We reveal the noncyclic Pancharatnam phase—arising from the coherent system-meter interaction—as a fundamental criterion that governs the optimal performance of quantum compression channels in postselected metrology. This phase embodies a geometric connection that enables precise control over the parallel evolution of the meter state, thereby maximizing the quantum Fisher information per trial and achieving lossless compression channels. Remarkably, fine-tuning the postselection parameter just below this optimal phase incurs substantial information loss, whereas tuning it just above fully suppresses undesired parallel evolution, enhancing information retention beyond that achievable in postselected protocols lacking Pancharatnam phase effects. We further reveal that leveraging qudit-meter states can unlock a substantial additional enhancement. These findings establish the Pancharatnam phase as a geometric benchmark, guiding the design of high-precision quantum parameter estimation protocols.
We reveal the noncyclic Pancharatnam phase—arising from the coherent system-meter interaction—as a fundamental criterion that governs the optimal performance of quantum compression channels in postselected metrology. This phase embodies a geometric connection that enables precise control over the parallel evolution of the meter state, thereby maximizing the quantum Fisher information per trial and achieving lossless compression channels. Remarkably, fine-tuning the postselection parameter just below this optimal phase incurs substantial information loss, whereas tuning it just above fully suppresses undesired parallel evolution, enhancing information retention beyond that achievable in postselected protocols lacking Pancharatnam phase effects. We further reveal that leveraging qudit-meter states can unlock a substantial additional enhancement. These findings establish the Pancharatnam phase as a geometric benchmark, guiding the design of high-precision quantum parameter estimation protocols.
In quantum metrology, information about unknown parameters θ = ( θ 1 , ... , θ M ) is accessed by measuring probe states ρ ̂ θ . In experimental settings where copies of ρ ̂ θ can be produced rapidly (e.g., in optics), the information-extraction bottleneck can stem from high postprocessing costs or detector saturation. In these regimes, it is desirable to compress the information encoded in ρ ̂ θ ⊗ n into m < n copies of a postselected state: ρ ̂ θ ps ⊗ m . Remarkably, recent works have shown that, in the absence of noise, compression can be lossless, for m / n arbitrarily small. Here, we fully characterize the family of filters that enable lossless compression. Further, we study the effect of noise on quantum-metrological information amplification. Motivated by experiments, we consider a popular family of filters, which we show is optimal for qubit probes. Further, we show that, for the optimal filter in this family, compression is still lossless if noise acts after the filter. However, in the presence of depolarizing noise before filtering, compression is lossy. In both cases, information extraction can be implemented significantly better than simply discarding a constant fraction of the states, even in the presence of strong noise. Published by the American Physical Society 2024
Nonlinear effects are widely utilized in quantum metrology to enhance measurement precision by leveraging complex dynamical behaviors. Here, we propose a quantum scrambling-integrated scheme that optimizes the selection of initial states and parameter encoding by exploiting the nonlinear dynamical trajectories and their geometric properties in phase space. We consider a two-mode Bose-Einstein condensate as a typical example. Within a certain parameter range, using uncorrelated spin coherent states located at saddle points and separatrices enables the measurement precision to reach the Heisenberg scaling. An analytical expression for the quantum Fisher information under long-time evolution is provided, and our analysis further reveals that the enhancement mechanism is governed by the sensitivity of the energy spectrum to parameter variations. Compared to the criticality-enhanced protocol that requires parameters to approach the critical point, our scheme offers a distinct advantage in its applicability over a broader range of parameters. Moreover, this scheme can also be applied to models that include one- and two-axis countertwisting interactions and chaotic dynamics. This Letter offers a new perspective for advancing the application of nonlinear dynamics to enhance the parameter estimation precision in quantum systems.
The postselected quantum metrological scheme is especially advantageous when the final measurements are either very noisy or expensive in practical experiments. In this Letter, we put forward a general theory on the compression channels in postselected quantum metrology. We define the basic notions characterizing the compression quality and illuminate the underlying structure of lossless compression channels. Previous experiments on postselected optical phase estimation and weak-value amplification are shown to be particular cases of this general theory. Furthermore, for two categories of bipartite systems, we show that the compression loss can be made arbitrarily small even when the compression channel acts only on one subsystem. These findings can be employed to distribute quantum measurements so that the measurement noise and cost are dramatically reduced.
This thesis explores various protocols which can be applied to quantum metrology, such that precision of the measurement can beat the best classical approaches. We first demonstrate that ancilla-assisted schemes can improve phase estimation in the presence of noise, and we propose an experiment to demonstrate these effects. Given that the use of ancillae helps, it is no surprise that there are noisy channels for which the optimal strategy may depend on the noise level. We show that there is a non-trivial crossover between the ancilla-assisted strategy and the parallel-entangled strategy for Pauli noise channels and the amplitude damping channel. We see that under certain circumstances, the environment cannot access the parameter of interest. We then integrated techniques from quantum communication, to derive a general framework that renders quantum metrology protocols into cryptographic ones. Here the protocol is unconditionally secure if the trusted parties wish only to achieve the standard quantum limit. If Heisenberg-limited precision is to be achieved, they sacrifice some security, where adversaries can access information, but only at the risk of getting caught at it (cheat-sensitivity). In many scenarios, the quantum Fisher information is achieved for only one value of the phase. In a particular phase estimation scheme that measures the parity at the output of a Mach-Zehnder interferometer where the input is a two-mode squeezed vacuum, this problem is particularly imminent. We apply an adaptive technique to resolve this issue, showing that one can achieve precisions substantially below the shot noise limit. The key to a quadratically enhanced improvement in quantum metrology is entanglement. Finally, we demonstrate in a photonic system how high-dimensional entanglement can be certified, and provide an alternate interpretation of entanglement from an information-theoretic perspective.
Postselection can compress the metrological information and improve sensitivity in the presence of certain types of technical noise. Postselected quantum metrology with pure states has been significantly advanced recently. However, extending this framework to mixed states leads to formidable challenges, such as the difficulty in searching for lossless postselection measurements or even the loss of metrological information. In this work, we leverage the intuition for the lossless postselection of pure states and generalize the theory to the lossless postselection of a class of mixed states, dubbed quasi-pure states. We illustrate our findings in postselected quantum imaging, unitary estimation problems, and show that the quasi-pure structure can be universally engineered through only classical correlation with an ancilla. Our findings extend the utility of postselection techniques to scenarios with decoherence and also offer new perspectives to foundational questions in quantum information geometry.
Quantum metrology utilizes quantum resources to enhance the precision of parameter estimation. A central objective is to maximize the Quantum Fisher information (QFI), which determines the ultimate estimation precision based on the Cramér-Rao bound. In this work, we formulate QFI optimization as an optimal control problem and apply Pontryagin’s Minimum Principle (PMP) to derive the optimal control protocol. We show that when the control amplitude is constrained below a certain threshold, the optimal solution reduces to a constant control. This strategy enables the QFI to scale quadratically with the total evolution time T, thereby improving estimation precision with longer probe durations.