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29 March 2024
 
  » arxiv » 0809.2037

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The Efficiency of Quantum Identity Testing of Multiple States
Masaru Kada ; Harumichi Nishimura ; Tomoyuki Yamakami ;
Date 11 Sep 2008
AbstractWe 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.
Source arXiv, 0809.2037
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