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arXiv · 0810.1417

Optimal purification of a generic n-qudit state

Giuliano Benenti·Giuliano Strini
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Abstract

We propose a quantum algorithm for the purification of a generic mixed state $ρ$ of a $n$-qudit system by using an ancillary $n$-qudit system. The algorithm is optimal in that (i) the number of ancillary qudits cannot be reduced, (ii) the number of parameters which determine the purification state $|Ψ>$ exactly equals the number of degrees of freedom of $ρ$, and (iii) $|Ψ>$ is easily determined from the density matrix $ρ$. Moreover, we introduce a quantum circuit in which the quantum gates are unitary transformations acting on a $2n$-qudit system. These transformations are determined by parameters that can be tuned to generate, once the ancillary qudits are disregarded, any given mixed $n$-qudit state.

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Giuliano Benenti, Giuliano Strini. 2009-01-13. Optimal purification of a generic n-qudit state. https://doi.org/10.1103/physreva.79.052301

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