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Abstract: We propose a quantum algorithm for the purification of a generic mixed state$ ho$ of a $n$-qudit system by using an ancillary $n$-qudit system.
Thealgorithm is optimal in that i the number of ancillary qudits cannot bereduced, ii the number of parameters which determine the purification state$|\Psi>$ exactly equals the number of degrees of freedom of $ ho$, and iii$|\Psi>$ is easily determined from the density matrix $ ho$.
Moreover, weintroduce a quantum circuit in which the quantum gates are unitarytransformations acting on a $2n$-qudit system.
These transformations aredetermined by parameters that can be tuned to generate, once the ancillaryqudits are disregarded, any given mixed $n$-qudit state.

Author: Giuliano Benenti, Giuliano Strini

Source: https://arxiv.org/


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