Fisher information of a squeezed-state interferometer with a finite photon-number resolution

Abstract

Squeezed-state interferometry plays an important role in quantum-enhanced optical phase estimation, as it allows the estimation precision to be improved up to the Heisenberg limit by using ideal photon-number-resolving detectors at the output ports. Here we show that for each individual N-photon component of the phase-matched coherent ⊗ squeezed vacuum input state, the classical Fisher information always saturates the quantum Fisher information. Moreover, the total Fisher information is the sum of the contributions from each individual Nphoton components, where the largest N is limited by the finite number resolution of available photon counters. Based on this observation, we provide an approximate analytical formula that quantifies the amount of lost information due to the finite photon number resolution, e.g., given the mean photon numbern in the input state, over 96 percent of the Heisenberg limit can be achieved with the number resolution larger than 5n.

Nonlinear phase estimation: Parity measurement approaches the quantum Cramér-Rao bound for coherent states

“…In order to simplify the calculation, we adopt numerical approach by terminating the sum at a sufficiently large total probability. By analyzing available quantum Fisher information rooting in the (n + m )photon weight in the input [43], we configure the truncated upper limit adhering to…”

Maximal quantum Fisher information for phase estimation without initial parity

“…1. Since Caves found the effects of vacuum fluctuation to the phase accuracy in Mach-Zehnder interferometers [25], various types of input states have been discussed, including squeezed state [25][26][27][28], NOON state [29][30][31], entangled coherent state [32][33][34][35][36][37][38], BAT state [39], and number squeezed state [40].…”

Data processing over single-port homodyne detection to realize superresolution and supersensitivity

“…To enlarge available information about the phase shift θ, the field amplitudes are chosen as α 0 ∈ R and ξ 0 = −r ∈ R (i.e., arg α 0 = 0 and arg ξ 0 = π); See Refs. [26][27][28] and also the Appendix. The total number of photons injected from the two input ports is given by n = α 2 0 + sinh 2 r. Furthermore, the Wigner function of the input state is given by [29]…”