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arXiv:2103.14402

Quantum sensing to suppress systematic errors with measurements in the Zeno regime

Alisa Shimada, Hideaki Hakoshima, Suguru Endo, Kaoru Yamamoto, Yuichiro Matsuzaki

Published Mar 26, 2021• 0 citations
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Abstract

Quantum magnetic field sensing is an important technology for material science and biology. Although experimental imperfections affect the sensitivity, repetitions of the measurements decrease the estimation uncertainty by a square root of the total number of the measurements if there are only statistical errors. However, it is difficult to precisely characterize the coherence time of the system because it fluctuates in time in realistic conditions, which induces systematic errors. In this case, due to residual bias of the measured values, estimation uncertainty cannot be lowered than a finite value even in the limit of the infinite number of measurements. On the basis of the fact that the decoherence dynamics in the so-called Zeno regime are not significant compared to other regimes, we propose a novel but very simple protocol to use measurements in the Zeno regime for reducing systematic errors. Our scheme allows the estimation uncertainty $δ^2 ω$ to scale as $L^{1/4}$ where $L$ denotes the number of the measurements even when we cannot precisely characterize the coherence time.

DOI
10.48550/arxiv.2103.14402

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Quantum magnetic field sensing is an important technology for material science and biology. Although experimental imperfections affect the sensitivity, repetitions of the measurements decrease the estimation uncertainty by a square root of the total number of the measurements if there are only statistical errors. However, it is difficult to precisely characterize the coherence time of the system because it fluctuates in time in realistic conditions, which induces systematic errors. In this case, due to residual bias of the measured values, estimation uncertainty cannot be lowered than a finite value even in the limit of the infinite number of measurements. On the basis of the fact that the decoherence dynamics in the so-called Zeno regime are not significant compared to other regimes, we propose a novel but very simple protocol to use measurements in the Zeno regime for reducing systematic errors. Our scheme allows the estimation uncertainty δ2ωδ^2 ωδ2ω to scale as L1/4L^{1/4}L1/4 where LLL denotes the number of the measurements even when we cannot precisely characterize the coherence time.
The sensitivity afforded by quantum sensors is limited by decoherence. Quantum error correction (QEC) can enhance sensitivity by suppressing decoherence, but it has a side effect: it biases a sensor's output in realistic settings. If unaccounted for, this bias can systematically reduce a sensor's performance in experiment, and also give misleading values for the minimum detectable signal in theory. We analyze this effect in the experimentally motivated setting of continuous-time QEC, showing both how one can remedy it, and how incorrect results can arise when one does not.
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Quantum sensors have the potential to outperform their classical counterparts. For classical sensing, the uncertainty of the estimation of the target fields scales inversely with the square root of the measurement time T. On the other hand, by using quantum resources, we can reduce this scaling of the uncertainty with time to 1/T. However, as quantum states are susceptible to dephasing, it has not been clear whether we can achieve sensitivities with a scaling of 1/T for a measurement time longer than the coherence time. Here, we propose a scheme that estimates the amplitude of globally applied fields with the uncertainty of 1/T for an arbitrary time scale under the effect of dephasing. We use one-way quantum-computing-based teleportation between qubits to prevent any increase in the correlation between the quantum state and its local environment from building up and have shown that such a teleportation protocol can suppress the local dephasing while the information from the target fields keeps growing. Our method has the potential to realize a quantum sensor with a sensitivity far beyond that of any classical sensor.
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Quantum sensing estimates a physical parameter encoded in the state of a probe; with independent spin probes the precision follows the standard quantum limit. Studies of sensing precision often assume that the parameters entering the model, such as the noise, are known. In practice these parameters are not always known, and a mismatch between the assumed and actual values induces a systematic error. Here we study single-qubit Ramsey magnetometry of a DC magnetic field under an unknown detuning between the actual and nominal spin frequencies: A first pulse puts the qubit into a superposition of its two states, the field to be sensed then adds a relative phase during an exposure stage, and a second pulse enables the readout. In our setting, the field acts only during the exposure stage, whereas the detuning acts throughout the whole protocol. We analyze how the detuning biases the estimate, preventing the total estimation error from following the standard quantum limit. We then construct a composite-pulse preparation and readout that exploits the difference in the intervals over which the field and the detuning act to cancel the detuning to first order. We evaluate the performance of this composite-pulse protocol and show that it suppresses the detuning-induced bias.
The signal to noise ratio of quantum sensing protocols scales with the square root of the coherence time. Thus, increasing this time is a key goal in the field. By utilizing quantum error correction, we present a novel way of prolonging such coherence times beyond the fundamental limits of current techniques. We develop an implementable sensing protocol that incorporates error correction, and discuss the characteristics of these protocols in different noise and measurement scenarios. We examine the use of entangled versue untangled states, and error correction's reach of the Heisenberg limit. The effects of error correction on coherence times are calculated and we show that measurement precision can be enhanced for both one-directional and general noise.