The Efficiency of Quantum Identity Testing of Multiple States

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.

13pages

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• Quantum fingerprinting
• Universal Quantum Estimator
• Direct estimations of linear and non-linear functionals of a quantum state
• Quantum Circuits with Mixed States
• Single-qubit optical quantum fingerprinting
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• On the Power of Quantum Distributed Proofs
• Topological state permutations in time-modulated non-Hermitian multiqubit systems with suppressed non-adiabatic transitions
• Symmetric functions of qubits in an unknown basis
• Preparing low-variance states using a distributed quantum algorithm