相关论文: The boundary is mixed

We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…

We study the equivalence of mixed states under local unitary transformations. First we express quantum states in Bloch representation. Then based on the coefficient matrices, some invariants are constructed. This method and results can be…

The foundational studies of the standard, unitary-only quantum theory revolve around the kinematical aspects of quantum entanglement and the improper quantum mixtures. In this paper, we introduce and argue for the foundational character of…

We present a review on the notion of pure states and mixtures as mathematical concepts that apply for both classical and quantum physical theories, as well as for any other theory depending on statistical description. Here, states will be…

In this paper we define a general setting for Martin boundary theory associated to quantum random walks, and prove a general representation theorem. We show that in the dual of a simply connected Lie subgroup of U(n), the extremal Martin…

Considering the recently established arbitrariness the Schroedinger equation has to be interpreted as an equation of motion for a statistical ensemble of particles. The statistical qualities of individual particles derive from the unknown…

The continuum of real numbers has served well as a model for physical space in mechanics and field theories. However it is a well-motivated and popular idea that at the fundamental Planck scale the combination of gravitational and quantum…

Following an article by John von Neumann on infinite tensor products, we develop the idea that the usual formalism of quantum mechanics, associated with unitary equivalence of representations, stops working when countable infinities of…

Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…

Discussed are some geometric aspects of the phase space formalism in quantum mechanics in the sense of Weyl, Wigner, Moyal and Ville. We analyze the relationship between this formalism and geometry of the Galilei group, classical momentum…

Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…

We give an introductory account of the general boundary formulation of quantum theory. We refine its probability interpretation and emphasize a conceptual and historical perspective. We give motivations from quantum gravity and illustrate…

Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…

In a recent paper (arXiv:1111.3328), Pusey, Barrett and Rudolph claim to prove that statistical interpretations of quantum mechanics do not work. In fact, their proof assumes that all statistical interpretations must be based on hidden…

We stress the notion of statistical experiment, which is mandatory for quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which provides the most general framework to deal with statistical experiments giving evidence…

Various physical effects resulting from decoherence are discussed in the algebraic framework. In particular, it is shown that the environment may induce not only classical properties like superselection rules, pointer states or even…

We study the role of context, complex of physical conditions, in quantum as well as classical experiments. It is shown that by taking into account contextual dependence of experimental probabilities we can derive the quantum rule for the…

The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…

We demonstrate the equilibration of isolated macroscopic quantum systems, prepared in non-equilibrium mixed states with significant population of many energy levels, and observed by instruments with a reasonably bound working range compared…

I show that frequentism, as an explanation of probability in classical statistical mechanics, can be extended in a natural way to a decoherent quantum history space, the analogue of a classical phase space. The result is a form of finite…