Distributed quantum sensing using continuous-variable multipartite entanglement

Abstract

Distributed quantum sensing uses quantum correlations between multiple sensors to enhance the measurement of unknown parameters beyond the limits of unentangled systems. We describe a sensing scheme that uses continuous-variable multipartite entanglement to enhance distributed sensing of field-quadrature displacement. By dividing a squeezed-vacuum state between multiple homodyne-sensor nodes using a lossless beam-splitter array, we obtain a root-mean-square (rms) estimation error that scales inversely with the number of nodes (Heisenberg scaling), whereas the rms error of a distributed sensor that does not exploit entanglement is inversely proportional to the square root of the number of nodes (standard quantum limit scaling). Our sensor's scaling advantage is destroyed by loss, but it nevertheless retains an rms-error advantage in settings in which there is moderate loss. Our distributed sensing scheme can be used to calibrate continuous-variable quantum key distribution networks, to perform multiple-sensor cold-atom temperature measurements, and to do distributed interferometric phase sensing.

Distributed quantum sensing enhanced by continuous-variable error correction

“…As shown in figure 1, the original distributed sensing protocol [31] {ˆ}. This is because for sensing applications like bio-sensing one wants to minimize the light power shining on the fragile samples to avoid any damage.…”

“…In principle, one can introduce extra ancilla modes; however, this is not necessary in the lossless case-one can show that each scheme is optimal in its own class, given the total mean photon number constraint. In the lossy case, the optimal protocol is still an open question, but [31,36] were able to show that the scheme in figure 1 maximizes the Fisher information among Gaussian states and achieves the best precision when homodyne measurement is applied. Recently [53] proved that this scheme is also the optimal Gaussian protocol for distributed phase sensing.…”

“…We set the beasmplitters such that The optimal separable-state scheme, for the scenario under consideration here, employs a product state, but its precision da h C does not have a closed solution in general. For the simple case of η m =η, w m =1/M, we have [31] da…”

“…The original distributed sensing protocol [31] only estimates displacements on a single quadrature. Because a GKP grid state enables the precise measurement of both quadratures [47,64] when the displacements are small, we hope to utilize GKP grid states to extend the distributed sensing protocol to estimate complex-valued displacements.…”

“…In contrast, in the absence of entanglement, the rms estimation error always obeys the standard quantum limit (SQL) scaling of µ M 1 , as dictated by the law of large numbers. More recently, 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]. In particular, [31] proposed a protocol to use continuous variable (CV) multi-partite entanglement to enhance the distributed sensing of displacements and phases, which led to the first experimental demonstration [34] of sensing advantage enabled by multi-partite entanglement.Despite being more robust against loss than their discrete variable (DV) cousins, the performance enhancement in CV distributed sensing protocols still decays in the presence of loss and noise [35].…”