Code accompanying the manuscript PRX Quantum 2, 010345 (2021) (arXiv:2002.06181).
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The code implements several of the measures considered in the manuscript, in particular the robustness of magic $\mathcal{R}$, the generalised robustness of magic $\Lambda^+$, and the dyadic negativity $\Lambda$. The functions take two arguments: one is the density matrix rho, and one is a list of pure stabiliser states in the given dimension, given as a matrix T whose columns are the state vectors. The T matrices for 1-4 qubits (expressed in the computational basis) are provided above. Each function returns the value of the measure as well as the optimal decomposition (as a k-dimensional vector in the case of the robustness measures or a kxk-dimensional matrix in the case of the dyadic negativity, where k is the number of stabiliser states in the given dimension). The implementation requires CVX.
function [cvx_optval, x] = RobMag(rho, T)
k = size(T,2);
cvx_begin quiet
variable x(k)
rho == T*diag(x)*T'
minimize norm(x,1)
cvx_end
end
function [cvx_optval, x] = RobMagG(rho, T)
k = size(T,2);
cvx_begin sdp quiet
variable x(k) nonnegative
rho <= T*diag(x)*T'
minimize sum(x)
cvx_end
end
function [cvx_optval, X] = Lambda(rho, T)
k = size(T,2);
cvx_begin quiet
variable X(k,k) complex
rho == T*X*T'
minimize sum(sum(abs(X)))
cvx_end
end