Abstract
We find and investigate the optimal scheme of quantum distributed Gaussian sensing for estimation of the average of independent phase shifts. We show that the ultimate sensitivity is achievable by using an entangled symmetric Gaussian state, which can be generated using a single-mode squeezed vacuum state, a beam-splitter network, and homodyne detection on each output mode in the absence of photon loss. Interestingly, the maximal entanglement of a symmetric Gaussian state is not optimal although the presence of entanglement is advantageous as compared to the case using a product symmetric Gaussian state. It is also demonstrated that when loss occurs, homodyne detection and other types of Gaussian measurements compete for better sensitivity, depending on the amount of loss and properties of a probe state. None of them provide the ultimate sensitivity, indicating that non-Gaussian measurements are required for optimality in lossy cases. Our general results obtained through a full-analytical investigation will offer important perspectives to the future theoretical and experimental study for quantum distributed Gaussian sensing.
Highlights
Quantum resources are known to be useful for further enhancing the precision and the sensitivity of estimation of various physical quantities beyond the standard quantum limit [1,2,3,4,5]
We have investigated the ultimate sensitivity of the average phase estimation in distributed quantum sensing using
Homodyne detection ceases to be optimal, but non-Gaussian measurement would be required for achieving the ultimate sensitivity
Summary
Quantum resources are known to be useful for further enhancing the precision and the sensitivity of estimation of various physical quantities beyond the standard quantum limit [1,2,3,4,5]. The advantage of exploiting quantum entanglement becomes more significant when sensing takes place in different locations and the parameter of interest is a global feature of the network, e.g., the average of distributed independent phases [13,14,15,16,17,18]. Such distributed sensing is related to applications such as global clock synchronization [19] and phase imaging [8] These inspire the use of more practical quantum resources that are feasible in a well-controlled manner with current technology, e.g., Gaussian systems [20].
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