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arXiv:1209.2731 · New Journal of Physics

Coherent measurements in quantum metrology

Kaonan Micadei, Daniel A. Rowlands, Felix A. Pollock, Lucas C. Céleri, Roberto M. Serra, Kavan Kishore Modi

Published Feb 18, 2015• 43 citations
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Abstract

It is well known that a quantum correlated probe can yield better precision in estimating an unknown parameter than classically possible. However, how such a quantum probe should be measured remains somewhat elusive. We examine the role of measurements in quantum metrology by considering two types of readout strategies: coherent , where all probes are measured simultaneously in an entangled basis; and adaptive , where probes are measured sequentially, with each measurement one way conditioned on the prior outcomes. Here we firstly show that for classically correlated probes the two readout strategies yield the same precision. Secondly, we construct an example of a noisy multipartite quantum system where coherent readout yields considerably better precision than adaptive readout. This highlights a fundamental difference between classical and quantum parameter estimation. From the practical point of view, our findings are relevant for the optimal design of precision-measurement quantum devices.

DOI
10.1088/1367-2630/17/2/023057

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It is well known that a quantum correlated probe can yield better precision in estimating an unknown parameter than classically possible. However, how such a quantum probe should be measured remains somewhat elusive. We examine the role of measurements in quantum metrology by considering two types of readout strategies: coherent , where all probes are measured simultaneously in an entangled basis; and adaptive , where probes are measured sequentially, with each measurement one way conditioned on the prior outcomes. Here we firstly show that for classically correlated probes the two readout strategies yield the same precision. Secondly, we construct an example of a noisy multipartite quantum system where coherent readout yields considerably better precision than adaptive readout. This highlights a fundamental difference between classical and quantum parameter estimation. From the practical point of view, our findings are relevant for the optimal design of precision-measurement quantum devices.
Quantum mechanical systems can be used to out perform classical ones in several tasks. For instance, quantum correlations can be employed to beat the shot-noise limit in metrology protocols. Such parameter estimation methods are crucial for both advances in science and the development of technologies. Almost all quantum technologies operate with some level of noise and how quantum-enhancement fares in the presence of noise is still unclear. Here we show that, when a system in mixed multipartite quantum state is used to estimate a parameter, the information must be decoded by coherent interactions between the parts of the probe. On the other hand, noiseless quantum metrology protocols are adaptively additive for any pure entangled states, that is, no coherent processing is necessary in this case. This leads to an operational interpretation for the ability of performing coherent interactions in noisy parameter estimation and highlights a cornerstone difference between mixed and pure states. This result has fundamental importance in the search for the source of quantum advantage and it also has practical relevance for the designing of new high-precision-measurement devices.
We introduce quantum parameter estimation with the encoding being via a quantum measurement. We quantify the precision for estimating parameters characterizing a general two-outcome qubit measurement, considering two cases: when the outcomes of the encoding measurement are recorded and when the same are ignored. We find that in a large variety of such estimation scenarios, forgetting the outcomes yields higher precision. We derive a necessary criterion under which remembering the measurement outcomes provides better precision in comparison to the outcome-forgotten strategy. Furthermore, we establish a necessary and sufficient criterion for the simultaneous estimation of multiple parameters encoded by an arbitrary quantum process, including those involving measurements, using qubit probes, and find when the quantum Cramér−-−Rao bound is valid and achievable. For simultaneous estimation of two parameters characterizing the measurement, we find that the achievable quantum Cramér−-−Rao bound can be a valid precision bound only when the measurement direction depends on the parameters of interest.
Quantum metrology aims to exploit quantum phenomena to overcome classical limitations in the estimation of relevant parameters. We consider a probe undergoing a phase shift $\ensuremath{\varphi}$ whose generator is randomly sampled according to a distribution with unknown concentration $\ensuremath{\kappa}$, which introduces a physical source of noise. We then investigate strategies for the joint estimation of the two parameters $\ensuremath{\varphi}$ and $\ensuremath{\kappa}$ given a finite number NNN of interactions with the phase imprinting channel. We consider both single qubit and multipartite entangled probes, and identify regions of the parameters where simultaneous estimation is advantageous, resulting in up to a twofold reduction in resources. Quantum enhanced precision is achievable at moderate NNN, while for sufficiently large NNN classical strategies take over and the precision follows the standard quantum limit. We show that full-scale entanglement is not needed to reach such an enhancement, as efficient strategies using significantly fewer qubits in a scheme interpolating between the conventional sequential and parallel metrological schemes yield the same effective performance. These results may have relevant applications in optimization of sensing technologies.
We report an experimental investigation of the role of measurement in quantum metrology when the states of the probes are mixed. In particular, we investigated optimized local measurements and general global projective measurements, involving entangling operations, on noisy Werner states of polarization entangled photons. We demonstrate experimentally that global measurement presents an advantage in parameter estimation with respect to the optimized local strategy. Moreover, the global strategy provides unambiguous information about the parameter of interest even when the amount of noise is not well characterized. This shows that the coherence in quantum operations, such as the Bell-state projection device used in our protocol, can be used to further boost the quantum advantage in metrology and play a fundamental role in the design of future quantum measurement devices.
The simultaneous estimation of multiple unknown parameters is the most general scenario in quantum sensing. Quantum multiparameter estimation theory provides fundamental bounds on the achievable precision of simultaneous estimation. However, these bounds can become singular (no finite bound exists) in multiparameter sensing due to parameter interdependencies, limited probe accessibility, and insufficient measurement outcomes. Here, we address the singularity issue in quantum sensing through a simple mechanism based on a sequential measurement strategy. This sensing scheme overcomes the singularity constraint and enables the simultaneous estimation of multiple parameters with a local and fixed measurement throughout the sensing protocol. This is because sequential measurements, involving consecutive steps of local measurements followed by probe evolution, inherently produce correlated measurement data that grows exponentially with the number of sequential measurements. Finally, through two different examples, namely a strongly correlated probe and a light-matter system, we demonstrate how such singularities are reflected when inferring the unknown parameters through Bayesian estimation.
Relevant metrological scenarios involve the simultaneous estimation of multiple parameters. The fundamental ingredient to achieve quantum-enhanced performance is based on the use of appropriately tailored quantum probes. However, reaching the ultimate resolution allowed by physical laws requires nontrivial estimation strategies from both a theoretical and a practical point of view. A crucial tool for this purpose is the application of adaptive learning techniques. Indeed, adaptive strategies provide a flexible approach to obtain optimal parameter-independent performance and optimize convergence to the fundamental bounds with a limited amount of resources. Here, we combine on the same platform quantum-enhanced multiparameter estimation attaining the corresponding quantum limit and adaptive techniques. We demonstrate the simultaneous estimation of three optical phases in a programmable integrated photonic circuit, in the limited-resource regime. The obtained results show the possibility of successfully combining different fundamental methodologies towards transition to quantum sensors applications.