Measurement incompatibility under loss

TL;DR

This paper studies how pure loss affects measurement incompatibility in continuous-variable quantum systems, showing thresholds for compatibility, designing robust incompatible measurements, and confirming that quantum steering persists despite losses.

Contribution

It introduces loss thresholds for measurement compatibility, proposes feasible measurements that withstand high losses, and proves that some incompatibility always remains.

Findings

Loss channels below 1/n transmissivity make measurements compatible

A set of measurements remains incompatible even under extreme losses

Quantum steering persists despite pure loss effects

Abstract

We investigate the measurement incompatibility of continuous-variable systems with infinite-dimensional Hilbert spaces under the influence of pure losses, a fundamental noise source in quantum optics, and a significant challenge for long-distance quantum communication. We show that loss channels with transmissivities less than $1/n$ make any set of $n$ measurements compatible. Additionally, we design a set of measurements that remains incompatible even under extreme losses, where the number of measurements in the set increases with the amount of loss. These measurements rely on on-off photodetectors and linear optics, making them feasible for implementation under realistic laboratory conditions. Furthermore, we demonstrate that no loss channel can break the incompatibility of all measurements. As a result, quantum steering remains achievable in the presence of pure loss.