相关论文: Coexistence of effects from an algebra of two proj…
Thermodynamics is a highly successful macroscopic theory widely used across the natural sciences and for the construction of everyday devices, from car engines and fridges to power plants and solar cells. With thermodynamics predating…
Quantum coherence, the ability of a quantum system to be in a superposition of orthogonal quantum states, is a distinct feature of the quantum mechanics, thus marking a deviation from classical physics. Coherence finds its applications in…
Recently a problem concerning the equivalence of joint measurability and coexistence of quantum observables was solved [15]. In this paper we generalize two known joint measurability results from sharp observables to the class of extreme…
Individual quantum objects display inseparable coexisting wave-like properties and particle-like properties; such inseparable coexistence can seem paradoxical and mind-boggling. The apparent paradox is resolved by the unified theory of…
One of the most remarkable features of quantum physics is that attributes of quantum objects, such as the wave-like and particle-like behaviors of single photons, can be complementary in the sense that they are equally real but cannot be…
Wave-particle duality, a fundamental principle of quantum mechanics, encapsulates the complementary relationship between the wave and particle behaviors of quantum systems. In this paper, we treat quantum coherence and classical…
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
The Stone-von Neumann Theorem is a fundamental result which unified the competing quantum mechanical models of matrix mechanics and wave mechanics. It's mechanism of proof ultimately involved the study of unitary group representations on a…
For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum algebras and to a new type of Noncommutative…
The subjective and the objective aspects of probabilities are incorporated in a simple duality axiom inspired by observer participation in quantum theory. Transcending the classical notion of probabilities, it is proposed and demonstrated…
We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model…
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…
Quantum coherence is a fundamental characteristic to distinguish quantum systems from their classical counterparts. Though quantum coherence persists in isolated non-interacting systems, interactions inevitably lead to decoherence, which is…
In order to figure out why quantum physics needs the complex Hilbert space, many attempts have been made to distinguish the C*-algebras and von Neumann algebras in more general classes of abstractly defined Jordan algebras (JB- and…
Classical mechanics, in the operatorial formulation of Koopman and von Neumann, can be written also in a functional form. In this form two Grassmann partners of time make their natural appearance extending in this manner time to a three…
The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the…
The mathematical formalism of quantum mechanics has been successfully employed in the last years to model situations in which the use of classical structures gives rise to problematical situations, and where typically quantum effects, such…
The Cuntz algebra carries in a natural way the structure of a module algebra over the quantized universal enveloping algebra $U_q(g)$, and the structure of a co-module algebra over the quantum group $G_q$ associated with $U_q(g)$. These two…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space…