Related papers: Maximally Localized States in Quantum Mechanics wi…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
There are four reasons why our present knowledge and understanding of quantum mechanics could be regarded as incomplete. Firstly, the principle of linear superposition has not been experimentally tested for position eigenstates of objects…
When working with quantum states, analysis of the final quantum state generated through probabilistic measurements is essential. This analysis is typically conducted by constructing the density matrix from either partial or full tomography…
We show a geometric formulation for minimum-error discrimination of qubit states, that can be applied to arbitrary sets of qubit states given with arbitrary a priori probabilities. In particular, when qubit states are given with equal…
The existence of a minimal measurable length as a characteristic length in the Planck scale is one of the main features of quantum gravity and has been widely explored in the context. Various different deformations of spacetime have been…
Partial electron localization in a finite-size superlattice placed in an electric field is considered. The role of electric field in forming of quasilocalized states is investigated. A quantitative criterion for the degree of partial…
We consider a general symplectic transformation (also known as linear canonical transformation) of quantum-mechanical observables in a quantized version of a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q}…
We develop a framework to extend resource measures from one domain to a larger one. We find that all extensions of resource measures are bounded between two quantities that we call the minimal and maximal extensions. We discuss various…
In classical Lorentz-invariant field theories, localized soliton solutions necessarily break translation symmetry. In the corresponding quantum field theories, the position is quantized and, if the theory is not compactified, they have…
Different candidates of quantum gravity proposal such as string theory, noncommutative geometry, loop quantum gravity and doubly special relativity, all predict the existence of a minimum observable length and/or a maximal momentum which…
Precision metrology underpins scientific and technological advancements. Quantum metrology offers a pathway to surpass classical sensing limits by leveraging quantum states and measurement strategies. However, measuring multiple…
We postulate that physical states are equivalent under coordinate transformations. We then implement this equivalence principle first in the case of one-dimensional stationary systems showing that it leads to the quantum analogue of the…
We perform a quantum information analysis for multi-mode Gaussian approximate position measurements, underlying noisy homodyning in quantum optics. The "Gaussian maximizer" property is established for the entropy reduction of these…
The existence of a minimal measurable length is a common feature of various approaches to quantum gravity such as string theory, loop quantum gravity and black-hole physics. In this scenario, all commutation relations are modified and the…
A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated to a nonzero minimal uncertainty in position measurements, which is encoded in…
I discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. Stated informally, these require that systems appear completely classical as…
We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…
We show that the introduction of a minimal length in the context of non-commutative spacetime gives rise (after some considerations) to higher-order theories. We then explicitly demonstrate how these higher-derivative theories appear as a…
We propose a method to measure the quantum state of a single mode of the electromagnetic field. The method is based on the interaction of the field with a probe qubit. The qubit polarizations along coordinate axes are functions of the…
We develop here a mechanism that, without making use of a cosmological constant, reproduces an accelerating universe. This is done by taking into account Casimir vacuum energy density, assuming that the underlying theory allows a maximum…