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The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets.…
The effects of the measurement apparatus on quantum coherence are studied by considering a purely dephasing model of a qubit. The initial state is prepared from a thermal state of the whole system by performing a nonselective measurement on…
Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…
Generically, a fully measured elasticity tensor has no material symmetry. For single crystals with a cubic lattice, or for the aeronautics turbine blades superalloys such as Nickelbased CMSX-4, cubic symmetry is nevertheless expected. It is…
This paper is concerned with constructing an optimal controller in the coherent quantum Linear Quadratic Gaussian problem. A coherent quantum controller is itself a quantum system and is required to be physically realizable. The use of…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
Determining the measurement uncertainty region is a difficult problem for generic sets of observables. For this reason the literature on exact measurement uncertainty regions is focused on symmetric sets of observables, where the symmetries…
Inspired by the work of Wheeler among others, we have studied the problem of quantum measurements of space-time distances by applying the general principles of quantum mechanics as well as those of general relativity. Contrary to the…
We describe a measure quantization procedure i.e., an algorithm which finds the best approximation of a target probability law (and more generally signed finite variation measure) by a sum of $Q$ Dirac masses ($Q$ being the quantization…
We study quantum steering experiments without assuming that the trusted party can perfectly control their measurement device. Instead, we introduce a scenario in which these measurements are subject to small imprecision. We show that small…
Measurement incompatibility, or joint measurability, is a cornerstone of quantum theory and a useful resource. For finite-dimensional systems, quantifying this resource and establishing universal bounds valid for all measurements is a…
Recently proposed idea of "protective" measurement of a quantum state is critically examined, and generalized. Earlier criticisms of the idea are discussed and their relevance to the proposal assessed. Several constraints on measuring…
Orthogonal geometric constructions are the basis of many many quantum error-correcting codes (QEC), but strict orthogonality constraints limit design flexibility and resource efficiency. We introduce a quasi-orthogonal geometric framework…
We introduce a generalization of symmetric measurements to collections of unequinumerous positive, operator-valued measures (POVMs). For informationally complete sets, we propose construction methods from orthonormal Hermitian operator…
A number of issues related to measurement show that self-consistency is lacking in quantum mechanics as this theory has been generally understood. Each issue is presented as a point in this paper. Each point can be resolved by incorporating…
Quantum metrology promises high-precision measurements beyond the capability of any classical techniques, and has the potential to be integral to investigative techniques. However, all sensors must tolerate imperfections if they are to be…
Joint or simultaneous measurements of non-commuting quantum observables are possible at the cost of increased unsharpness or measurement uncertainty. Many different criteria exist for defining what an "optimal" joint measurement is, with…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
Quantum fidelity is a measure to quantify the closeness of two quantum states. In an operational sense, it is defined as the minimal overlap between the probability distributions of measurement outcomes and the minimum is taken over all…
Given a conformal metric with finite total Q-curvature, we show that the assumptions on scalar curvature sensitively govern the Q-curvature integral. Additionally, we introduce a conformal mass for such manifolds. Using such mass, we…