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arXiv:2102.00609 · Physical Review Applied

Threshold for a Discrete-Variable Sensor of Quantum Reservoirs

Wei Wu, Zhen Peng, Si-Yuan Bai, Jun-Hong An

Published May 19, 2021• 19 citations
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Abstract

Quantum sensing employs quantum resources of a sensor to attain a smaller estimation error of physical quantities than the limit constrained by classical physics. To measure a quantum reservoir, which is significant in decoherence control, a nonunitary-encoding sensing scheme becomes necessary. However, previous studies showed that the reservoir-induced degradation to quantum resources of the sensor makes the errors divergent with the increase of encoding time. We here propose a scheme to use $N$ two-level systems as the sensor to measure a quantum reservoir. A threshold, above which the shot-noise-limited sensing error saturates or even persistently decreases with the encoding time, is uncovered. Our analysis reveals that it is due to the formation of a bound state of the total sensor-reservoir system. Solving the outstanding error-divergency problem in previous studies, our result supplies an insightful guideline in realizing a sensitive measurement of quantum reservoirs.

DOI
10.1103/physrevapplied.15.054042

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Quantum sensing employs quantum resources of a sensor to attain a smaller estimation error of physical quantities than the limit constrained by classical physics. To measure a quantum reservoir, which is significant in decoherence control, a nonunitary-encoding sensing scheme becomes necessary. However, previous studies showed that the reservoir-induced degradation to quantum resources of the sensor makes the errors divergent with the increase of encoding time. We here propose a scheme to use NNN two-level systems as the sensor to measure a quantum reservoir. A threshold, above which the shot-noise-limited sensing error saturates or even persistently decreases with the encoding time, is uncovered. Our analysis reveals that it is due to the formation of a bound state of the total sensor-reservoir system. Solving the outstanding error-divergency problem in previous studies, our result supplies an insightful guideline in realizing a sensitive measurement of quantum reservoirs.
Quantum sensing explores protocols using the quantum resource of sensors to achieve highly sensitive measurement of physical quantities. The conventional schemes generally use unitary dynamics to encode quantities into sensor states. In order to measure the spectral density of a quantum reservoir, which plays a vital role in controlling the reservoir-caused decoherence to microscopic systems, we propose a nonunitary-encoding optical sensing scheme. Although the nonunitary dynamics for encoding in turn degrades the quantum resource, we surprisingly find a mechanism to make the encoding time a resource to improve the precision and to make the squeezing of the sensor a resource to surpass the shot-noise limit. Our result shows that it is due to the formation of a sensor-reservoir bound state. Enriching the family of quantum sensing, our scheme gives an efficient way to measure the quantum reservoir and might supply an insightful support to decoherence control.
The rapidly developing quantum technologies and thermodynamics have put forward a requirement to precisely control and measure the temperature of microscopic matter at the quantum level. Many quantum thermometry schemes have been proposed. However, precisely measuring low temperature is still challenging because the obtained sensing errors generally tend to diverge with decreasing temperature. Using a continuous-variable system as a thermometer, we propose non-Markovian quantum thermometry to measure the temperature of a quantum reservoir. A mechanism to make the sensing error $\ensuremath{\delta}T$ scale with the temperature TTT as the Landau bound $\ensuremath{\delta}T\ensuremath{\simeq}T$ in the full-temperature regime is discovered. Our analysis reveals that it is the quantum criticality of the total thermometer-reservoir system that causes this enhanced sensitivity. Efficiently avoiding the error-divergence problem, our result gives an efficient way to precisely measure the low temperature of quantum systems.
Quantum sensors hold great promise for achieving better sensitivity in the measurement of physical quantities compared to their classical counterparts. However, the conditions under which quantum advantage in sensing can be achieved are rather restrictive, and most quantum enhancements in sensing are lost in the presence of noise, errors, or a poorly calibrated system. To overcome these limitations, we are motivated to import ideas from fault-tolerant quantum computing to quantum sensing. Specifically, we consider a qubit noise model where the probability of phase-flip errors is exponentially smaller (in qubit number) compared to the probability of bit-flip errors that occur with probability ppp. For this noise structure, we demonstrate that, given a total sensing time TTT, Heisenberg scaling can be attained for times up to T∝1/p(N+1)/2T\propto 1/p^{(N+1)/2}T∝1/p(N+1)/2 for a NNN-qubit repetition code, in contrast with T∝1/pT\propto 1/pT∝1/p without using a fault-tolerant sensing protocol.
We propose an approach to implement a supersensitive estimation of the key parameters of the Ohmic-family spectral density with coherent spin states as the quantum sensor. This method can dramatically improve the estimation precision of the reservoir coupling strength as well as the cutoff frequency of the spectral density, by using both the number of spins NNN and encoding time ttt as effective resources. The quantum Fisher information indicates that the estimation sensitivity of the spectral density can surpass the shot-noise limit for all the sub-Ohmic, Ohmic, and super-Ohmic reservoirs. In particular, for super-Ohmic reservoirs, the precision can achieve a scaling $\ensuremath{\propto}1/(Nt)$. We also present the measurement scheme which can saturate the quantum Cram\'er-Rao bound.
Abstract Quantum Fisher information quantifies the sensitivity encoded in a parameter-dependent quantum state, whereas the performance of a practical sensor is limited by the information that survives the physical channel and can be extracted by the available receiver. We introduce an accessible Fisher-information framework based on a physically admissible family of measurements and use it to separate state-level sensitivity, channel degradation, and receiver limitations. The framework is applied to Ramsey and NOON interferometry, squeezed-state displacement sensing, two-level thermometry, and multiparameter qubit sensing. We show that resource normalization, finite visibility, readout errors, measurement rank, shot allocation, calibration uncertainty, and nuisance parameters can substantially modify the experimentally available advantage. For squeezed-state sensing, homodyne-axis misalignment produces a finite optimal squeezing, while bounded calibration uncertainty leads to a robust operating rule. In the pure-loss model considered here, attenuation reduces the attainable information without shifting this optimum. The results provide practical design rules that connect quantum-enhanced state preparation with realistic measurement constraints and experimentally extractable sensing performance.
We propose a continuous-variable quantum sensing scheme, in which a harmonic oscillator is employed as the probe to estimate the parameters in the spectral density of a quantum reservoir, within a non-Markovian dynamical framework. It is revealed that the sensing sensitivity can be effectively boosted by (i) optimizing the weight of the momentum-position-type coupling in the whole probe-reservoir interaction Hamiltonian, (ii) the initial quantum squeezing resource provided by the probe, (iii) the noncanonical equilibration induced by the non-Markovian effect, and (iv) applying an external driving field. Our results may have some potential applications in understanding and controlling the decoherence of dissipative continuous-variable systems.