Description
In private distributed sensing, multiple parties aim to collectively estimate a global function of local parameters while retaining privacy of the individual parameters. We introduce a new protocol for distributed phase sensing using continuous-variable quantum states and measurements. We consider a multipartite network in which each node encodes a local phase into a shared entangled Gaussian state. We show that the average phase can be estimated with high precision, exhibiting Heisenberg scaling in the total photon number, while individual phases are inaccessible. Complete privacy is unattainable for finite squeezing but emerges in the large-squeezing limit. We investigate the impact of displacements and optical losses and study trade-offs between estimation accuracy and privacy.
