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Quantum Information and Measurement (QIM)

Sensitivity Limits for Multiparameter Quantum Metrology

Manuel Gessner, Luca Pezzè, Augusto Smerzi

Published Jan 1, 2019• 1 citation
Publisher

Abstract

We present sensitivity limits for a multimode interferometer as matrix bounds for the covariance matrix. Quantum strategies to improve the precision beyond classical limits may consist in entanglement among the modes or among the particles.
DOI
10.1364/qim.2019.s3b.4

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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.
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Quantum metrology studies the use of entanglement and other quantum resources to improve precision measurement. An interferometer using N independent particles to measure a parameter χ can achieve at best the "standard quantum limit" (SQL) of sensitivity δχ ∝ N-1/2. The same interferometer using N entangled particles can achieve in principle the "Heisenberg limit" δχ ∝ N-1, using exotic states, e.g., NooN states. Recent theoretical work argues that interactions among particles may be a valuable resource for quantum metrology, allowing scaling beyond the Heisenberg limit. Specifically, a k-particle interaction will produce sensitivity δχ ∝ N-kwith appropriate entangled states and δχ ∝ N-(k-1/2)even without entanglement. Here we demonstrate this "super-Heisenberg" scaling in a nonlinear, non-destructive measurement of the magnetisation of an atomic ensemble.