Using entanglement against noise in quantum metrology

We analyze the role of entanglement among probes and with external ancillas in quantum metrology. In the absence of noise, it is known that unentangled sequential strategies can achieve the same Heisenberg scaling of entangled strategies and that external ancillas are useless. This changes in the presence of noise: here we prove that entangled strategies can have higher precision than unentangled ones and that the addition of passive external ancillas can also increase the precision. We analyze some specific noise models and use the results to conjecture a general hierarchy for quantum metrology strategies in the presence of noise.Comment: 7 pages, 4 figures, published versio

Optimal Gaussian Metrology for Generic Multimode Interferometric Circuit

Bounds on the ultimate precision attainable in the estimation of a parameter in Gaussian quantum metrology are obtained when the average number of bosonic probes is fixed. We identify the optimal input probe state among generic (mixed in general) Gaussian states with a fixed average number of probe photons for the estimation of a parameter contained in a generic multimode interferometric optical circuit, namely, a passive linear circuit preserving the total number of photons. The optimal Gaussian input state is essentially a single-mode squeezed vacuum, and the ultimate precision is achieved by a homodyne measurement on the single mode. We also reveal the best strategy for the estimation when we are given $L$ identical target circuits and are allowed to apply passive linear controls in between with an arbitrary number of ancilla modes introduced.Comment: 31 pages, 4 figure

Nonexponential motional damping of impurity atoms in Bose-Einstein condensates

We demonstrate that the damping of the motion of an impurity atom injected at a supercritical velocity into a Bose-Einstein condensate can exhibit appreciable deviation from the exponential law on time scales of $10^{-5}$ s.Comment: revtex, 4 pages + 2 figures (epsi format

Quantum measurement bounds beyond the uncertainty relations

We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision is typically bounded in terms of the variance of an observable.Comment: 6 pages, 3 figure

Minkowski Spacetime and QED from Ontology of Time

Classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the necessary number of postulates. We uncover the intrinsic connection of these areas of physics and describe them using a common symplectic Hamiltonian formalism. Our approach is based on a proper distinction between variables and constants, i.e. on a basic but rigorous ontology of time. We link these concept with the obvious conditions for the possibility of measurements. The derived consequences put the measurement problem of quantum mechanics and the Copenhagen interpretation of the quantum mechanical wavefunction into perspective. According to our (onto-) logic we find that spacetime can not be fundamental. We argue that a geometric interpretation of symplectic dynamics emerges from the isomorphism between the corresponding Lie algebra and the representation of a Clifford algebra. Within this conceptional framework we derive the dimensionality of spacetime, the form of Lorentz transformations and of the Lorentz force and fundamental laws of physics as the Planck-Einstein relation, the Maxwell equations and finally the Dirac equation.Comment: 36 pages, 3 figures, several typos corrected, references with title

Optimal networks for Quantum Metrology: semidefinite programs and product rules

We investigate the optimal estimation of a quantum process that can possibly consist of multiple time steps. The estimation is implemented by a quantum network that interacts with the process by sending an input and processing the output at each time step. We formulate the search of the optimal network as a semidefinite program and use duality theory to give an alternative expression for the maximum payoff achieved by estimation. Combining this formulation with a technique devised by Mittal and Szegedy we prove a general product rule for the joint estimation of independent processes, stating that the optimal joint estimation can achieved by estimating each process independently, whenever the figure of merit is of a product form. We illustrate the result in several examples and exhibit counterexamples showing that the optimal joint network may not be the product of the optimal individual networks if the processes are not independent or if the figure of merit is not of the product form. In particular, we show that entanglement can reduce by a factor K the variance in the estimation of the sum of K independent phase shifts.Comment: 19 pages, no figures, published versio

Probabilistic Perspectives on Collecting Human Uncertainty in Predictive Data Mining

In many areas of data mining, data is collected from humans beings. In this contribution, we ask the question of how people actually respond to ordinal scales. The main problem observed is that users tend to be volatile in their choices, i.e. complex cognitions do not always lead to the same decisions, but to distributions of possible decision outputs. This human uncertainty may sometimes have quite an impact on common data mining approaches and thus, the question of effective modelling this so called human uncertainty emerges naturally. Our contribution introduces two different approaches for modelling the human uncertainty of user responses. In doing so, we develop techniques in order to measure this uncertainty at the level of user inputs as well as the level of user cognition. With support of comprehensive user experiments and large-scale simulations, we systematically compare both methodologies along with their implications for personalisation approaches. Our findings demonstrate that significant amounts of users do submit something completely different (action) than they really have in mind (cognition). Moreover, we demonstrate that statistically sound evidence with respect to algorithm assessment becomes quite hard to realise, especially when explicit rankings shall be built

