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arXiv · 0809.2037

The Efficiency of Quantum Identity Testing of Multiple States

Masaru Kada·Harumichi Nishimura·Tomoyuki Yamakami
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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.

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Masaru Kada, Harumichi Nishimura, Tomoyuki Yamakami. 2008-09-11. The Efficiency of Quantum Identity Testing of Multiple States. https://doi.org/10.1088/1751-8113/41/39/395309

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