Related papers: Left residuated operators induced by posets with a…
We show that including both the system and the apparatus in the quantum description of the measurement process, and using the concept of conditional probabilities, it is possible to deduce the statistical operator of the system after a…
We study caustics in classical and quantum mechanics for systems with quadratic Lagrangians. We derive a closed form of the transition amplitude on caustics and discuss their physical implications in the Gaussian slit (gedanken-)experiment.…
We show that an atomic orthomodular lattice L can be reconstructed up to isomorphism from the poset B(L) of Boolean subalgebras of L. A motivation comes from quantum theory and the so-called topos approach, where one considers the poset of…
We consider the problem of existence of the diagonal representation for operators in the space of a family of generalized coherent states associated with an unitary irreducible representation of a (compact) Lie group. We show that necessary…
We consider symmetries and reduction in non-relativistic many-body quantum mechanics, with the aim of identifying physically meaningful observables in systems such as molecules and crystalline solids. To this end, we propose a unified…
This paper presents methods for using zonotopes and constrained zonotopes to improve the practicality of a wide variety of set-based operations commonly used in control theory. The proposed methods extend the use of constrained zonotopes to…
It is proved that both oscillatory integral operators and fractional oscillatory integral operators are bounded on weighted Morrey spaces. The corresponding commutators generated by $BMO$ functions are also considered.
Supersymmetric quantum mechanics has many applications, and typically uses a raising and lowering operator formalism. For one dimensional problems, we show how such raising and lowering operators may be generalized to include an arbitrary…
Quantum operations are used to describe the observed probability distributions and conditional states of the measured system. In this paper, we address the problem of their joint measurability (coexistence). We derive two equivalent…
In the context of constrained quantum mechanics, reference systems are used to construct relational observables that are invariant under the action of the symmetry group. Upon measurement of a relational observable, the reference system…
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…
Unlike standard quantum mechanics, dynamical reduction models assign no particular a priori status to `measurement processes', `apparata', and `observables', nor self-adjoint operators and positive operator valued measures enter the…
Reduction of the left regular representation of quantum algebra $sl_q(3)$ is studied and ~$q$-difference intertwining operators are constructed. The irreducible representations correspond to the spaces of local sections of certain line…
In a recent paper the notion of {\em quantum perceptron} has been introduced in connection with projection operators. Here we extend this idea, using these kind of operators to produce a {\em clustering machine}, i.e. a framework which…
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…
By a physical system we recognize a set of propositions about a given system with their truth-values depending on the states of the system. Since every physical system can go from one state in another one, there exists a binary relation on…
In quantum resource theories (QRTs) certain quantum states and operations are deemed more valuable than others. While the determination of the ``free'' elements is usually guided by the constraints of some experimental setup, this can make…
It is proved that: each collectively order continuous set of operators from an Archimedean OVS with a generating cone to an OVS is collectively order bounded; and each collectively order to norm bounded set of operators from an ordered…
The generation of arbitrary single-mode quantum states from the vacuum by alternate coherent displacement and photon adding as well as the measurement of the overlap of a signal with an arbitrarily chosen quantum state are studied. With…
We consider pseudo-unitary quantum systems and discuss various properties of pseudo-unitary operators. In particular we prove a characterization theorem for block-diagonalizable pseudo-unitary operators with finite-dimensional diagonal…