Optimal purification of a generic n-qudit state

Details Optimal purification of a generic n-qudit state Optimal purification of a generic n-qudit state

2008-10-08

arxiv.org/abs/0810.1417v2

PhysRevA.79, 052301 (2009)

Physics

Quantum Physics

8 pages, 9 figures, remarks added

Scientific paper

10.1103/PhysRevA.79.052301

We propose a quantum algorithm for the purification of a generic mixed state $\rho$ 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 $|\Psi>$ exactly equals the number of degrees of freedom of $\rho$, and (iii) $|\Psi>$ is easily determined from the density matrix $\rho$. 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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