Estimation with ultimate quantum precision of the transverse displacement between two photons via two-photon interference sampling measurements

We present a quantum sensing scheme achieving the ultimate quantum sensitivity in the estimation of the transverse displacement between two photons interfering at a balanced beam splitter, based on transverse-momentum sampling measurements at the output. This scheme can possibly lead to enhanced high-precision nanoscopic techniques, such as super-resolved single-molecule localization microscopy with quantum dots, by circumventing the requirements in standard direct imaging of cameras resolution at the diffraction limit, and of highly magnifying objectives. Interestingly, the ultimate spatial precision in nature is achieved irrespectively of the overlap of the two displaced photonic wavepackets. This opens a new research paradigm based on the interface between spatially resolved quantum interference and quantum-enhanced spatial sensitivity.Comment: 13 pages, 4 figure

The Role of Auxiliary Stages in Gaussian Quantum Metrology

The optimization of the passive and linear networks employed in quantum metrology, the field that studies and devises quantum estimation strategies to overcome the levels of precision achievable via classical means, appears to be an essential step in certain metrological protocols achieving the ultimate Heisenberg-scaling sensitivity. This optimization is generally performed by adding degrees of freedom by means of auxiliary stages, to optimize the probe before or after the interferometric evolution, and the choice of these stages ultimately determines the possibility to achieve a quantum enhancement. In this work we review the role of the auxiliary stages and of the extra degrees of freedom in estimation schemes, achieving the ultimate Heisenberg limit, which employ a squeezed-vacuum state and homodyne detection. We see that, after the optimization for the quantum enhancement has been performed, the extra degrees of freedom have a minor impact on the precision achieved by the setup, which remains essentially unaffected for networks with a larger number of channels. These degrees of freedom can thus be employed to manipulate how the information about the structure of the network is encoded into the probe, allowing us to perform quantum-enhanced estimations of linear and non-linear functions of independent parameters

Momentum-entangled two-photon interference for quantum-limited transverse-displacement estimation

We propose a scheme achieving the ultimate quantum precision for the estimation of the transverse displacement between two interfering photons. Such a transverse displacement could be caused, for example, by the refracting properties of the propagation medium, or by the orientation of a system of mirrors. By performing transverse-momentum sampling interference between polarization-entangled pairs of photons that propagate with different momenta, we show that it is possible to perform transverse-displacement estimation with a precision that increases with the difference of the transverse momenta of the photons. Moreover, we show that for the estimation of small displacements, it is possible to simplify the measurement scheme replacing the transverse-momentum resolving detectors with bucket detectors without any loss in sensitivity. More fundamentally, we demonstrate that it is the quantum interference arising from two-photon entanglement in the transverse momenta at the very heart of the foreseen quantum-limited sensitivity in the spatial domain.Comment: 5 pages, 3 figure

Distance sensing emerging from second-order interference of thermal light

We introduce and describe a technique for distance sensing, based on second-order interferometry of thermal light. The method is based on measuring correlation between intensity fluctuations on two detectors, and provides estimates of the distances separating a remote mask from the source and the detector, even when such information cannot be retrieved by first-order intensity measurements. We show how the sensitivity to such distances is intimately connected to the degree of correlation of the measured interference pattern in different experimental scenarios and independently of the spectral properties of light. Remarkably, this protocol can be also used to measure the distance of remote reflective objects in the presence of turbulence. We demonstrate the emergence of new critical parameters which benchmark the degree of second-order correlation, describing the counterintuitive emergence of spatial second-order interference not only in the absence of (first-order) coherence at both detectors but also when first order interference is observed at one of the two detectors.Comment: 6 pages, 3 figure

Antiphospholipid Antibodies and Heart Failure with Preserved Ejection Fraction. The Multicenter ATHERO-APS Study

The prevalence of heart failure with preserved ejection fraction (HFpEF) in patients with antiphospholipid syndrome (APS) is unknown. A prospective multicenter cohort study including 125 patients was conducted: 91 primary APS (PAPS), 18 APS-SLE, and 16 carriers. HFpEF was diagnosed according to the 2019 European Society of Cardiology criteria: patients with ≥5 points among major and minor functional and morphological criteria including NT-ProBNP > 220 pg/mL, left atrial (LA) enlargement, increased left ventricular filling pressure. Overall, 18 (14.4%) patients were diagnosed with HFpEF; this prevalence increased from 6.3% in carriers to 13.2% in PAPS and 27.8% in APS-SLE. Patients with HFpEF were older and with a higher prevalence of hypertension and previous arterial events. At logistic regression analysis, age, arterial hypertension, anticardiolipin antibodies IgG > 40 GPL (odds ratio (OR) 3.43, 95% confidence interval (CI) 1.09-10.77, p = 0.035), anti β-2-glycoprotein-I IgG > 40 GPL (OR 5.28, 1.53-18.27, p = 0.009), lupus anticoagulants DRVVT > 1.25 (OR 5.20, 95% CI 1.10-24.68, p = 0.038), and triple positivity (OR 3.56, 95% CI 1.11-11.47, p = 0.033) were associated with HFpEF after adjustment for age and sex. By multivariate analysis, hypertension (OR 19.49, 95% CI 2.21-171.94, p = 0.008), age (OR 1.07, 95% CI 1.00-1.14, p = 0.044), and aβ2GPI IgG > 40 GPL (OR 8.62, 95% CI 1.23-60.44, p = 0.030) were associated with HFpEF. HFpEF is detectable in a relevant proportion of APS patients. The role of aPL in the pathogenesis and prognosis of HFpEF needs further investigation

