%0 Journal Article
%T The Efficiency of Quantum Identity Testing of Multiple States
%A Masaru Kada
%A Harumichi Nishimura
%A Tomoyuki Yamakami
%J Mathematics
%D 2008
%I arXiv
%R 10.1088/1751-8113/41/39/395309
%X 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.
%U http://arxiv.org/abs/0809.2037v1