Related papers: Quantum Wasserstein isometries on the qubit state …
The Schr\"odinger cat states, constructed from Glauber coherent states and applied for description of qubits are generalized to the kaleidoscope of coherent states, related with regular n-polygon symmetry and the roots of unity. This…
We attempt to reconstruct the irreducible unitary representations of the Banach Lie group $U_0(\H)$ of all unitary operators $U$ on a separable Hilbert space $\H$ for which $U-{\mathbb I}$ is compact, originally found by Kirillov and…
A parity-dependent squeezing operator is introduced which imposes different SU(1,1) rotations on the even and odd subspaces of the harmonic oscillator Hilbert space. This operator is used to define parity-dependent squeezed states which…
In the report we analyze the indicator/measure of classicality of quantum states defined as the probability to find a state with a positive Wigner function within a unitary invariant random ensemble. The indicators of classicality of three…
A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum…
In this manuscript we investigate the equivalence of Fourier-based metrics on discrete state spaces with the well-known Wasserstein distances. While the use of Fourier-based metrics in continuous state spaces is ubiquitous since its…
We describe some applications of group- and bundle-theoretic methods in solid state physics, showing how symmetries lead to a proof of the localization of electrons in gapped crystalline solids, as e.g. insulators and semiconductors. We…
We adopt the perspective of similarity equivalence, in gate set tomography called the gauge, to analyze various properties of quantum operations belonging to a semigroup, $\Phi= e^{{\cal L}t}$,and therefore given through the Lindblad…
Using concepts of geometric orthogonality and linear independence, we logically deduce the form of the Pauli spin matrices and the relationships between the three spatially orthogonal basis sets of the spin-1/2 system. Rather than a…
Symmetries of the finite Heisenberg group represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. As is well known, these symmetries are properly expressed in terms of certain normalizer. This…
A quantum Schwarzschild spacetime and a quantum Schwarzschild-de Sitter spacetime with cosmological constant $\Lambda$ are constructed within the framework of a noncommutative Riemannian geometry developed in an earlier publication. The…
Wasserstein geometry and information geometry are two important structures to be introduced in a manifold of probability distributions. Wasserstein geometry is defined by using the transportation cost between two distributions, so it…
For $\mu \in (0,1), c> 0,$ we identify the quantum group $SO_\mu(3)$ as the universal object in the category of compact quantum groups acting by `orientation and volume preserving isometries' in the sense of \cite{goswami2} on the natural…
Bloch wave functions of electrons have properties called quantum geometry, which has recently attracted much attention as the origin of intriguing physical phenomena. In this paper, we introduce the notion of the quantum-geometric pair…
Inspired by some problems in Quantum Information Theory, we present some results concerning decompositions of positive operators acting on finite dimensional Hilbert spaces. We focus on decompositions by families having geometrical symmetry…
In this paper we extend Schwinger's quantization approach to the case of a supermanifold considered as a coset space of the Poincare group by the Lorentz group. In terms of coordinates parametrizing a supermanifold, quantum mechanics for a…
The concept of positively and negatively compatible null vectors arises in the study of Clifford geometric algebras with a Lorentz-Minkowski metric. In previous works, the basic properties of such algebras have been set down in terms of a…
We consider the kinematics of bi-partite quantum states as determined by observable quantities, in particular the Bloch vectors of the subsystems. In examining the simplest case of a pair of two-level systems, there is a remarkable…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
In quantum mechanics, the connection between the operator algebraic realization and the logical models of measurement of state observables has long been an open question. In the approach that is presented here, we introduce a new…