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The concept of discrepancy plays an important role in the study of uniformity properties of point sets. For sets of random points, the discrepancy is a random variable. We apply techniques from quantum field theory to translate the problem…
Polarization is one of light's most versatile degrees of freedom for both classical and quantum applications. The ability to measure light's state of polarization and changes therein is thus essential; this is the science of polarimetry. It…
We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors…
The process of measuring a two-level quantum system was examined by applying Hamiltonian formalism. For the measurement of an observable that does not commute with the system Hamiltonian, a non-trivial relationship among the strength of…
We re-analyse the optomechanical interferometer experiment proposed by Marshall, Simon, Penrose and Bouwmeester with the help of a recently developed quantum-classical hybrid theory. This leads to an alternative evaluation of the mirror…
We provide a setup by which one can recover the geometry of spacetime from local measurements of quantum particle detectors coupled to a quantum field. Concretely, we show how one can recover the field's correlation function from…
In this paper, we use the non-linear dynamics of the individual quantum trajectories of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with an accuracy above the…
A quadrature mirror filter (QMF) function can be considered as the transition function for a Markov process on the unit interval. The QMF functions that generate scaling functions for multiresolution analyses are then distinguished by…
We study the detection of weak coherent forces by means of an optomechanical device formed by a highly reflecting isolated mirror shined by an intense and highly monochromatic laser field. Radiation pressure excites a vibrational mode of…
We show that optomechanical systems in the quantum regime can be used to demonstrate EPR-type quantum entanglement between the optical field and the mechanical oscillator, via quantum-state steering. Namely, the conditional quantum state of…
An exploratory approach to the possibility of analyzing nonorthogonality as a quantifiable property is presented. Three different measures for the nonorthogonality of pure states are introduced, and one of these measures is extended to…
The spherometer used for measuring radius of curvature of spherical surfaces is explicitly based on a geometric relation unique to circles and spheres. We present an alternate approach using coordinate geometry, which reproduces the…
Magnetic interaction between a weighing sample and an external magnetic field allows to measure characteristics of magnetic field (a sample with known magnetic characteristics), as well as the magnetic properties of a sample (a known…
Finite resolution quantum nondemolition (QND) measurements allow a determination of light field properties while preserving some of the original quantum coherence of the input state. It is thus possible to measure correlations between the…
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…
We consider an optical cavity enclosed by a freely moving mirror attached to a spring and we study the quantum friction effect exerted by the dynamical Casimir emission on the mechanical motion of the mirror. Observable signatures of this…
We review and compare several measures that identify quantum states that are "macroscopically quantum". These measures were initially formulated either for photonic systems or spin ensembles. Here, we compare them through a simple model…
The coherent states for a quantum particle on a M\"{o}bius strip are constructed and their relation with the natural phase space for fermionic fields is shown. The explicit comparison of the obtained states with previous works where the…
Noncommuting spatial coordinates are studied in the context of a charged particle moving in a strong non-uniform magnetic field. We derive a relation involving the commutators of the coordinates, which generalizes the one realized in a…
We show that conditional measurements on atoms following their interaction with a resonant cavity field mode can be used to effectively counter the decoherence of Fock-state superpositions due to cavity leakage.