Compressively certifying quantum measurements

TL;DR

This paper presents a new compressive method for uniquely characterizing low-rank quantum measurements using minimal probe states, demonstrating efficiency and effectiveness through numerical and experimental results.

Contribution

It introduces a quantum measurement certification procedure that is more efficient than classical methods, requiring fewer probe states based on quantum constraints.

Findings

Minimal probe states scale linearly with system dimension

Numerical evidence shows fewer probe states needed than classical phase retrieval

Experimental results demonstrate significant compression for multi-qubit detectors

Abstract

We introduce a reliable compressive procedure to uniquely characterize any given low-rank quantum measurement using a minimal set of probe states that is based solely on data collected from the unknown measurement itself. The procedure is most compressive when the measurement constitutes pure detection outcomes, requiring only an informationally complete number of probe states that scales linearly with the system dimension. We argue and provide numerical evidence showing that the minimal number of probe states needed is even generally below the numbers known in the closely-related classical phase-retrieval problem because of the quantum constraint. We also present affirmative results with polarization experiments that illustrate significant compressive behaviors for both two- and four-qubit detectors just by using random product probe states.