Related papers: Little-used Mathematical Structures in Quantum Mec…
Einstein's article on the EPR paradox is the most cited of his works, but not many know that it was not fully representative of the way he thought about the incompleteness of the quantum formalism. Indeed, his main worry was not…
Probabilities of the outcomes of consecutive quantum measurements can be obtained by construction probability amplitudes, thus implying unitary evolution of the measured system, broken each time a measurement is made. In practice, the…
We note the separation of a quantum description of an experiment into a statement of results (as probabilities) and an explanation of these results (in terms of linear operators). The inverse problem of choosing an explanation to fit given…
We define a deformed kinetic energy operator for a discrete position space with a finite number of points. The structure may be either periodic or nonperiodic with well-defined end points. It is shown that for the nonperiodic case the…
Quantum superposition states are behind many of the curious phenomena exhibited by quantum systems, including Bell non-locality, quantum interference, quantum computational speed-up, and the measurement problem. At the same time, many…
In this paper, we investigate finite-dimensional irreducible representations of the quantum affine general linear superalgebra $\mathrm{U}_q\big(\widehat{\mathfrak{gl}}_{m|n,\mathbf{s}}\big)$ for arbitrary 01-sequences $\mathbf{s}$, using…
For an arbitrary preparation, quantum mechanical descriptions refer to the complementary contexts set by incompatible measurements. We argue that an arbitrary preparation, therefore, should be described with respect to such a context by its…
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…
We show that Bohr's principle of complementarity between position and momentum descriptions can be formulated rigorously as a claim about the existence of representations of the CCRs. In particular, in any representation where the position…
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…
Group representations play a central role in theoretical physics. In particular, in quantum mechanics unitary --- or, in general, projective unitary --- representations implement the action of an abstract symmetry group on physical states…
Quantum coherence is an essential feature of quantum mechanics which is responsible for the departure between classical and quantum world. The recently established resource theory of quantum coherence studies possible quantum technological…
Given a unitary representation of a Lie group $G$ on a Hilbert space $\mathcal{H}$, we develop the theory of $G$-invariant self-adjoint extensions of symmetric operators both using von Neumann's theorem and the theory of quadratic forms. We…
Quantum mechanics allows processes to be superposed, leading to a genuinely quantum lack of causal structure. For example, the process known as the quantum switch applies two operations ${\cal A}$ and ${\cal B}$ in a superposition of the…
The difference in the properties of the spin correlation tensor for factorizable and nonfactorizable two-particle states is analyzed. The inequalities for linear combinations of the components of this tensor are obtained for the case of…
Coordinate atypical representation of the orthosymplectic superalgebra osp(2/2) in a Hilbert superspace of square integrable functions constructed in a special way is given. The quantum nonrelativistic free particle Hamiltonian is an…
Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of…
An important result in the theory of quantum control is the "universality" of $2$-local unitary gates, i.e. the fact that any global unitary evolution of a system of $L$ qudits can be implemented by composition of $2$-local unitary gates.…
The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields,…
A symmetry in quantum mechanics is described by the projective representations of a Lie symmetry group that transforms between physical quantum states such that the square of the modulus of the states is invariant. The Heisenberg…