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Quantum Communications and Quantum Imaging

Is time a resource for quantum sensing? (Conference Presentation)

Kae Nemoto, Michael Hanks

Published Sep 10, 2019• 0 citations
Publisher

Abstract

It is now widely believed that in the near future quantum sensing devices will be realized to outperform some of our current sensing devices. As quantum metrology protocols are comprised of three stages: probe state preparation, sensing followed by readout, it is important that the time for all three steps are accounted when the performance is determined. Historically the time required for the first and last stages has usually been neglected, which could be unrealistic when entangled resources are used. Entangled resources lose their sensitivity in time under noise, and hence the sensing time with these resources is limited. To avoid this degradation of sensitivity, we could repeat the protocol to refresh the entanglement in the resources. However, as the process of the preparation and the readout of the entangled probe state costs us a certain period of time, we need to optimize the sensing protocol throughout the three stages. We find that an entangled state probe can give an advantage over separable ones only if the entangled state preparation and readout times are lower than a certain threshold and illustrate this result in an optical setting.

DOI
10.1117/12.2529207

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It is now widely believed that in the near future quantum sensing devices will be realized to outperform some of our current sensing devices. As quantum metrology protocols are comprised of three stages: probe state preparation, sensing followed by readout, it is important that the time for all three steps are accounted when the performance is determined. Historically the time required for the first and last stages has usually been neglected, which could be unrealistic when entangled resources are used. Entangled resources lose their sensitivity in time under noise, and hence the sensing time with these resources is limited. To avoid this degradation of sensitivity, we could repeat the protocol to refresh the entanglement in the resources. However, as the process of the preparation and the readout of the entangled probe state costs us a certain period of time, we need to optimize the sensing protocol throughout the three stages. We find that an entangled state probe can give an advantage over separable ones only if the entangled state preparation and readout times are lower than a certain threshold and illustrate this result in an optical setting.
A quantum metrology protocol for parameter estimation is typically comprised of three stages: probe state preparation, sensing and then readout, where the time required for the first and last stages is usually neglected. In the present work we consider non-negligible state preparation and readout times, and the tradeoffs in sensitivity that come when a limited time resource T must be divided between the three stages. To investigate this, we focus on the problem of magnetic field sensing with spins in one-axis twisted or two-axis twisted states. We find that (accounting for the time necessary to prepare a twisted state) no advantage is gained unless the time T is sufficiently long or the twisting sufficiently strong. However, we also find that the limited time resource is used more effectively if we allow the twisting and the magnetic field to be applied concurrently, which possibly represents a more realistic sensing scenario. We extend this result into an optical setting by utilizing the exact correspondence between a spin system and a bosonic field mode as given by the Holstein-Primakoff transformation.
There is growing belief that the next decade will see the emergence of sensing devices based on the laws of quantum physics that outperform some of our current sensing devices. For example, in frequency estimation, using a probe prepared in an entangled state can, in principle, lead to a precision gain compared to a probe prepared in a separable state. Even in the presence of some forms of decoherence, it has been shown that the precision gain can increase with the number of probe particles NNN. Usually, however, the entangled and separable state preparation and readout times are assumed to be negligible. We find that a probe in a maximally entangled (GHZ) state can give an advantage over a separable state only if the entangled state preparation and readout times are lower than a certain threshold. When the probe system suffers dephasing, this threshold is much lower (and more difficult to attain) than it is for an isolated probe. Further, we find that in realistic situations the maximally entangled probe gives a precision advantage only up to some finite number of probe particles Ncutoff{N}_{\text{cutoff}}Ncutoff​ that is lower for a dephasing probe than it is for an isolated probe.
