);
        0 <= C <= G <= eye(d);
        trace(C*rho) >= (1-e)*trace(G*rho);
cvx_end

cvx_begin sdp quiet
    variable G(d,d)
    variable C(d,d)
    pDIO = trace(G*rho);
    maximize pDIO
    subject to
        diag(G) == m*diag(C);
        0 <= C <= G <= eye(d);
        trace(C*rho) >= (1-e)*trace(G*rho);
        G == diag(diag(G));
cvx_end

The MATLAB file can be downloaded at here.