Related papers: On Quantum Indeterminacy
Quantum operators of coordinates and momentum components of a particle in Minkowski space-time belong to a noncommutative algebra and give rise to a quantum phase space. Under some constraints, in particular, the Lorentz invariance…
A positive definite symmetric matrix {\sigma} qualifies as a quantum mechanical covariance matrix if and only if {\sigma}+(1/2)i\hbar{\Omega}\geq0 where {\Omega} is the standard symplectic matrix. This well-known condition is a strong…
Quantum coherence is an important quantum resource and it is intimately related to various research fields. The geometric coherence is a coherence measure both operationally and geometrically. We study the trade-off relation of geometric…
It is well known that nonrelativistic quantum mechanics presents a clear asymmetry between space and time. Much of this asymmetry is attributed to the lack of Lorentz invariance of the theory. Nonetheless, a recent work [Phys. Rev. A…
The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the…
The Heisenberg Uncertainty Principle (HUP) limits the accuracy in the simultaneous measurements of the position and momentum variables of any quantum system. This is known to be true in the context of non-relativistic quantum mechanics.…
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles: positions constitute a configuration…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…
Geometrical structures of quantum mechanics provide us with new insightful results about the nature of quantum theory. In this work we consider mixed quantum states represented by finite rank density operators. We review our geometrical…
We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms of the functions on the projective Hilbert space, and its Hilbert space analog, with a noncommutative product in terms of explicit…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
The continuum of real numbers has served well as a model for physical space in mechanics and field theories. However it is a well-motivated and popular idea that at the fundamental Planck scale the combination of gravitational and quantum…
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…
A generalisation of the classical covariance for quantum mechanical observables has previously been presented by Gibilisco, Hiai and Petz. Gibilisco and Isola has proved that the usual quantum covariance gives the sharpest inequalities for…
For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by $N$ linear combinations of position and momentum observables. The state-independent bounds depend on their…
In Phys. Rev. A 70, 032104 (2004), M. Montesinos and G. F. Torres del Castillo consider various symplectic structures on the classical phase space of the two-dimensional isotropic harmonic oscillator. Using Dirac's quantization condition,…
An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit…
Quantum uncertainty is the cornerstone of quantum mechanics which underlies many counterintuitive nonclassical phenomena. Recent studies remarkably showed that it also fundamentally limits nonclassical correlation, and crucially, a…