A quantum metrology protocol for parameter estimation is typically comprised of three stages: probe state preparation, sensing and then readout, where the time required for the first and last stages is usually neglected. In the present work we consider non-negligible state preparation and readout times, and the tradeoffs in sensitivity that come when a limited time resource τ must be divided between the three stages. To investigate this, we focus on the problem of magnetic field sensing with spins in one-axis twisted or two-axis twisted states. We find that (accounting for the time necessary to prepare a twisted state) no advantage is gained unless the time τ is sufficiently long or the twisting sufficiently strong. However, we also find that the limited time resource is used more effectively if we allow the twisting and the magnetic field to be applied concurrently, which possibly represents a more realistic sensing scenario. We extend this result into an optical setting by utilising the exact correspondence between a spin system and a bosonic field mode as given by the Holstein–Primakoff transformation.
There is growing belief that the next decade will see the emergence of sensing devices based on the laws of quantum physics that outperform some of our current sensing devices. For example, in frequency estimation, using a probe prepared in an entangled state can, in principle, lead to a precision gain compared to a probe prepared in a separable state. Even in the presence of some forms of decoherence, it has been shown that the precision gain can increase with the number of probe particles NNN. Usually, however, the entangled and separable state preparation and readout times are assumed to be negligible. We find that a probe in a maximally entangled (GHZ) state can give an advantage over a separable state only if the entangled state preparation and readout times are lower than a certain threshold. When the probe system suffers dephasing, this threshold is much lower (and more difficult to attain) than it is for an isolated probe. Further, we find that in realistic situations the maximally entangled probe gives a precision advantage only up to some finite number of probe particles Ncutoff{N}_{\text{cutoff}}Ncutoff​ that is lower for a dephasing probe than it is for an isolated probe.
Quantum metrology enables parameter estimation beyond classical limits by exploiting nonclassical resources such as squeezing and entanglement. In distributed quantum sensing, Heisenberg scaling has been extended from 1/N21/N^21/N2 to 1/(NM)21/(NM)^21/(NM)2 through entanglement across both particles and spatial modes, where NNN denotes the photon number and MMM the number of spatially distributed modes. However, the overall sensitivity has remained limited to linear scaling with the number of measurement repetitions RRR. Here, we show that exploiting entanglement across temporal modes via time-domain multiplexing enables a scaling advantage with respect to RRR. As a result, the sensitivity can asymptotically approach simultaneous Heisenberg scaling in photons, spatial modes, and repetitions, yielding an overall sensitivity approaching Δ2φ∝1/(NMR)2Δ^2 φ\propto 1/(NMR)^2Δ2φ∝1/(NMR)2. Using the Bogoliubov transformation formalism, we prove the optimality of the protocol within the class of Gaussian states and show that the scaling is realizable via homodyne detection and maximum-likelihood estimation. We further show that the advantage persists under optical loss and propose an experimentally feasible loop-based photonic sensing scheme. Our results open a route to incorporating time-multiplexing techniques into quantum metrology.
The foundational theory of quantum enhanced metrology for parameter estimation is of fundamental importance to the progression of science and technology as the scientific method is built upon empirical evidence, the acquisition of which is entirely reliant on measurement. Quantum mechanical properties can be exploited to yield measurement results to a greater precision (lesser uncertainty) than that which is permitted by classical methods. This has been mathematically demonstrated by the derivation of theoretical bounds which place a fundamental limit on the uncertainty of a measurement. Furthermore, quantum metrology is of immediate interest in the application of quantum technologies since measurement plays a central role. This thesis focuses on the role of quantum correlations and uncertainty relations which govern the precision bounds. We show how correlations can be distributed amongst limited resources in realistic scenarios, as permitted by current experimental capabilities, to achieve higher precision measurements than current approaches. This is extended to the setting of multiparameter estimation in which we demonstrate a more technologically feasible method of correlation distribution than those previously posited which perform as well as, or worse than, our scheme. Furthermore, a quantum metrology protocol is typically comprised of three stages: probe state preparation, sensing and then readout, where the time required for the first and last stages is usually neglected. We consider the more realistic sensing scenario of time being a limited resource which is divided amongst the three stages and demonstrate the most efficient use of this resource. Additionally, we take an information theoretic approach to quantum mechanical uncertainty relations and derive a one-parameter class of uncertainty relations which supplies more information about the quantum mechanical system of interest than conventional uncertainty relations. Finally, we demonstrate how we can use this class of uncertainty relations to reconstruct information of the state of the quantum mechanical system.