Optimal quantum-programmable projective measurements with coherent states

TL;DR

This paper presents practical linear-optics schemes for programmable quantum measurements on coherent states, enabling efficient verification and improved quantum fingerprinting with minimal resources.

Contribution

It introduces three optimal, non-destructive programmable projective measurement schemes using only beam splitters and threshold detectors, extending to untrusted input states.

Findings

Three practical implementations for programmable measurements.

Efficient verification of untrusted sources with local coherent states.

Quadratic improvement in quantum fingerprinting protocols.

Abstract

We consider a device which can be programmed using coherent states of light to approximate a given projective measurement on an input coherent state. We provide and discuss three practical implementations of this programmable projective measurement device with linear optics, involving only balanced beam splitters and single photon threshold detectors. The three schemes optimally approximate any projective measurement onto a program coherent state in a non-destructive fashion. We further extend these to the case where there are no assumptions on the input state. In this setting, we show that our scheme enables an efficient verification of an unbounded untrusted source with only local coherent states, balanced beam splitters, and threshold detectors. Exploiting the link between programmable measurements and generalised swap test, we show as a direct application that our schemes provide an asymptotically quadratic improvement in existing quantum fingerprinting protocol to approximate the Euclidean distance between two unit vectors.