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arXiv:1008.0844 · International Conference on Quantum Information

General Cramér-Rao Bound for Parameter Estimation using Gaussian Multimode Quantum Resources

Olivier Pinel, Nicolas Treps, Claude Fabre, Julien Fade

Published Jan 1, 2011• 3 citations
arXivHTMLPDF

Abstract

Multimode Gaussian quantum light, which includes coherent light, but also all kinds of multimode squeezed and/or multipartite quadrature entangled states, is a very general and powerful quantum resource that is now currently produced in various laboratories in the world, and is successfully used in various applications to quantum information processing[1]. In contrast to non-classical states based on the manipulation of Fock states (such as the NOON states), such quantum light can be produced with very high values of the mean photon number N (up to 1016). It is therefore a very good candidate for quantum metrology purposes, i.e. to improve as much as possible the estimation of a parameter p that is encoded on the spatio-temporal variation of a light beam, as all the limits in parameter estimation scale with some inverse power of N.

DOI
10.1364/icqi.2011.qtuh1

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Multimode Gaussian quantum light, which includes coherent light, but also all kinds of multimode squeezed and/or multipartite quadrature entangled states, is a very general and powerful quantum resource that is now currently produced in various laboratories in the world, and is successfully used in various applications to quantum information processing[1]. In contrast to non-classical states based on the manipulation of Fock states (such as the NOON states), such quantum light can be produced with very high values of the mean photon number N (up to 1016). It is therefore a very good candidate for quantum metrology purposes, i.e. to improve as much as possible the estimation of a parameter p that is encoded on the spatio-temporal variation of a light beam, as all the limits in parameter estimation scale with some inverse power of N.
Multimode Gaussian quantum light, which includes coherent light, but also all kinds of multimode squeezed and/or multipartite quadrature entangled states, is a very general and powerful quantum resource that is now currently produced in various laboratories in the world, and is successfully used in various applications to quantum information processing. In contrast to non-classical states based on the manipulation of Fock states (such as the NOON states), such quantum light can be produced with very high values of the mean photon number N (up to 1016). It is therefore a very good candidate for quantum metrology purposes, i.e. to improve as much as possible the estimation of a parameter p that is encoded on the spatio-temporal variation of a light beam, as all the limits in parameter estimation scale with some inverse power of N.
Multimode Gaussian quantum light, which includes multimode squeezed and multipartite quadrature entangled light, is a very general and powerful quantum resource with promising applications in quantum information processing and metrology. In this paper, we determine the ultimate sensitivity in the estimation of any parameter when the information about this parameter is encoded in such light, irrespective of the information extraction protocol used in the estimation and of the quantity measured. In addition we show that an appropriate homodyne detection scheme allows us to reach the Quantum Cramer-Rao bound. We show that, for a given set of available quantum resources, the most economical way to maximize the sensitivity is to put the most squeezed state available in a well-defined light mode. This implies that it is not relevant to take advantage of the existence of squeezed fluctuations in other modes, nor of quantum correlations and entanglement between different modes. We finally apply these considerations to the problem of optimal phase shift estimation.
Multimode Gaussian quantum light, which includes multimode squeezed and multipartite quadrature entangled light, is a very general and powerful quantum resource with promising applications in quantum information processing and metrology. In this paper, we determine the ultimate sensitivity in the estimation of any parameter when the information about this parameter is encoded in such light when the mean photon number is large, irrespective of the information extraction protocol used in the estimation and of the measured observable. In addition, we show that an appropriate homodyne detection scheme allows us to reach this ultimate sensitivity. We show that, for a given set of available quantum resources, the most economical way to maximize the sensitivity is to put the most squeezed state available in a well-defined light mode. This implies that it is not possible to take advantage of the existence of squeezed fluctuations in other modes, nor of quantum correlations and entanglement between different modes.
Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote sensing, the parameter of interest is not only encoded in the quantum state of the field, but also in its spatio-temporal distribution, i.e. in its mode structure. In this mode-encoded parameter estimation setting, we derive an analytical expression for the quantum Fisher information valid for arbitrary multimode Gaussian fields. To illustrate the power of our approach, we apply our results to the estimation of the transverse displacement of a beam and to the temporal separation between two pulses. For these examples, we show how the estimation sensitivity can be enhanced by adding squeezing into specific modes.
Abstract Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote sensing, the parameter of interest is not only encoded in the quantum state of the field, but also in its spatio-temporal distribution, i.e. in its mode structure. In this mode-encoded parameter estimation setting, we derive an analytical expression for the quantum Fisher information valid for arbitrary multimode Gaussian fields. To illustrate the power of our approach, we apply our results to the estimation of the transverse displacement of a beam and to the temporal separation between two pulses. For these examples, we show how the estimation sensitivity can be enhanced by adding squeezing into specific modes.
We investigate the ultimate precision achievable in Gaussian quantum metrology. We derive general analytical expressions for the quantum Fisher information matrix and for the measurement compatibility condition, ensuring asymptotic saturability of the quantum Cram\'er-Rao bound, for the estimation of multiple parameters encoded in multimode Gaussian states. We then apply our results to the joint estimation of a phase shift and two parameters characterizing Gaussian phase covariant noise in optical interferometry. In such a scheme, we show that two-mode displaced squeezed input probes with optimally tuned squeezing and displacement fulfill the measurement compatibility condition and enable the simultaneous estimation of all three parameters, with an advantage over individual estimation schemes that quickly rises with increasing mean energy of the probes.