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arXiv:2006.08455 · Physical Review A

Experimental demonstration of the advantage of using coherent measurements for phase estimation in the presence of depolarizing noise

Rodrigo S. Piera, Stephen Patrick Walborn, G. H. Aguilar

Published Jan 7, 2021• 7 citations
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Abstract

We report an experimental investigation of the role of measurement in quantum metrology when the states of the probes are mixed. In particular, we investigate optimized local measurements and general global projective measurements, involving entangling operations, of 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.

DOI
10.1103/physreva.103.012602

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We report an experimental investigation of the role of measurement in quantum metrology when the states of the probes are mixed. In particular, we investigate optimized local measurements and general global projective measurements, involving entangling operations, of 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.
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 metrological ability of carefully designed probes can be wrecked by the presence of noise which alters their evolution, reducing the information on the parameter of interest. This spoils the signal-to-noise ratio of any possible measurement. Here we show an experiment in which the introduction of an ancilla improves the estimation of an optical phase with respect to a standard single-qubit strategy. The advantage originates from the coherent coupling of the probe and the ancilla both at the initialization and measurement stages, generating and selecting a subset of overall configurations less affected by the noise.
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.
A generic qubit unitary operator affected by quantum noise is duplicated and inserted in a coherently superposed channel, superposing two paths offered to a probe qubit across the noisy unitary, and driven by a control qubit. A characterization is performed of the transformation realized by the superposed channel on the joint state of the probe-control qubit pair. The superposed channel is then specifically analyzed for the fundamental metrological task of phase estimation on the noisy unitary, with the performance assessed by the Fisher information, classical or quantum. A comparison is made with conventional estimation techniques and also with a quantum switched channel with indefinite causal order recently investigated for a similar task of phase estimation. In the analysis here, a first important observation is that the control qubit of the superposed channel, although it never directly interacts with the unitary being estimated, can nevertheless be measured alone for effective estimation, while discarding the probe qubit that interacts with the unitary. This property is also present with the switched channel but is inaccessible with conventional techniques. The optimal measurement of the control qubit here is characterized in general conditions. A second important observation is that the noise plays an essential role in coupling the control qubit to the unitary, and that the control qubit remains operative for phase estimation at very strong noise, even with a fully depolarizing noise, whereas conventional estimation and the switched channel become inoperative in these conditions. The results extend the analysis of the capabilities of coherently controlled channels which represent novel devices exploitable for quantum signal and information processing.
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.
The quantum Fisher information and quantum correlation parameters are employed to study the application of nonclassical light to the problem of parameter estimation. It is shown that the optimal measurement sensitivity of a quantum state is determined by its intermode correlations (which depends on path entanglement) and intramode correlations (which depends on the photon statistics). In light of these results, we consider the performance of quantum-enhanced optical interferometers. Furthermore, we propose a Heisenberg-limited metrology protocol involving standard elements from passive and active linear optics, for which the quantum Cram\'er-Rao bound is saturated with an intensity measurement. Interestingly, the quantum advantage for this scheme is derived solely from the nonclassical photon statistics of the probe state and does not depend on entanglement. We study the performance of this scheme in the presence of realistic losses and consequently predict a substantial enhancement over the shot-noise limit with current technological capabilities.