Abstract
A distributed sensing protocol uses a network of local sensing nodes to estimate a global feature of the network, such as a weighted average of locally detectable parameters. In the noiseless case, continuous-variable (CV) multipartite entanglement shared by the nodes can improve the precision of parameter estimation relative to the precision attainable by a network without shared entanglement; for an entangled protocol, the root mean square estimation error scales like 1/M with the number M of sensing nodes, the so-called Heisenberg scaling, while for protocols without entanglement, the error scales like . However, in the presence of loss and other noise sources, although multipartite entanglement still has some advantages for sensing displacements and phases, the scaling of the precision with M is less favorable. In this paper, we show that using CV error correction codes can enhance the robustness of sensing protocols against imperfections and reinstate Heisenberg scaling up to moderate values of M. Furthermore, while previous distributed sensing protocols could measure only a single quadrature, we construct a protocol in which both quadratures can be sensed simultaneously. Our work demonstrates the value of CV error correction codes in realistic sensing scenarios.
Highlights
We show that using CV error correction codes can enhance the robustness of sensing protocols against imperfections and reinstate Heisenberg scaling up to moderate values of M
In the absence of entanglement, the rms estimation error always obeys the standard quantum limit (SQL) scaling of μ1 M, as dictated by the law of large numbers. This separation between Heisenberg and SQL scaling has been generalized to the scenario of distributed sensing, where an array of sensors aims to sense a global feature, such as a weighted average, of some local parameters detected by different sensor nodes [29,30,31,32,33]
CV error correction codes such as GKP-stabilizer codes may be used to enhance the reliability of any protocol that makes use of CV quantum information
Summary
In the absence of entanglement, the rms estimation error always obeys the standard quantum limit (SQL) scaling of μ1 M , as dictated by the law of large numbers This separation between Heisenberg and SQL scaling has been generalized to the scenario of distributed sensing, where an array of sensors aims to sense a global feature, such as a weighted average, of some local parameters detected by different sensor nodes [29,30,31,32,33]. For applications like radio-frequency (RF) sensing or bio-sensing, the sensing process on each spatially distributed sensing node is modeled as a quantum channel In such a distributedchannel parameter estimation scenario, the distribution loss is a major source of imperfection; we propose to use CV error correction to mitigate this loss.
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