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Physical Review A

States of the optimum Fisher measure of information for quantum interferometry

Vlasta Peřinová, A. Lukš, J. Křepelka

Published Jun 6, 2006• 3 citations
Publisher

Abstract

Fisher's measure of information is compared to the usual measure of sensitivity of the SU(2) and SU(1,1) interferometers. The states of optimum Fisher information measure and prescribed mean photon-number difference are defined, and the properties of these states are studied in the SU(2) interferometer.
DOI
10.1103/physreva.73.063807

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The SU(2) group is used in two different fields of quantum optics, the quantum polarization and quantum interferometry.Quantum degrees of polarization may be based on distances of a polarization state from the set of unpolarized states.The maximum polarization is achieved in the case where the state is pure and then the distribution of the photon-number sums is optimized.In quantum interferometry, the SU(2) intelligent states have also the property that the Fisher measure of information is equal to the inverse minimum detectable phase shift on the usual simplifying condition.Previously, the optimization of the Fisher information under a constraint was studied.Now, in the framework of constraint optimization, states similar to the SU(2) intelligent states are treated.
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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 NNN-photon component of the phase-matched coherent $\ensuremath{\bigotimes}$ 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 NNN-photon component, where the largest NNN 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 number n‾\overline{n}n in the input state, over 96% of the Heisenberg limit can be achieved with the number resolution larger than 5n‾5\overline{n}5n.
We theoretically derive the lower and upper bounds of quantum Fisher information (QFI) of an SU(1,1) interferometer whatever the input state chosen. According to the QFI, the crucial resource for quantum enhancement is shown to be large intramode correlations indicated by the Mandel QQQ parameter. The subtraction of photons from the squeezed vacuum state has the effect of increasing the average photon number of the new field state, as well as the intramode correlations. For example, for a coherent state $\ensuremath{\bigotimes}$ a squeezed vacuum state with a given fixed input mean number of photons as the input, if ppp photons are subtracted from the squeezed-vacuum state before inputting the SU(1,1) interferometer, the phase sensitivities can be improved due to the intramode-correlation increment.