Experimental realization and self-testing of semisymmetric informationally complete measurements via a one-dimensional photonic quantum walk

TL;DR

This paper experimentally implements and self-tests semisymmetric informationally complete measurements using a one-dimensional photonic quantum walk, advancing quantum certification techniques with generalized measurements.

Contribution

It demonstrates the first experimental realization and self-testing of semi-SIC POVMs via a photonic quantum walk, expanding quantum measurement capabilities.

Findings

Successful experimental realization of semi-SIC POVMs

Self-testing of semi-SIC POVMs in a semi-device-independent manner

Paves the way for quantum certification with generalized measurements

Abstract

Generalized quantum measurements play a crucial role in quantum mechanics, and symmetric informationally complete positive operator-valued measurements (SIC POVMs) provide a powerful and flexible framework for extracting information from quantum systems. However, the existence of SIC-POVMs in every finite dimension remains an open question, which has stimulated extensive research into alternative classes of POVMs. Recently, Geng $et$ $al$. [Phys. Rev. Lett. 126, 100401 (2021)] proposed a broader class of SIC POVM, called semisymmetric informationally complete POVM (semi-SIC POVM), which extends beyond SIC POVM. In this work, we focus on the four-outcome POVMs and experimentally realize the semi-SIC POVMs using a one-dimensional discrete-time quantum walk. Additionally, employing single photons and linear optics, we perform an experimental self-testing of semi-SIC POVMs in the semi-device-independent manner. Our results pave the way for exploring quantum certification with generalized quantum measurements.