Quantum metrology explores optimal quantum protocols for parameter estimation. In the context of optical atomic clocks, conventional protocols focus on optimal input states and measurements to achieve enhanced sensitivities. However, such protocols are typically limited by phase slip errors inflicted due to the decoherence of the local oscillator. Here, we study schemes to extend the dynamic range and overcome phase slip noise through weak measurements with ancilla qubits. Using coherent spin states, we find optimal weak measurements protocols: we identify optimal measurement strength for any given interrogation time and number of atoms. Then, we combine weak and projective measurements to construct a protocol that asymptotically saturates the noiseless precision limits and outperforms previously proposed methods for phase slip noise suppression.
Quantum metrology explores optimal quantum protocols for parameter estimation. In the context of optical atomic clocks, conventional protocols focus on optimal input states and measurements to achieve enhanced sensitivities. However, such protocols are typically limited by phase slip errors inflicted due to the decoherence of the local oscillator. Here, we study schemes to extend the dynamic range and overcome phase slip noise through weak measurements with ancilla qubits. Using coherent spin states, we find optimal weak measurements protocols: we identify optimal measurement strength for any given interrogation time and number of atoms. Then, we combine weak and projective measurements to construct a protocol that asymptotically saturates the noiseless precision limits and outperforms previously proposed methods for phase slip noise suppression.
Balancing high sensitivity with a broad dynamic range is a fundamental challenge in measurement science, as improving one often compromises the other. While traditional quantum metrology has prioritized enhancing local sensitivity, a large dynamic range is crucial for applications such as atomic clocks, where extended phase interrogation times contribute to wider phase range. In this Letter, we introduce a novel quantum deamplification mechanism that extends dynamic range at a minimal cost of sensitivity. Our approach uses two sequential spin-squeezing operations to generate and detect an entangled probe state, respectively. We demonstrate that the optimal quantum interferometer limit can be approached through two-axis countertwisting dynamics. Further expansion of dynamic range is possible by using sequential quantum deamplification interspersed with phase encoding processes. Additionally, we show that robustness against detection noise can be enhanced by a hybrid sensing scheme that combines quantum deamplification with quantum amplification. Our protocol is within the reach of state-of-the-art atomic-molecular-optical platforms, offering a scalable, noise-resilient pathway for entanglement-enhanced metrology.
Frequency metrology is a cornerstone of modern precision measurements and optical atomic clocks have emerged as one of the most precise measurement devices. In this progress report, we explore various Ramsey interrogation schemes tailored to optical atomic clocks primarily limited by laser noise. To incorporate frequency fluctuations directly into the theoretical model, we consider a Bayesian framework. In this context, we review fundamental bounds arising in Bayesian estimation theory, which serve as a benchmark throughout this work. We investigate the trade-off between entanglement-enhanced sensitivity and robustness against laser noise in order to identify optimal initial states, measurement schemes and estimation strategies. Beside standard protocols based on coherent spin states, spin-squeezed states and Greenberger-Horne-Zeilinger states, we consider variational Ramsey protocols implemented via low-depth quantum circuits based on one-axis twisting operations to approach optimal stability. In particular, we review known and identify new optimal Ramsey interrogation schemes for a variety of scenarios, including different experimental platforms, ensemble sizes and regimes characterized by a wide range of interrogation durations and dead times. Hence, this work establishes a comprehensive theoretical framework for optimizing Ramsey interrogation schemes, providing guidance for the development of next-generation optical atomic clocks.
Quantum optimal control (QOC) schemes can be employed to enhance the sensitivity of quantum metrology (QM) protocols undergoing Markovian noise, which can limit their precision to a standard quantum limit (SQL)-like scaling. In this paper, we propose a QOC scheme for QM that leverages entanglement and optimized coupling interactions with an ancillary system to provide enhanced metrological performance under general Markovian dynamics. We perform a comparative analysis of our entanglement-enhanced scheme against the unentangled scheme conventionally employed in QOC-enabled QM for varying evolution times and decoherence levels, revealing that the entanglement-enhanced scheme enables significantly better noise performance, even when a noisy ancilla is employed. We further extend our investigation to time-inhomogeneous noise models, specifically focusing on a noisy frequency estimation scenario within a spin-boson bath, and evaluate the protocol's performance under completely dissipative and dephasing dynamics. Our findings indicate that, in certain situations, schemes employing coherent control of a single particle are severely limited. In such cases, employing the entanglement-enhanced scheme can provide improved performance.
We present a protocol for simultaneous estimation of both quadratures of a displacement channel on a quantum harmonic oscillator using a single ancilla qubit, without complex state preparation or adaptive control. The qubit is coupled to the quantum harmonic oscillator via controlled displacements of strength A and undergoes N rounds of measurement and reset, while the oscillator coherently accumulates the displacement signal. The non-commuting displacements imprint an order-dependent geometric phase at each round, giving a quantum Fisher information that scales as O(A2N3). Although the measurement record space grows as 2N, we show that exact likelihoods for any individual measurement record can be computed in O(N2) time. With this, we show that measurement in the computational basis approximately saturates the quantum bound and maintains the O(A2N3) scaling. Furthermore, the periodic information extraction makes the protocol robust to decoherence. Our results provide a framework for the design and analysis of sequential measurement in ancilla-assisted protocols.
Quantum error correction has been successfully applied to enhance the precision of parameter estimation in the presence of noise. Nonetheless, existing methods require a number of noiseless, controllable ancillae and lack efficient encoding and decoding procedures. In this Letter, we demonstrate that subsystem error correction provides a new direction that can substantially simplify the metrological protocol. We derive general conditions under which subsystem stabilizer codes achieve the Heisenberg limit and show that, for broad classes of noise, this can be realized by syndrome-free protocols using at most a single ancilla qubit. Furthermore, we extend this framework to dynamical error correction and show that Floquet codes can protect time-dependent metrological signals in reaching the Heisenberg limit.
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.