Estimation with Heisenberg-Scaling Sensitivity of a Single Parameter Distributed in an Arbitrary Linear Optical Network

Quantum sensing and quantum metrology propose schemes for the estimation of physical properties, such as lengths, time intervals, and temperatures, achieving enhanced levels of precision beyond the possibilities of classical strategies. However, such an enhanced sensitivity usually comes at a price: the use of probes in highly fragile states, the need to adaptively optimise the estimation schemes to the value of the unknown property we want to estimate, and the limited working range, are some examples of challenges which prevent quantum sensing protocols to be practical for applications. This work reviews two feasible estimation schemes which address these challenges, employing easily realisable resources, i.e., squeezed light, and achieve the desired quantum enhancement of the precision, namely the Heisenberg-scaling sensitivity. In more detail, it is here shown how to overcome, in the estimation of any parameter affecting in a distributed manner multiple components of an arbitrary M-channel linear optical network, the need to iteratively optimise the network. In particular, we show that this is possible with a single-step adaptation of the network based only on a prior knowledge of the parameter achievable through a “classical” shot-noise limited estimation strategy. Furthermore, homodyne measurements with only one detector allow us to achieve Heisenberg-limited estimation of the parameter. We further demonstrate that one can avoid the use of any auxiliary network at the price of simultaneously employing multiple detectors

Estimation with Heisenberg-Scaling Sensitivity of a Single Parameter Distributed in an Arbitrary Linear Optical Network

Quantum sensing and quantum metrology propose schemes for the estimation of physical properties, such as lengths, time intervals, and temperatures, achieving enhanced levels of precision beyond the possibilities of classical strategies. However, such an enhanced sensitivity usually comes at a price: the use of probes in highly fragile states, the need to adaptively optimise the estimation schemes to the value of the unknown property we want to estimate, and the limited working range, are some examples of challenges which prevent quantum sensing protocols to be practical for applications. This work reviews two feasible estimation schemes which address these challenges, employing easily realisable resources, i.e., squeezed light, and achieve the desired quantum enhancement of the precision, namely the Heisenberg-scaling sensitivity. In more detail, it is here shown how to overcome, in the estimation of any parameter affecting in a distributed manner multiple components of an arbitrary M-channel linear optical network, the need to iteratively optimise the network. In particular, we show that this is possible with a single-step adaptation of the network based only on a prior knowledge of the parameter achievable through a “classical” shot-noise limited estimation strategy. Furthermore, homodyne measurements with only one detector allow us to achieve Heisenberg-limited estimation of the parameter. We further demonstrate that one can avoid the use of any auxiliary network at the price of simultaneously employing multiple detectors.</jats:p

Quantum enhancement in time-delays estimation through spectrally resolved two-photon interference

The quantum interference occurring between two indistinguishable photons impinging on the two input faces of a beam-splitter can be exploited for a range of applications, from quantum optical coherence tomography, to quantum metrology including time intervals measurements. In the latter, recent advances managed to reach a resolution in the estimation of the delay between the two photons of the order of attoseconds, i.e. in the nanometer scale. Unfortunately, these techniques are highly affected in the estimation precision by any experimental distinguishability between the photons at the detectors. Here, we perform an analysis of the precision achievable in the estimation of the delay between two independent photons interfering at a beam-splitter when frequency-resolved measurements are employed. Remarkably, we show that the observation of the spectra of the photons at the output ports when coincidence and bunching events are recorded, largely enhance the precision of the estimation for any degree of distinguishability between the photons at the detectors. In particular, we find that such scheme is effective also for temporal delays much larger than the coherence time of each photons, a regime in which standard two-photon interferometers or spectral analyses at the single-photon level, do not provide any information. Furthermore, we show that by increasing the bandwidth of the photons it is possible to further increase quadratically the precision in the estimation, differently from non-resolved two-photon interference where the precision degrades for large bandwidth values. Therefore, such estimation scheme with frequency-resolving detectors allows to substantially enhance the precision of measurements of time delays. Relevant applications can range form the characterization of two-dimensional nanomaterials to the analysis of biological samples, including DNA and cell membranes.Comment: 16 pages, 3 figure

Non-adaptive Heisenberg-limited metrology with multi-channel homodyne measurements

AbstractWe show a protocol achieving the ultimate Heisenberg-scaling sensitivity in the estimation of a parameter encoded in a generic linear network, without employing any auxiliary networks, and without the need of any prior information on the parameter nor on the network structure. As a result, this protocol does not require a prior coarse estimation of the parameter, nor an adaptation of the network. The scheme we analyse consists of a single-mode squeezed state and homodyne detectors in each of the M output channels of the network encoding the parameter, making it feasible for experimental applications.</jats:p