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arXiv:1907.10340

Dissipative Quantum Metrology

Da-Jian Zhang, Jiangbin Gong

Published Jul 24, 2019• 0 citations
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Abstract

Conventional strategies of quantum metrology are built upon POVMs, thereby possessing several general features, including the demolition of the state to be measured, the need of performing a number of measurements, and the degradation of performance under decoherence and dissipation. Here, we propose an innovative measurement scheme, called dissipative adiabatic measurements (DAMs), based on which, we further develop an approach to estimation of parameters characterizing dissipative processes. Unlike a POVM, whose outcome is one of the eigenvalues of an observable, a DAM yields the expectation value of the observable as its outcome, without collapsing the state to be measured. By virtue of the very nature of DAMs, our approach is capable of solving the estimation problem in a state-protective fashion with only $M$ measurements, where $M$ is the number of parameters to be estimated. More importantly, contrary to the common wisdom, it embraces decoherence and dissipation as beneficial effects and offers a Heisenberg-like scaling of precision, thus outperforming conventional strategies. Our DAM-based approach is direct, efficient, and expected to be immensely useful in the context of dissipative quantum information processing.

DOI
10.48550/arxiv.1907.10340

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Conventional strategies of quantum metrology are built upon POVMs, thereby possessing several general features, including the demolition of the state to be measured, the need of performing a number of measurements, and the degradation of performance under decoherence and dissipation. Here, we propose an innovative measurement scheme, called dissipative adiabatic measurements (DAMs), based on which, we further develop an approach to estimation of parameters characterizing dissipative processes. Unlike a POVM, whose outcome is one of the eigenvalues of an observable, a DAM yields the expectation value of the observable as its outcome, without collapsing the state to be measured. By virtue of the very nature of DAMs, our approach is capable of solving the estimation problem in a state-protective fashion with only MMM measurements, where MMM is the number of parameters to be estimated. More importantly, contrary to the common wisdom, it embraces decoherence and dissipation as beneficial effects and offers a Heisenberg-like scaling of precision, thus outperforming conventional strategies. Our DAM-based approach is direct, efficient, and expected to be immensely useful in the context of dissipative quantum information processing.
It is challenged only recently that the precision attainable in any measurement of a physical parameter is fundamentally limited by the quantum Cramér-Rao Bound (QCRB).Here, targeting at measuring parameters in strongly dissipative systems, we propose an innovative measurement scheme called dissipative adiabatic measurement and theoretically show that it can beat the QCRB.Unlike projective measurements, our measurement scheme, though consuming more time, does not collapse the measured state and, more importantly, yields the expectation value of an observable as its measurement outcome, which is directly connected to the parameter of interest.Such a direct connection allows us to extract the value of the parameter from the measurement outcomes in a straightforward manner, with no fundamental limitation on precision, in principle.Our findings not only provide a marked insight into quantum metrology but also are highly useful in dissipative quantum information processing.
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We investigate quantum-enhanced metrology in a triple point criticality and discover that quantum criticality does not always enhance measurement precision. We have developed suitable adiabatic evolution protocols to effectively restrain excitations, which could accelerate the adiabatic evolutions and lead to an exponential super-Heisenberg scaling. This scaling behavior is quite valuable in practical parameter estimating experiments with limited coherence time. Dissipation can strengthen the super-Heisenberg scaling until decoherence increases to dominate in the dissipative dynamics. Additionally, measurement precisions beyond Heisenberg scaling can be experimentally achieved in the trapped ion system. Our findings strongly indicate that criticality-enhanced metrology can indeed significantly enhance measurement precisions to a super-Heisenberg scaling when combining a triple point and beneficial parameter modulations, which will be conducive to the exploration of other super-Heisenberg scaling and their applications.
Experimental characterizations of a quantum system involve the measurement of expectation values of observables for a preparable state $\ensuremath{\mid}\ensuremath{\psi}⟩$ of the quantum system. Such expectation values can be measured by repeatedly preparing $\ensuremath{\mid}\ensuremath{\psi}⟩$ and coupling the system to an apparatus. For this method, the precision of the measured value scales as 1N\frac{1}{\sqrt{N}}N​1​ for NNN repetitions of the experiment. For the problem of estimating the parameter $\ensuremath{\phi}$ in an evolution ${e}^{\ensuremath{-}i\ensuremath{\phi}H}$, it is possible to achieve precision 1N\frac{1}{N}N1​ [the quantum metrology limit; see Giovannetti et al., Phys. Rev. Lett. 96, 010401 (2006)] provided that sufficient information about HHH and its spectrum is available. We consider the more general problem of estimating expectations of operators AAA with minimal prior knowledge of AAA. We give explicit algorithms that approach precision 1N\frac{1}{N}N1​ given a bound on the eigenvalues of AAA or on their tail distribution. These algorithms are particularly useful for simulating quantum systems on quantum computers because they enable efficient measurement of observables and correlation functions. Our algorithms are based on a method for efficiently measuring the complex overlap of $\ensuremath{\mid}\ensuremath{\psi}⟩$ and $U\ensuremath{\mid}\ensuremath{\psi}⟩$, where UUU is an implementable unitary operator. We explicitly consider the issue of confidence levels in measuring observables and overlaps and show that, as expected, confidence levels can be improved exponentially with linear overhead. We further show that the algorithms given here can typically be parallelized with minimal increase in resource usage.