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arXiv:2507.09172 · EPJ Quantum Technology

The temporal resolution limit in quantum sensing

Cong-Gang Song, Qing-yu Cai

Published Jun 16, 2025• 0 citations
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Abstract

Temporal resolution is a critical figure of merit in quantum sensing. This study combines the distinguishable condition of quantum states with quantum speed limits to establish a lower bound on interrogation time. When the interrogation time falls below this bound, the output state becomes statistically indistinguishable from the input state, and the information will inevitably be lost in noise. Without loss of generality, we extend these conclusions to time-dependent signal Hamiltonian. In theory, leveraging certain quantum control techniques allows us to calculate the minimum interrogation time for arbitrary signal Hamiltonian. Finally, we illustrate the impact of quantum speed limits on magnetic field measurements and temporal resolution.

DOI
10.1140/epjqt/s40507-025-00377-8

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Temporal resolution is a critical figure of merit in quantum sensing. This study combines the distinguishable condition of quantum states with quantum speed limits to establish a lower bound on interrogation time. When the interrogation time falls below this bound, the output state becomes statistically indistinguishable from the input state, and the information will inevitably be lost in noise. Without loss of generality, we extend these conclusions to time-dependent signal Hamiltonian. In theory, leveraging certain quantum control techniques allows us to calculate the minimum interrogation time for arbitrary signal Hamiltonian. Finally, we illustrate the impact of quantum speed limits on magnetic field measurements and temporal resolution.
Time-resolution protocol of quantum sensing aims to measure the fast temporal variation of an external field and demands a high field sensitivity in a short interrogation time $\ensuremath{\tau}$. Since any operation that evolves the quantum state takes time and is counted as part of the interrogation, evaluating the performance of the time-resolution protocol requires a complete end-to-end description of the measurement process. In particular, the initial state has to be one of the quantum sensor's eigenstates in the absence of external fields, and the final projective measurements must be performed in the same eigenstate basis. Building upon prior works which proposed limits for time-resolved sensing using a quantum sensor, we apply optimal control theory to optimize the time-resolution protocol. Our analysis indicates that there exists a critical interrogation time T∗{T}^{*}T∗: When $\ensuremath{\tau}<{T}^{*}$ the optimal protocol is a purely bang-bang strategy; when $\ensuremath{\tau}>{T}^{*}$ the optimal protocol involves a singular control during the interrogation. In the short-$\ensuremath{\tau}$ regime, which is relevant to high time resolution, we propose a detune protocol that involves only smooth control during the entire interrogation. As the discontinuities of control pose the main obstacles to experimental realization, we expect the presented detune protocol to be practically useful. In the long-$\ensuremath{\tau}$ regime, the optimal protocol closely resembles the Ramsey sequence; protocols based on maximizing quantum Fisher information are constructed to highlight the difference between the theoretically optimal and practically implementable measurements. Effective use of the time-resolution protocol requires a setup where the unknown time-domain signal of interest can be identically and repeatedly generated. As a potentially relevant application, we outline the calibration of baseband flux pulse distortion in the control of superconducting qubits.
Quantum sensors capitalize on advanced control sequences for maximizing sensitivity and precision. However, protocols are not usually optimized for temporal resolution. Here, we establish the limits for time-resolved sensing of dynamical signals using qubit probes. We show that the best possible time resolution is closely related to the quantum speed limit (QSL), which describes the minimum time needed to transform between basis states. We further show that a composite control sequence consisting of two phase-shifted pulses reaches the QSL. Practical implementation is discussed based on the example of the spin-1 qutrit of a nitrogen-vacancy center in diamond.
The field of quantum sensing explores the use of quantum phenomena to measure a broad range of physical quantities, of both static and time-dependent types. While for static signals the main figure of merit is sensitivity, for time dependent signals it is spectral resolution, i.e. the ability to resolve two different frequencies. Here we study this problem, and develop new superresolution methods that rely on quantum features. We first formulate a general criterion for superresolution in quantum problems. Inspired by this, we show that quantum detectors can resolve two frequencies from incoherent segments of the signal, irrespective of their separation, in contrast to what is known about classical detection schemes. The main idea behind these methods is to overcome the vanishing distinguishability in resolution problems by nullifying the projection noise.
High-sensitivity accelerometers and gravimeters, achieving the ultimate limits of measurement sensitivity are key tools for advancing both fundamental and applied physics. While numerous platforms have been proposed to achieve this goal, from atom interferometers to optomechanical systems, all of these studies neglect the effects of intrinsic quantum uncertainty in time estimation. Starting from the Hamiltonian of a generic linear quantum sensor, we derive the two-parameter quantum Fisher information matrix and establish the corresponding Cram'er-Rao bound, treating time as an uncertain (nuisance) parameter. Our analysis reveals a fundamental coupling between time and signal estimation that inherently degrades measurement sensitivity, with the standard single-parameter quantum limit recovered only at specific interrogation times or under special decoupling conditions. We then apply these results to an optomechanical gravimeter and explicitly derive an optimal decoupling condition under which the effects of time uncertainty are averaged out in a continuous measurement scheme. Our approach is general and can be readily extended to a broad class of quantum sensors.
The ability to determine precisely the separation of two frequencies is fundamental to spectroscopy, yet the resolution limit poses a critical challenge: distinguishing two incoherent signals becomes impossible when their frequencies are sufficiently close. Here, we demonstrate a simple and powerful approach, dubbed superresolution quantum sensing, which experimentally resolves two nearly identical incoherent signals using a solid-state spin quantum sensor. By carefully choosing interrogation times that satisfy the superresolution condition, we eliminate quantum projection noise, overcoming the vanishing distinguishability of signals with near-identical frequencies. This leads to improved resolution, which scales as t^{-2} in comparison to the standard t^{-1} scaling. Together with a greatly reduced classical readout noise assisted by a nuclear spin, we are able to achieve sub-kHz resolution with a signal detection time of 80 μs. Our results highlight the potential of quantum sensing to overcome conventional frequency resolution limitations, with broad implications for precision measurements.
Abstract The field of quantum sensing explores the use of quantum phenomena to measure a broad range of physical quantities, of both static and time-dependent types. While for static signals the main figure of merit is sensitivity, for time dependent signals it is spectral resolution, i.e. the ability to resolve two different frequencies. Here we study this problem, and develop new superresolution methods that rely on quantum features. We first formulate a general criterion for superresolution in quantum problems. Inspired by this, we show that quantum detectors can resolve two frequencies from incoherent segments of the signal, irrespective of their separation, in contrast to what is known about classical detection schemes. The main idea behind these methods is to overcome the vanishing distinguishability in resolution problems by nullifying the projection noise.