Quantum metrology involves the application of quantum resources to enhance measurements. Several communities have developed quantum-metrology strategies that leverage effective time reversals. These strategies, we posit, form four classes. First, echo metrology begins with a preparatory unitary and ends with that unitary's time-reverse. The protocol amplifies the visibility of a small parameter to be sensed. Similarly, weak-value amplification enhances a weak coupling's detectability. The technique exhibits counterintuitive properties captured by a retrocausal model. Using the third strategy, one simulates closed timelike curves, worldlines that loop back on themselves in time. The fourth strategy involves indefinite causal order, which characterises channels applied in a superposition of orderings. We review these four strategies, which we unify under the heading of time-reverse metrology. We also outline opportunities for this toolkit in quantum metrology; quantum information science; quantum foundations; atomic, molecular, and optical physics; and solid-state physics.
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11 pages, including 1 table and 4 figures. Name "echo metrology" changed to "mirror metrology," to align with a similar term in the benchmarking literature
Quantum metrology involves the application of quantum resources to enhance measurements. Several communities have developed quantum-metrology strategies that leverage effective time reversals. These strategies, we posit, form four classes. First, echo metrology begins with a preparatory unitary and ends with that unitary's time-reverse. The protocol amplifies the visibility of a small parameter to be sensed. Similarly, weak-value amplification enhances a weak coupling's detectability. The technique exhibits counterintuitive properties captured by a retrocausal model. Using the third strategy, one simulates closed timelike curves, worldlines that loop back on themselves in time. The fourth strategy involves indefinite causal order, which characterises channels applied in a superposition of orderings. We review these four strategies, which we unify under the heading of time-reverse metrology. We also outline opportunities for this toolkit in quantum metrology; quantum information science; quantum foundations; atomic, molecular, and optical physics; and solid-state physics.
Quantum-enhanced metrology relies on entanglement to achieve sensitivities beyond the standard quantum limit. While remarkable progress has been made in generating highly entangled many-body states, extracting their metrological advantage remains a central challenge because the encoded information is often inaccessible to realistic measurements. A key development of the past decade has been the realization that many-body interactions can play a dual role: they can be used not only to generate entanglement, but also to decode it. This idea underlies interaction-based readout and time-reversal protocols, in which controlled non-linear dynamics transform weakly encoded signals into experimentally accessible observables. Cavity quantum electrodynamics (QED) provides a particularly powerful setting for these approaches because it combines collective enhancement, tunable interactions, and controllable reversibility within a single platform. In this review, we discuss the emergence of time-reversal protocols in cavity QED, from their conceptual roots in Loschmidt echoes to modern implementations of signal amplification through a time-reversed interaction (SATIN), scrambling-enhanced metrology, and more general interaction-based readout schemes. We examine the physical mechanisms that enable reversible many-body dynamics, review key experimental demonstrations, and discuss future directions involving complex entangled states, nonlinear decoding, and emerging quantum platforms. Together, these developments suggest that the ability to decode quantum information may become as important as the ability to generate it, establishing reversible many-body dynamics as a central resource for quantum-enhanced sensing.
We present a review on quantum metrology and sensing, from its foundations to current applications. Highlights of the review include consideration of both frequentist and Bayesian approaches to parameter estimation; single as well as multiparameter estimation; estimation for different encoding processes comprising unitary as well as noisy channels, quantum thermometry, and channels involving indefinite causal order; different estimation strategies incorporating also recent advances like quantum error correction-aided methods and reservoir engineering; usefulness of quantum Fisher information to detect resources; applications of quantum metrology in diverse arenas covering quantum many-body sensors, sensing protocols in atomic ensembles, atom-photon systems, and continuous-variable systems, quantum imaging, quantum illumination, atomic clocks and atom interferometry, etc; and experimental realizations of quantum sensors in different physical platforms.
