Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox

Experimental demonstration of topological bounds in quantum metrology

Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of band structures can dictate strict lower bounds on metrological properties, hence establishing a strong connection between topology and quantum metrology. In this work, we provide a first experimental verification of such topological bounds, by performing optimal quantum multi-parameter estimation and achieving the best possible measurement precision. By emulating the band structure of a Chern insulator, we experimentally determine the metrological potential across a topological phase transition, and demonstrate strong enhancement in the topologically non-trivial regime. Our work opens the door to metrological applications empowered by topology, with potential implications for quantum many-body systems.

Quantum Speed Limit for States and Observables of Perturbed Open Systems

Quantum speed limits provide upper bounds on the rate with which a quantum system can move away from its initial state. Here, we provide a different kind of speed limit, describing the divergence of a perturbed open system from its unperturbed trajectory. In the case of weak coupling, we show that the divergence speed is bounded by the quantum Fisher information under a perturbing Hamiltonian, up to an error which can be estimated from system and bath timescales. We give three applications of our speed limit. First, it enables experimental estimation of quantum Fisher information in the presence of decoherence that is not fully characterized. Second, it implies that large quantum work fluctuations are necessary for a thermal system to be driven quickly out of equilibrium under a quench. Moreover, it can be used to bound the response to perturbations of expectation values of observables in open systems.

Hierarchies of Frequentist Bounds for Quantum Metrology: From Cramér-Rao to Barankin

We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all possible quantum measurements and estimators that satisfy the given constraints. We obtain hierarchies of increasingly tight bounds that include the quantum Cramér-Rao bound at the lowest order. In the opposite limit, the quantum Barankin bound is the variance of the locally best unbiased estimator in quantum metrology. Our results reveal generalizations of the quantum Fisher information that are able to avoid regularity conditions and identify threshold behavior in quantum measurements with mixed states, caused by finite data.

Self-healing of Einstein-Rosen-Podolsky steering after an obstruction

Einstein-Rosen-Podolsky (EPR) steering describes the "spooky action at a distance" that one party can instantaneously affect the states of another distant party if they share quantum correlations. Due to its intriguing properties, EPR steering is recognized as an essential resource for a number of quantum information tasks. However, EPR steering may be destroyed when distributed in practical environments. Here, we experimentally show that EPR steering can self-heal after being destroyed by an obstruction. Such self-healing of EPR steering originates from the self-healing property of Bessel-Gaussian beams which are utilized to distribute EPR steering. For comparison, we show that when distributed using fundamental Gaussian beams, EPR steering cannot self-heal after an obstruction under similar conditions. Our results shed new light on constructing EPR-steering-based quantum information tasks in practical environments and provide a promising platform to study EPR steering.

Two-colour high-purity Einstein-Podolsky-Rosen photonic state

We report a high-purity Einstein-Podolsky-Rosen (EPR) state between light modes with the wavelengths separated by more than 200 nm. We demonstrate highly efficient EPR-steering between the modes with the product of conditional variances \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{{\mathcal{E}}}}}}}}}^{2}=0.11\pm 0.01\ll 1$$\end{document}E2=0.11±0.01≪1. The modes display − 7.7 ± 0.5 dB of two-mode squeezing and an overall state purity of 0.63 ± 0.16. EPR-steering is observed over five octaves of sideband frequencies from RF down to audio-band. The demonstrated combination of high state purity, strong quantum correlations, and extended frequency range enables new matter-light quantum protocols.

Engineering quantum correlations between light modes at different frequency would open new avenues for quantum networks and sensing. Here, the authors propose and demonstrate a way for obtaining high-purity strongly entangled continuous variable states with more than 200 nm difference in wavelength.

Many-Body Nonlocality as a Resource for Quantum-Enhanced Metrology

We demonstrate that the many-body nonlocality witnessed by a broad family of Bell inequalities is a resource for ultraprecise metrology. We formulate a general scheme which allows one to track how the sensitivity grows with the nonlocality extending over an increasing number of particles. We illustrate our findings with some prominent examples-a collection of spins forming an Ising chain and a gas of ultracold atoms in any two-mode configuration. We show that in the vicinity of a quantum critical point the rapid increase of the sensitivity is accompanied by the emergence of the many-body Bell nonlocality. The method described in this work allows for a systematic study of highly quantum phenomena in complex systems, and also extends the understanding of the beneficial role played by fundamental nonclassical effects in implementations of quantum-enhanced protocols.