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arXiv · 1403.5720

Nonlocal and controlled unitary operators of Schmidt rank three

Lin Chen·Li Yu
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Abstract

Implementing nonlocal unitary operators is an important and hard question in quantum computing and cryptography. We show that any bipartite nonlocal unitary operator of Schmidt rank three on the $(d_A \times d_B)$-dimensional system is locally equivalent to a controlled unitary when $d_A$ is at most three. This operator can be locally implemented assisted by a maximally entangled state of Schmidt rank $r=\min\{d_A^2,d_B\}$. We further show that stochastic-equivalent nonlocal unitary operators are indeed locally equivalent, and propose a sufficient condition on which nonlocal and controlled unitary operators are locally equivalent. We also provide the solution to a special case of a conjecture on the ranks of multipartite quantum states.

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Lin Chen, Li Yu. 2014-06-23. Nonlocal and controlled unitary operators of Schmidt rank three. https://doi.org/10.1103/physreva.89.062326

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