2008/09/08 by Masaru Kada, Harumichi Nishimura, Tomoyuki Yamakami · 1 citation
Computer Science · Physics and Astronomy · #Computability, Logic, AI Algorithms #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #quant-ph
paper · pdf · doi:10.1088/1751-8113/41/39/395309
published as J. Phys. A: Math. Theor. 41 (2008) 395309 · 13pages
openalex publication_date 2008/09/08 · arxiv created 2008/09/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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 the help of classical preprocessing, a single use of the circle test can approximate the permutation test efficiently for an arbitrary input size n .