Fig. 3: 2-LUI-RE Protocol with Independent Encodings.
From: Informationally complete distributed metrology without a shared reference frame
Two copies of the GHZ state (ρ0) are shared by separated sites in a network, and then each site applies reversed-encoding on two on-hand photons with opposing encoding Θi and \({\Theta }_{i}^{{{\dagger}} }\), forming two reversely encoded network states \({\rho }_{\overrightarrow{{{{\boldsymbol{\theta }}}}}}\) and \({\rho }_{-\overrightarrow{{{{\boldsymbol{\theta }}}}}}\). Afterward, each site performs local randomized rotations \(\widehat{U}{=\bigotimes }_{i=1}^{N}{\widehat{U}}_{i}\) to the two photons to generate the LUI state \({\widetilde{\rho }}_{\overrightarrow{{{{\boldsymbol{\theta }}}}}}\). The averaged parameter \(\overline{\theta }=\frac{1}{N}{\sum }_{i=1}^{N}{\theta }_{i}\) can be estimated through a specific measurement strategy geared toward \({\widetilde{\rho }}_{\overrightarrow{{{{\boldsymbol{\theta }}}}}}\).