Magnon Condensation in a Dense Nitrogen-Vacancy Spin Ensemble

The feasibility of creating a Bose-Einstein condensate of magnons using a dense ensemble of nitrogen-vacancy spin defects in diamond is investigated. Through assessing a density-dependent spin exchange interaction strength and the magnetic phase transition temperature ($T_c$) using the Sherrington-Kirkpatrick model, the minimum temperature-dependent concentration for magnetic self-ordering is estimated. For a randomly dispersed spin ensemble, the calculated average exchange constant exceeds the average dipole interaction strengths for concentrations approximately greater than 70 ppm, while $T_c$ is estimated to exceed 10 mK beyond 90 ppm, reaching 300 K at a concentration of approximately 450 ppm. On this basis, the existence of dipole-exchange spin waves and their plane-wave dispersion is postulated and estimated using a semiclassical magnetostatic description. This is discussed along with a $T_c$-based estimate of the four-magnon scattering rate, which indicates magnons and their condensation may be detectable in thin films for concentrations greater than 90 ppm.Comment: 14 pages, 6 figure

Multi-scale metrology for automated non-destructive testing systems

This thesis was previously held under moratorium from 5/05/2020 to 5/05/2022The use of lightweight composite structures in the aerospace industry is now commonplace. Unlike conventional materials, these parts can be moulded into complex aerodynamic shapes, which are diffcult to inspect rapidly using conventional Non-Destructive Testing (NDT) techniques. Industrial robots provide a means of automating the inspection process due to their high dexterity and improved path planning methods. This thesis concerns using industrial robots as a method for assessing the quality of components with complex geometries. The focus of the investigations in this thesis is on improving the overall system performance through the use of concepts from the field of metrology, specifically calibration and traceability. The use of computer vision is investigated as a way to increase automation levels by identifying a component's type and approximate position through comparison with CAD models. The challenges identified through this research include developing novel calibration techniques for optimising sensor integration, verifying system performance using laser trackers, and improving automation levels through optical sensing. The developed calibration techniques are evaluated experimentally using standard reference samples. A 70% increase in absolute accuracy was achieved in comparison to manual calibration techniques. Inspections were improved as verified by a 30% improvement in ultrasonic signal response. A new approach to automatically identify and estimate the pose of a component was developed specifically for automated NDT applications. The method uses 2D and 3D camera measurements along with CAD models to extract and match shape information. It was found that optical large volume measurements could provide suffciently high accuracy measurements to allow ultrasonic alignment methods to work, establishing a multi-scale metrology approach to increasing automation levels. A classification framework based on shape outlines extracted from images was shown to provide over 88% accuracy on a limited number of samples.The use of lightweight composite structures in the aerospace industry is now commonplace. Unlike conventional materials, these parts can be moulded into complex aerodynamic shapes, which are diffcult to inspect rapidly using conventional Non-Destructive Testing (NDT) techniques. Industrial robots provide a means of automating the inspection process due to their high dexterity and improved path planning methods. This thesis concerns using industrial robots as a method for assessing the quality of components with complex geometries. The focus of the investigations in this thesis is on improving the overall system performance through the use of concepts from the field of metrology, specifically calibration and traceability. The use of computer vision is investigated as a way to increase automation levels by identifying a component's type and approximate position through comparison with CAD models. The challenges identified through this research include developing novel calibration techniques for optimising sensor integration, verifying system performance using laser trackers, and improving automation levels through optical sensing. The developed calibration techniques are evaluated experimentally using standard reference samples. A 70% increase in absolute accuracy was achieved in comparison to manual calibration techniques. Inspections were improved as verified by a 30% improvement in ultrasonic signal response. A new approach to automatically identify and estimate the pose of a component was developed specifically for automated NDT applications. The method uses 2D and 3D camera measurements along with CAD models to extract and match shape information. It was found that optical large volume measurements could provide suffciently high accuracy measurements to allow ultrasonic alignment methods to work, establishing a multi-scale metrology approach to increasing automation levels. A classification framework based on shape outlines extracted from images was shown to provide over 88% accuracy on a limited number of samples