Related papers: No labeling quantum mechanics of indiscernible par…
It is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying instead solely on the density matrix as the description of reality. With this definition of a physical…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…
It is well known that an (in general, non-commutative) set of non-Hermitian operators $\Lambda_j$ with real eigenvalues need not necessarily represent observables. We describe a specific class of quantum models in which these operators plus…
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and…
Quantum simulation has become a promising avenue of research that allows one to simulate and gain insight into the models of High Energy Physics whose experimental realizations are either complicated or inaccessible with current technology.…
It is shown that quantum mechanics is noncontextual if quantum properties are represented by subspaces of the quantum Hilbert space (as proposed by von Neumann) rather than by hidden variables. In particular, a measurement using an…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
The concept of individuality in quantum mechanics shows radical differences from the concept of individuality in classical physics, as E. Schroedinger pointed out in the early steps of the theory. Regarding this fact, some authors suggested…
In this paper we discuss and analyse the idea of trying to see (non-relativistic) quantum mechanics as a ``space-time statistical mechanics'', by using the classical statistical mechanical method on objective microscopic space-time…
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
We study the local indistinguishability problem of quantum states. By introducing an easily calculated quantity, non-commutativity, we present an criterion which is both necessary and sufficient for the local indistinguishability of a…
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead…
The purpose of this paper is to show that the mathematics of quantum mechanics (QM) is the mathematics of set partitions (which specify indefiniteness and definiteness) linearized to vector spaces, particularly in Hilbert spaces. That is,…
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…
In this paper, we present a formalism for representing infinite systems in quantum mechanics by employing a strategy that embraces divergences rather than avoiding them. We do this by representing physical quantities such as inner products,…
Standard quantum mechanics unquestionably violates the separability principle that classical physics (be it point-like analytic, statistical, or field-theoretic) accustomed us to consider as valid. In this paper, quantum nonseparability is…
According to quantum theory, pure physical states correspond to equivalence classes of state vectors, where any two members of one class differ by a complex factor. The point is that such a factor does not change the probability for the…
In this work we discuss a formal way of dealing with properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable…
Entanglement is often regarded as an inherently quantum feature. We show that this does not have to be the case: under restricted operational access, classical correlations can appear nonseparable when expressed in the formalism of quantum…