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 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.

Oct 30, 20190 citations

Multiparameter squeezing for optimal quantum enhancements in sensor networks

Manuel Gessner, Augusto Smerzi, Luca Pezzè

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.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.

arXiv:1910.14014Nature CommunicationsJul 30, 202088 citations

The quantum measurement problem enhanced

Gebhard Grübl

arXiv:quant-ph/0202101Physics Letters AAug 8, 20035 citations

Mitigating sloppiness with intermediate controls in sequential multiparameter spin interferometry

Hai Feng, Xinwei Li, Rong Lu +1 more

Multiparameter quantum sensing requires different parameters to produce distinguishable probe responses while allowing their information to be extracted simultaneously. In sequential sensing without intermediate control, two phases encoded through the same generator are locally indistinguishable. Here we show that parameter-independent intermediate controls overcome this limitation in a collective-spin interferometer by separating the corresponding effective generators in the probe covariance geometry. Specifically, a transverse collective rotation provides an analytically tractable realization, and intermediate one-axis twisting (OAT) generates additional nonlinear operator directions and a broad regime of enhanced joint estimation. For fixed total particle number $N$ and matched twisting resource, both marginal precision bounds lie below those of a separated-OAT strategy while measurement incompatibility remains weak. For intermediate OAT, conditional optimization of an upper bound on the Holevo cost yields asymptotic $N^{-2}$ scaling. For this protocol, a fixed rotated-Dicke measurement retains simultaneous two-parameter enhancement over a broad phase region. These results show that nonlinear intermediate control can mitigate sloppiness while preserving quantum-enhanced precision with a common readout.Multiparameter quantum sensing requires different parameters to produce distinguishable probe responses while allowing their information to be extracted simultaneously. In sequential sensing without intermediate control, two phases encoded through the same generator are locally indistinguishable. Here we show that parameter-independent intermediate controls overcome this limitation in a collective-spin interferometer by separating the corresponding effective generators in the probe covariance geometry. Specifically, a transverse collective rotation provides an analytically tractable realization, and intermediate one-axis twisting (OAT) generates additional nonlinear operator directions and a broad regime of enhanced joint estimation. For fixed total particle number $N$ and matched twisting resource, both marginal precision bounds lie below those of a separated-OAT strategy while measurement incompatibility remains weak. For intermediate OAT, conditional optimization of an upper bound on the Holevo cost yields asymptotic $N^{-2}$ scaling. For this protocol, a fixed rotated-Dicke measurement retains simultaneous two-parameter enhancement over a broad phase region. These results show that nonlinear intermediate control can mitigate sloppiness while preserving quantum-enhanced precision with a common readout.

quant-pharXiv:2611.01737Nov 3, 2026

Quantum Rotation and Spin

Otto C. W. Kong

Chinese Journal of PhysicsOct 1, 20260 citations

N

and matched twisting resource, both marginal precision bounds lie below those of a separated-OAT strategy while measurement incompatibility remains weak. For intermediate OAT, conditional optimization of an upper bound on the Holevo cost yields asymptotic

N^{-2}

scaling. For this protocol, a fixed rotated-Dicke measurement retains simultaneous two-parameter enhancement over a broad phase region. These results show that nonlinear intermediate control can mitigate sloppiness while preserving quantum-enhanced precision with a common readout.