General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology

The estimation of parameters characterizing dynamical processes is central to science and technology. The estimation error changes with the number N of resources employed in the experiment (which could quantify, for instance, the number of probes or the probing energy). Typically, it scales as 1/N^(1/2). Quantum strategies may improve the precision, for noiseless processes, by an extra factor 1/N^(1/2). For noisy processes, it is not known in general if and when this improvement can be achieved. Here we propose a general framework for obtaining attainable and useful lower bounds for the ultimate limit of precision in noisy systems. We apply this bound to lossy optical interferometry and atomic spectroscopy in the presence of dephasing, showing that it captures the main features of the transition from the 1/N to the 1/N^(1/2) behaviour as N increases, independently of the initial state of the probes, and even with use of adaptive feedback.Comment: Published in Nature Physics. This is the revised submitted version. The supplementary material can be found at http://www.nature.com/nphys/journal/v7/n5/extref/nphys1958-s1.pd

Quantum sensing networks for the estimation of linear functions

The theoretical framework for networked quantum sensing has been developed to a great extent in the past few years, but there are still a number of open questions. Among these, a problem of great significance, both fundamentally and for constructing efficient sensing networks, is that of the role of inter-sensor correlations in the simultaneous estimation of multiple linear functions, where the latter are taken over a collection local parameters and can thus be seen as global properties. In this work we provide a solution to this when each node is a qubit and the state of the network is sensor-symmetric. First we derive a general expression linking the amount of inter-sensor correlations and the geometry of the vectors associated with the functions, such that the asymptotic error is optimal. Using this we show that if the vectors are clustered around two special subspaces, then the optimum is achieved when the correlation strength approaches its extreme values, while there is a monotonic transition between such extremes for any other geometry. Furthermore, we demonstrate that entanglement can be detrimental for estimating non-trivial global properties, and that sometimes it is in fact irrelevant. Finally, we perform a non-asymptotic analysis of these results using a Bayesian approach, finding that the amount of correlations needed to enhance the precision crucially depends on the number of measurement data. Our results will serve as a basis to investigate how to harness correlations in networks of quantum sensors operating both in and out of the asymptotic regime

Thermal quantum metrology in memoryless and correlated environments

In bosonic quantum metrology, the estimate of a loss parameter is typically performed by means of pure states, such as coherent, squeezed or entangled states, while mixed thermal probes are discarded for their inferior performance. Here we show that thermal sources with suitable correlations can be engineered in such a way to approach, or even surpass, the error scaling of coherent states in the presence of general Gaussian decoherence. Our findings pave the way for practical quantum metrology with thermal sources in optical instruments (e.g., photometers) or at different wavelengths (e.g., far infrared, microwave or X-ray) where the generation of quantum features, such as coherence, squeezing or entanglement, may be extremely challenging

Energy-efficient quantum frequency estimation

The problem of estimating the frequency of a two-level atom in a noisy environment is studied. Our interest is to minimise both the energetic cost of the protocol and the statistical uncertainty of the estimate. In particular, we prepare a probe in a `GHZ-diagonal' state by means of a sequence of qubit gates applied on an ensemble of n atoms in thermal equilibrium. Noise is introduced via a phenomenological time-nonlocal quantum master equation, which gives rise to a phase-covariant dissipative dynamics. After an interval of free evolution, the n-atom probe is globally measured at an interrogation time chosen to minimise the error bars of the final estimate. We model explicitly a measurement scheme which becomes optimal in a suitable parameter range, and are thus able to calculate the total energetic expenditure of the protocol. Interestingly, we observe that scaling up our multipartite entangled probes offers no precision enhancement when the total available energy E is limited. This is at stark contrast with standard frequency estimation, where larger probes---more sensitive but also more `expensive' to prepare---are always preferred. Replacing E by the resource that places the most stringent limitation on each specific experimental setup, would thus help to formulate more realistic metrological prescriptions

The elusive Heisenberg limit in quantum enhanced metrology

We provide efficient and intuitive tools for deriving bounds on achievable precision in quantum enhanced metrology based on the geometry of quantum channels and semi-definite programming. We show that when decoherence is taken into account, the maximal possible quantum enhancement amounts generically to a constant factor rather than quadratic improvement. We apply these tools to derive bounds for models of decoherence relevant for metrological applications including: dephasing,depolarization, spontaneous emission and photon loss.Comment: 10 pages, 4 figures, presentation imporved, implementation of the semi-definite program finding the precision bounds adde

Wpływ zmian klimatycznych na choroby zakaźne

Impacts of climate change on infectious diseases. Climate warming may have significant impacts on human health, including changes in the distribution and seasonality of vector-borne diseases. We discuss the consequences of climate change on infectious diseases. Effects of transmission of the imported tropical diseases in Europe are discussed

The anatomy of a working class neighbourhood West Sparkbrook 1871 to 1914

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN038987 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Improved Quantum Magnetometry beyond the Standard Quantum Limit

Under ideal conditions, quantum metrology promises a precision gain over classical techniques scaling quadratically with the number of probe particles. At the same time, no-go results have shown that generic, uncorrelated noise limits the quantum advantage to a constant factor. In frequency estimation scenarios, however, there are exceptions to this rule and, in particular, it has been found that transversal dephasing does allow for a scaling quantum advantage. Yet, it has remained unclear whether such exemptions can be exploited in practical scenarios. Here, we argue that the transversal-noise model applies to the setting of recent magnetometry experiments and show that a scaling advantage can be maintained with one-axis-twisted spin-squeezed states and Ramsey-interferometry-like measurements. This is achieved by exploiting the geometry of the setup that, as we demonstrate, has a strong influence on the achievable quantum enhancement for experimentally feasible parameter settings. When, in addition to the dominant transversal noise, other sources of decoherence are present, the quantum advantage is asymptotically bounded by a constant, but this constant may be significantly improved by exploring the geometry.Peer Reviewe