Quantum Edge Detection

TL;DR

This paper develops an optimal quantum edge detection protocol for identifying boundaries of uniform quantum states in particle strings, using advanced mathematical techniques and analyzing its performance for long strings and mixed states.

Contribution

It introduces a novel quantum edge detection method with an asymptotically optimal protocol based on square root measurement, applicable to pure and mixed quantum states.

Findings

Success probability analyzed as string length increases

Square root measurement protocol proven asymptotically optimal

Applicable to detecting malfunctions in quantum devices

Abstract

This paper introduces quantum edge detection, aimed at locating boundaries of quantum domains where all particles share the same pure state. Focusing on the 1D scenario of a string of particles, we develop an optimal protocol for quantum edge detection, efficiently computing its success probability through Schur-Weyl duality and semidefinite programming techniques. We analyze the behavior of the success probability as a function of the string length and local dimension, with emphasis in the limit of long strings. We present a protocol based on square root measurement, which proves asymptotically optimal. Additionally, we explore a mixed quantum change point detection scenario where the state of particles transitions from known to unknown, which may find practical applications in detecting malfunctions in quantum devices