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arXiv · 2006.15003

Truncated moment sequences and a solution to the channel separability problem

Nadia Milazzo·Daniel Braun·Olivier Giraud
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Abstract

We consider the problem of separability of quantum channels via the Choi matrix representation given by the Choi-Jamiołkowski isomorphism. We explore three classes of separability across different cuts between systems and ancillae and we provide a solution based on the mapping of the coordinates of the Choi state (in a fixed basis) to a truncated moment sequence (tms) $y$. This results in an algorithm which gives a separability certificate using semidefinite programming. The computational complexity and the performance of it depend on the number of variables $n$ in the tms and on the size of the moment matrix $M_t(y)$ of order $t$. We exploit the algorithm to numerically investigate separability of families of 2-qubit and single-qutrit channels; in the latter case we can provide an answer for examples explored earlier through the criterion based on the negativity $N$, a criterion which remains inconclusive for Choi matrices with $N=0$.

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Nadia Milazzo, Daniel Braun, Olivier Giraud. 2020-06-26. Truncated moment sequences and a solution to the channel separability problem. https://doi.org/10.1103/physreva.102.052406

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