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  • Featured in Physics
  • Open Access

Classification of Joint Quantum Measurements Based on Entanglement Cost of Localization

Jef Pauwels, Alejandro Pozas-Kerstjens, Flavio Del Santo, and Nicolas Gisin

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Phys. Rev. X 15, 021013 – Published 14 April, 2025

DOI: https://doi.org/10.1103/PhysRevX.15.021013

Abstract

Despite their importance in quantum theory, joint quantum measurements remain poorly understood. An intriguing conceptual and practical question is whether joint quantum measurements on separated systems can be performed without bringing them together. Remarkably, by using shared entanglement, this can be achieved perfectly when disregarding the postmeasurement state. However, existing localization protocols typically require unbounded entanglement. In this work, we address the fundamental question: “Which joint measurements can be localized with a finite amount of entanglement?” We develop finite-resource versions of teleportation-based schemes and analytically classify all two-qubit measurements that can be localized in the first levels of the resulting hierarchies. These levels include several measurements with exceptional properties and symmetries, such as the Bell state measurement and the elegant joint measurement. This leads us to propose a systematic classification of joint measurements based on entanglement cost, which we argue directly connects with the complexity of implementing those measurements. We illustrate how to numerically explore higher levels and construct generalizations to higher dimensions and multipartite settings.

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Physics Subject Headings (PhySH)

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Entanglement as the Currency of Quantum Measurement

Published 14 April, 2025

A powerful framework allows scientists to understand and classify joint quantum measurements—procedures essential for many quantum technologies.

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Popular Summary

Quantum entanglement, where particles become so interconnected that the state of one affects the other instantaneously, has captivated physicists for decades and led to groundbreaking technologies such as quantum cryptography. While entanglement in quantum states is well studied, a related area—entanglement in measurements involving multiple particles—has not been explored as thoroughly. Here, we address this gap by investigating how joint quantum measurements can be performed without physically bringing the particles together.

It was already known that localizing a measurement (performing a multiparticle measurement without bringing the subsystems together) is always possible but typically requires infinite entanglement. We show that certain simple or symmetric measurements can be localized with a finite entanglement cost. By studying different types of measurements, we create a classification system that organizes them based on their entanglement requirements and complexity.

Advancing our understanding of quantum measurements is crucial for quantum network applications such as conference key agreement or randomness generation. Our work marks a significant step toward a systematic understanding of measurements in composite quantum systems.

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Phys. Rev. X 15, 021013– Published 14 April, 2025
  • Received 19 August 2024
  • Accepted 19 February 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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