Fig. 2: EPR-assisted metrology with twin Fock states. | Nature Communications

Fig. 2: EPR-assisted metrology with twin Fock states.

From: Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox

Fig. 2

a We consider a twin Fock state with N = 200 particles, that is split into two parts with NA = NB = N/2, here represented by the Wigner function on the Bloch sphere. b The reduced state on either side is a mixture of Dicke states, resulting from tracing out the other half of the system. c The two subsystems show perfect correlations for both measurement settings Jx and Jz: When Alice measures \({J}_{z}^{{\rm{A}}}\) (\({J}_{x}^{{\rm{A}}}\)) and obtains the result kA, she steers Bob’s system into an eigenstate of \({J}_{z}^{{\rm{B}}}\) (\({J}_{x}^{{\rm{B}}}\)) with eigenvalue N/2 − kA. This can be used for assisted quantum metrology, and to reveal an EPR paradox. In the plot we show Bob’s sensitivity \({F}_{{\rm{Q}}}[{\rho }_{{k}_{{\rm{A}}}| {J}_{x}^{{\rm{A}}}}^{{\rm{B}}},{J}_{z}^{{\rm{B}}}]\) when Alice obtains the result kA from measuring \({J}_{x}^{{\rm{A}}}\) (blue line). Alice’s results are all equally probable with \(p({k}_{{\rm{A}}}| {J}_{x}^{{\rm{A}}})=2/(N+2)\). Bob’s average sensitivity \({F}_{{\rm{Q}}}^{{\rm{B}}| {\rm{A}}}[|{{\rm{SD}}}_{N,N/2}\rangle ,{J}_{z}^{{\rm{B}}}]\) coincides with the variance for the reduced state \(4{\rm{Var}}[{\rho }^{{\rm{B}}},{J}_{z}^{{\rm{B}}}]\) (yellow line), indicating that the measurement is optimal (Supplementary Note 4).

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