The Efficiency of Quantum Identity Testing of Multiple States
Quantum Physics
2009-11-13 v1
Abstract
We examine two quantum operations, the Permutation Test and the Circle Test, which test the identity of n quantum states. These operations naturally extend the well-studied Swap Test on two quantum states. We first show the optimality of the Permutation Test for any input size n as well as the optimality of the Circle Test for three input states. In particular, when n=3, we present a semi-classical protocol, incorporated with the Swap Test, which approximates the Circle Test efficiently. Furthermore, we show that, with help of classical preprocessing, a single use of the Circle Test can approximate the Permutation Test efficiently for an arbitrary input size n.
Keywords
Cite
@article{arxiv.0809.2037,
title = {The Efficiency of Quantum Identity Testing of Multiple States},
author = {Masaru Kada and Harumichi Nishimura and Tomoyuki Yamakami},
journal= {arXiv preprint arXiv:0809.2037},
year = {2009}
}
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13pages