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Metrological Multiparameter Squeezing

Manuel Gessner, Augusto Smerzi, Luca Pezzè

Published Oct 30, 2019• 0 citations
OpenAlex

Abstract

Squeezing currently represents the leading strategy to obtain quantum enhancements for precision measurements of single parameters in a variety of continuous- and discrete-variable settings. However, many important physical problems including imaging and field sensing require the simultaneous measurement of multiple unknown parameters. Here, we derive a general, operational concept of multiparameter squeezing from the sensitivity matrix of quantum metrology. Our formalism identifies metrologically useful multiparameter squeezing of arbitrary observables and systems. We provide an analytical solution to the optimization over the measurement observables and the phase-imprinting Hamiltonians to maximize sensitivity. When applied to spin- or continuous-variable systems, our results generalize widely-used concepts of spin- or quadrature squeezing parameters. The squeezing matrix provides a practical and versatile tool for the development of quantum-enhanced multiparameter measurements and the efficient characterization of multimode quantum states.

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Squeezing currently represents the leading strategy to obtain quantum enhancements for precision measurements of single parameters in a variety of continuous- and discrete-variable settings. However, many important physical problems including imaging and field sensing require the simultaneous measurement of multiple unknown parameters. Here, we derive a general, operational concept of multiparameter squeezing from the sensitivity matrix of quantum metrology. Our formalism identifies metrologically useful multiparameter squeezing of arbitrary observables and systems. We provide an analytical solution to the optimization over the measurement observables and the phase-imprinting Hamiltonians to maximize sensitivity. When applied to spin- or continuous-variable systems, our results generalize widely-used concepts of spin- or quadrature squeezing parameters. The squeezing matrix provides a practical and versatile tool for the development of quantum-enhanced multiparameter measurements and the efficient characterization of multimode quantum states.
Squeezing currently represents the leading strategy for quantum enhanced precision measurements of a single parameter in a variety of continuous- and discrete-variable settings and technological applications. However, many important physical problems including imaging and field sensing require the simultaneous measurement of multiple unknown parameters. The development of multiparameter quantum metrology is yet hindered by the intrinsic difficulty in finding saturable sensitivity bounds and feasible estimation strategies. Here, we derive the general operational concept of multiparameter squeezing, identifying metrologically useful states and optimal estimation strategies. When applied to spin- or continuous-variable systems, our results generalize widely-used spin- or quadrature-squeezing parameters. Multiparameter squeezing provides a practical and versatile concept that paves the way to the development of quantum-enhanced estimation of multiple phases, gradients, and fields, and for the efficient characterization of multimode quantum states in atomic and optical sensor networks.
The well-known metrological linear squeezing parameters (such as quadrature or spin squeezing) efficiently quantify the sensitivity of Gaussian states. Yet, these parameters are insufficient to characterize the much wider class of highly sensitive non-Gaussian states. Here, we introduce a class of metrological nonlinear squeezing parameters obtained by analytical optimization of measurement observables among a given set of accessible (possibly nonlinear) operators. This allows for the metrological characterization of non-Gaussian quantum states of discrete and continuous variables. Our results lead to optimized and experimentally feasible recipes for a high-precision moment-based estimation of a phase parameter and can be used to systematically construct multipartite entanglement and nonclassicality witnesses for complex quantum states.
Abstract We identify the multiparameter sensitivity of entangled spin states, such as spin-squeezed and Dicke states that are spatially distributed into several addressable spatial modes. Analytical expressions for the spin-squeezing matrix of families of states that are accessible by current atomic experiments reveal the quantum gain in multiparameter metrology, as well as the optimal strategies to maximize the sensitivity gain for the estimation of any linear combination of parameters. We further study the mode entanglement of these states by deriving a witness for genuine k-partite mode entanglement from the spin-squeezing matrix. Our results highlight the advantage of mode entanglement for distributed sensing, and outline optimal protocols for multiparameter estimation with nonclassical spatially-distributed spin ensembles. We illustrate our findings with the design of a protocol for gradient sensing with a Bose–Einstein condensate in an entangled spin state in two 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.
We present an innovative, platform-independent concept for multiparameter sensing where the measurable parameters are in series, or cascaded, enabling measurements as a function of position. With temporally resolved detection, we show that squeezing can give a quantum enhancement in sensitivity over that of classical states by a factor of e2r{e}^{2r}e2r, where $r\ensuremath{\approx}1$ is the squeezing parameter. As an example, we have modeled an interferometer that senses multiple phase shifts along the same path, demonstrating a maximal quantum advantage by combining a coherent state with squeezed vacuum. Further classical modeling with up to 100 phases shows linear scaling potential for adding nodes to the sensor. The approach can be applied to remote sensing, geophysical surveying, and infrastructure monitoring.
We present a framework for simultaneously estimating all four real parameters of a general two-channel unitary U(2)\mathrm{U}(2)U(2) with Heisenberg-scaling precision. We derive analytical expressions for the quantum Fisher information matrix and show that all parameters attain the 1/N1/N1/N scaling in the precision by using experimentally feasible Gaussian probes, such as two-mode squeezed states or two single-mode squeezed states. Our results extend multiparameter metrology to its most general two-mode setting and establish concrete design principles for experimental implementations of Heisenberg-scaling, multiparameter optical interferometry with experimentally feasible resources. It not only sheds light on the fundamental interface between quantum interference of squeezed light and quantum metrological advantage in multiparameter estimation, but it also provides an important stepping stone towards the development of a wide range of quantum technologies based on distributed quantum metrology in arbitrary optical networks.