It is now well appreciated that quantum physics can be used to build better sensors. Such sensors can be based on unitary systems [1,2] like interferometers or open systems based on scattering and lossy transmission channels [3-5]. The framework of the quantum Fisher information enables one to obtain best estimates of the parameters and then one can design possible experiments that can reach Cramer- Rao bounds. I would bring out not only the importance of the quantum states used as probes, but also the importance of the ‘quantum’ measurement schemes especially the ones that depend on time reversed arrangements. I would illustrate the great usefulness of squeezed states of matter and light for metrology. [1] S. C. Burd et al., Quantum amplification of mechanical oscillator motion, Science 364, 1163 (2019). [2] G. S. Agarwal, and L. Davidovich, Quantifying quantum-amplified metrology via Fisher information, Phys. Rev. Res. 4, L 012014 (2022). [3] J. Wang, L. Davidovich, and G. S. Agarwal, Quantum sensing of open systems: Estimation of damping constants and temperature, Phys. Rev. Res. 2, 033389 (2020). [4] F. Li, T. Li, M. O. Scully, and G. S. Agarwal, Quantum advantage with seeded squeezed light for absorption measurement, Phys. Rev. Applied 15, 044030 (2021). [5] T.Li, F. Li, X. Liu, V. Yakovlev and G. S. Agarwal, Quantum-enhanced stimulated Brillouin scattering spectroscopy and imaging, OPTICA 9, 959 (2022).
I discuss the time reversal of nonlinear many-body Hamiltonians and its application to the fields of quantum metrology and quantum information science. I present the experimental realization of such a protocol in an optically engineered many-body spin Hamiltonian. We used time-reversed Hamiltonian approach to achieve metrological gains well beyond the limit of the readout scheme. Moreover, with the same protocol, we experimentally elucidate the intimate relation between quantum information scrambling, out-of-time-order correlators, and metrological gain. In particular, I will highlight the robustness of time reversal protocols, and how these render many fast-scrambling and complex Hamiltonians useful for quantum-enhanced metrology.
ABSTRACT Weak measurement has emerged as a pivotal technique in precision metrology, utilizing unique amplification effects to enhance the capabilities of quantum sensing and quantum imaging. Quantum sensing can provide systems with unprecedented accuracy and sensitivity by utilizing its quantum properties. Quantum imaging uses entangled photon states to capture information, enabling signal‐to‐noise ratio and resolution that surpass the limits of classical imaging. The synergistic integration of weak measurement with quantum sensing and imaging paves the way for next‐generation technologies with practical value, significantly advancing frontiers of precision metrology and imaging science. This review elucidates the fundamental theory of weak value amplification and comprehensively discusses the performance of weak measurement strategies in quantum sensing and imaging frameworks, highlighting both classical techniques and emerging quantum applications. It covers four main directions: nanostructure, 2D atomic crystal, biochemistry, and optical imaging, including from structural parameters characterization to chemical reaction sensing to nonlocal weak measurement microscopy. This work aims to discuss recent advances in weak measurement applications for quantum sensing and imaging platforms, while outlining future development opportunities arising from the convergence of these three fields.
We propose a quantum metrology protocol based on a two-step joint evolution of the probe system and an ancillary qubit and quantum measurement. With a proper initial state of the ancillary qubit and an optimized evolution time, the quantum Fisher information (QFI) about the phase parameter encoded in the probe system is found to be determined by the expectation value of the square of a phase generator, irrespective of the probe initial state. Consequently, even if the probe is prepared as a finite-temperature state, faraway from the so-called resource state, e.g., the squeezed spin state or the Greenberger-Horne-Zeilinger state in atomic systems, the QFI in our protocol can approach the Heisenberg scaling N2 with respect to the probe size N. This quadratic scaling behavior shows robustness against the imperfections about the initial state of the ancillary qubit and the optimized evolution time of the whole system. Also it is not sensitive to the deviation in system parameters and the qubit decoherence. Using the time-reversal strategy and a single-shot projective measurement, the classical Fisher information (CFI) in our metrology protocol is saturated with its quantum counterpart. Our work thus provides an economical method to reach the Heisenberg limit in metrology precision with no input of entanglement or squeezing.