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arXiv:2605.00287 · Physical Review A

Sequential Measurements as a Resource for Quantum Metrology

Koray Mentesoglu, Rahul Trivedi, Sara Mouradian

quant-phSubmitted Apr 30, 2026• Announced May 4, 2026• 0 citations
v1 · Apr 30, 2026v2 · Sep 2, 2026
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Abstract

We present a protocol in which sequential weak measurements of a quantum harmonic oscillator enable simultaneous estimation of both quadratures of a displacement channel. Calculations of the quantum Fisher information show that the measurement backaction can increase the information gained for a range of measurement strengths. The protocol distributes information over a $N$-bit string after $N$ weak measurements. Thus we find that post-processing can be used to avoid information loss due to phase wrapping, increasing the effective dynamic range. Finally, the periodic information extraction makes the protocol robust to decoherence. Our results establish mid-sensing measurement as a resource for single- and multi-parameter quantum metrology.

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16 pages, 7 figures, including supplemental material

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We present a protocol in which sequential weak measurements of a quantum harmonic oscillator enable simultaneous estimation of both quadratures of a displacement channel. Calculations of the quantum Fisher information show that the measurement backaction can increase the information gained for a range of measurement strengths. The protocol distributes information over a NNN-bit string after NNN weak measurements. Thus we find that post-processing can be used to avoid information loss due to phase wrapping, increasing the effective dynamic range. Finally, the periodic information extraction makes the protocol robust to decoherence. Our results establish mid-sensing measurement as a resource for single- and multi-parameter quantum metrology.
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{N}^{2}N2 with respect to the probe size NNN. 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.
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.
High-precision measurement of oscillating signal is a ubiquitous issue in fundamental science and a critical task in practical technologies. In quantum metrology, quantum lock-in detection provide an efficient method for measuring such signal. In general, when the initial phase of the oscillating signal is unknown,quantum double lock-in detection can effectively extract complete information about the signal's amplitude, frequency, and initial phase. Conventional quantum double lock-in detection requires two individual quantum interferometry, each of which must undergo state preparation and readout. However, the time for state preparation and readout need not be negligible in practical experiments. In particular, the time for state preparation is longer than the time for sensing. To save experimental resources, it is challenging to achieve quantum double lock-in detection just via a single quantum interferometry while still extracting complete information about the signal's amplitude, frequency, and initial phase. Here, we present a general protocol for achieving a quantum double lock-in detection just via a single quantum interferometry under a sequential orthogonal periodic multipulse sequences. In particular, if the input state is a Greenberger-Horne-Zeilinger state and two interaction-based operations are applied during interferometry, the measurement precisions for frequency, amplitude, and initial phase can both approach the Heisenberg limit. Our study paves a new way for measuring oscillating signals with a single quantum interferometry, and provides a feasible method for achieving Heisenberg-limited detection of alternating signals.
In the scenario of the probe-ancilla interaction, we propose a quantum metrology protocol by the unconditional measurement on the ancillary qubit after an optimized period of joint evolution from a product state. Its key element is the construction of two parallel evolution paths by the measurement that can transform the probe system (a spin ensemble) from an eigenstate of a collective angular momentum operator $|j,m\ensuremath{\rangle}$ to a superposed state $(|j,m\ensuremath{\rangle}+|j,\ensuremath{-}m\ensuremath{\rangle})/\sqrt{2}$. With synchronous parametric encoding and qubit measurement, the quantum Fisher information about the phase encoded in the probe system with optimized initial states can exactly attain the Heisenberg scaling N2{N}^{2}N2 with respect to the probe size (spin number) NNN. The quadratic scaling behavior is not sensitive to the imprecise control over the joint evolution time, the time delay between encoding and measurement, and the coherence in the probe ensemble or the ancillary system that would be degraded by local dephasing. The classical Fisher information of the spin ensemble is found to saturate with its quantum counterpart, irrespective of the idle joint evolution after the parametric encoding. We suggest that both Greenberger-Horne-Zeilinger (GHZ)-like states and nonlinear Hamiltonian are not necessary resources for exceeding the standard quantum limit in metrology precision since in our protocol even thermal states can hold an asymptotic quadratic scaling.
Quantum metrology overcomes standard precision limits and plays a central role in science and technology. Practically, it is vulnerable to imperfections such as decoherence. Here we demonstrate quantum metrology for noisy channels such that entanglement with ancillary qubits enhances the quantum Fisher information for phase estimation but not otherwise. Our photonic experiment covers a range of noise for various types of channels, including for two randomly alternating channels such that assisted entanglement fails for each noisy channel individually. We simulate noisy channels by implementing space-multiplexed dual interferometers with quantum photonic inputs. We demonstrate the advantage of entanglement-assisted protocols in a phase estimation experiment run with either a single-probe or multiprobe approach. These results establish that entanglement with ancillae is a valuable approach for delivering quantum-enhanced metrology. Our approach to entanglement-assisted quantum metrology via a simple linear-optical interferometric network with easy-to-prepare photonic inputs provides a path towards practical quantum metrology.
The Heisenberg scaling is an ultimate precision limit of parameter estimation allowed by the principles of quantum mechanics, with no counterpart in the classical realm, and has been a long-pursued goal in quantum metrology. It has been known that interactions between the probes can help reach the Heisenberg scaling without entanglement. In this paper, we show that interactions between the probes and the additional dimensions of an ancillary system may also increase the precision of parameter estimation to surpass the standard quantum limit and attain the Heisenberg scaling without entanglement, if the measurement scheme is properly designed. The quantum Fisher information exhibits periodic patterns over the evolution time, implying the existence of optimal time points for measurements that can maximize the quantum Fisher information. By implementing optimizations over the Hamiltonian, the initial states of the probes and the ancillary system, the interaction strength, and the time points for measurements, our protocol achieves the Heisenberg scaling for the parameter of the probe Hamiltonian, in terms of both evolution time and probe number. Our protocol features two aspects: (i) the Heisenberg scaling can be achieved by a product state of the probes and (ii) mere local measurement on the ancilla is sufficient, both of which reduce the quantum resources and the implementation complexity to achieve the Heisenberg scaling. The paper is concluded by the investigation of the effects of noise on this protocol.