相关论文: The four postulates of quantum mechanics are three
A composite quantum system comprising a finite number k of subsystems which are described with position and momentum variables in Z_{n_{i}}, i=1,...,k, is considered. Its Hilbert space is given by a k-fold tensor product of Hilbert spaces…
A two-dimensional quantum mechanical system consisting of a particle coupled to two magnetic impurities of different strengths, in a harmonic potential, is considered. Topological boundary conditions at impurity locations imply that the…
A new quantum mechanical notion -- Conditional Density Matrix -- is discussed and is applied to describe some physical processes. This notion is a natural generalization of von Neumann density matrix for such processes as divisions of…
Due to the existence of incompatible observables, the propositional calculus of a quantum system does not form a Boolean algebra but an orthomodular lattice. Such lattice can be realised as a lattice of subspaces on a real, complex or…
Why does quantum theory need the complex numbers? With a view toward answering this question, this paper argues that the usual Hilbert-space formalism is a special case of the general method of Markovian embeddings. This paper then…
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
The principle of relativity is extended to accommodate finite-mass observers with quantum properties by introducing two operational requirements: (i) equivalence of observers at the level of transition amplitudes, and (ii) the impossibility…
In this article, the weakest possible theorem providing a foundation for the Hilbert space formalism of quantum theory is stated. The necessary postulates are formulated, and the mathematics is spelt out in detail. It is argued that, from…
Quantum theory is usually formulated in terms of abstract mathematical postulates, involving Hilbert spaces, state vectors, and unitary operators. In this work, we show that the full formalism of quantum theory can instead be derived from…
The measurement process in quantum mechanics is usually described by the von Neumann projection postulate, which forms a basic constituent of the laws of quantum mechanics. Since this postulate requires the outside observer of the system,…
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional quantum systems and entail the specification of only a…
Quantum groupoids are a joint generalization of groupoids and quantum groups. We propose a definition of a compact quantum groupoid that is based on the theory of C*-algebras and Hilbert bimodules. The essential point is that whenever one…
Both classical and quantum mechanics assume that physical laws are invariant under changes in the way that the world is labeled. This Principle of Decompositional Equivalence is formalized, and shown to forbid finite experimental…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the possibility of entanglement between two or more…
Consider a situation in which a quantum system is secretly prepared in a state chosen from the known set of states. We present a principle that gives a definite distinction between the operations that preserve the states of the system and…
Observables in a quantum system, represented by a Hilbert space, are given by the orthogonal bases of the aforementioned Hilbert space. Categorical Quantum Mechanics provides further abstraction of such observables, allowing for a…
How can quantum mechanics be (i) the fundamental theoretical framework of contemporary physics and (ii) a probability calculus that presupposes the events to which, and on the basis of which, it assigns probabilities? The question is…
This paper represents one approach to making explicit some of the assumptions and conditions implied in the widespread representation of numbers by composite quantum systems. Any nonempty set and associated operations is a set of natural…