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Beyond the Swap Test: Optimal Estimation of Quantum State Overlap.

M Fanizza¹, M Rosati², M Skotiniotis²

¹NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy.

Physical Review Letters

|February 29, 2020

Summary

This study introduces a more precise method for estimating quantum state overlap using collective measurements, outperforming the traditional swap test, especially for small overlaps in high-dimensional systems.

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Area of Science:

Quantum Information Science
Quantum Metrology
Quantum State Estimation

Background:

Estimating the overlap between unknown quantum states is crucial for quantum information processing.
The conventional method uses N swap tests, a joint measurement on one copy of each state.

Purpose of the Study:

To develop a more precise estimation strategy for quantum state overlap.
To compare the efficiency of new methods against the standard swap test.

Main Methods:

Derivation of optimal measurement statistics for collective measurements on multiple copies of quantum states.
Computation of optimal mean squared error in asymptotic pointwise and finite Bayesian settings.
Analysis of state estimation strategies and their performance relative to the swap test.

Main Results:

Collective measurements yield more precise overlap estimates than individual swap tests.
New strategies outperform the swap test, particularly for small overlap values.
Optimal measurements are less invasive than the swap test and show robustness to depolarizing noise.

Conclusions:

General collective measurements offer a superior approach to quantum state overlap estimation.
The findings have implications for improving quantum information processing tasks and understanding measurement invasiveness.