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arXiv · 2411.05920

Measurement incompatibility under loss

Mohammad Mehboudi·Fatemeh Rezaeinia·Saleh Rahimi-Keshari
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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.

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Mohammad Mehboudi, Fatemeh Rezaeinia, Saleh Rahimi-Keshari. 2024-11-08. Measurement incompatibility under loss. https://arxiv.org/abs/2411.05920

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