Optimal phase estimation with photon-number difference measurement using twin-Fock states of light<xref rid="cpb_28_12_120303fn1" ref-type="fn">*</xref><fn id="cpb_28_12_120303fn1"><label>*</label><p>Project supported by the National Natural Science Foundation of China (Grant Nos. 91636108, 11775190, and 11774024), Science Foundation of Zhejiang Sci-Tech University, China (Grant No. 18062145-Y), Open Foundation of Key Laboratory of Optical Field Manipulation of Zhejiang Province, China (Grant No. ZJOFM-2019-002), and Science Challenge Project, China (Grant No. TZ2018003).</p></fn>

Optimal phase estimation with photon-number difference measurement using twin-Fock states of light**

Project supported by the National Natural Science Foundation of China (Grant Nos. 91636108, 11775190, and 11774024), Science Foundation of Zhejiang Sci-Tech University, China (Grant No. 18062145-Y), Open Foundation of Key Laboratory of Optical Field Manipulation of Zhejiang Province, China (Grant No. ZJOFM-2019-002), and Science Challenge Project, China (Grant No. TZ2018003).

Xu J H¹, Wang J Z¹, Chen A X¹, Li Y², Jin G R^{1, †}

For each given true value of the phase shift θ₀ ∈ (0, π/2), statistical average of Nσ (the solid circles) and its standard derivation (the bars), simulated by M = 20 replicas of N=5000 random numbers. Blue solid line is the CRB of the J^z measurement; and black dashed line is the CRB of the single-fringe measurement. The inset: statistical average of (θ₀ − θ_est) as a function of θ₀ and the standard derivation. Horizontal grid lines are the shot-noise limit 1/N and the ideal result of the QCRB 2/N(N+2) for N = 6. The vertical grid lines give θ0=arctan2/3 and arctan 2.