Related papers: Coexistence of qubit effects
It is sometimes pointed out as a curiosity that the state space of quantum two-level systems, i.e. the qubit, and actual physical space are both three-dimensional and Euclidean. In this paper, we suggest an information-theoretic analysis of…
This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators. These relations, including various…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
A fundamental feature of quantum mechanics is that there are observables which can be measured jointly only when some noise is added to them. Their sharp versions are said to be incompatible. In this work we investigate time-continuous…
Coherent states in a projected Hilbert space have many useful properties. When there are conserved quantities, a representation of the entire Hilbert space is not necessary. The same issue arises when conditional observations are made with…
It often goes unnoticed that, even for a finite number of degrees of freedom, the canonical commutation relations have many inequivalent irreducible unitary representations; the free particle and a particle in a box provide examples that…
Quantum inequalities are lower bounds for local averages of quantum observables that have positive classical counterparts, such as the energy density or the Wick square. We establish such inequalities in general (possibly interacting)…
A formulation of the consistent histories approach to quantum mechanics in terms of generalized observables (POV measures) and effect operators is provided. The usual notion of `history' is generalized to the notion of `effect history'. The…
The recently established resource theory of quantum coherence allows for a quantitative understanding of the superposition principle, with applications reaching from quantum computing to quantum biology. While different quantifiers of…
We take Co-Operative Phenomena as a common physical conceptual base to speculate on the existence of a medium and the properties that it must have to physically understand some of the problems in Special Relativity, Gravitation and Quantum…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
We introduce the notion of hidden quantum correlations. We present the mean values of observables depending on one classical random variable described by the probability distribution in the form of correlation functions of two (three, etc.)…
We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this…
We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends…
We study a family of physical observable quantities in quantum gravity. We denote them W functions, or n-net functions. They represent transition amplitudes between quantum states of the geometry, are analogous to the n-point functions in…
The structure of quantum interactions with fields of helicity two ("gravitons") is strongly constrained by three principles: positivity (Hilbert space), covariance, and locality of observables. To fulfil them simultaneously, some…
We analyze a conceivable type of local realistic theory, which we call a co-operative phenomena type local realistic theory. In an experimental apparatus to measure second or fourth order interference effects, it images that their exists a…
It is known that the momentum operator canonically conjugated to the position operator for a particle moving in some bounded interval of the line {(with Dirichlet boundary conditions) is not essentially self-adjoint}: it has a continuous…
A complete set of mutually unbiased bases for a Hilbert space of dimension N is analogous in some respects to a certain finite geometric structure, namely, an affine plane. Another kind of quantum measurement, known as a symmetric…
We show that the correct mathematical foundation of quantum decision theory, dealing with uncertain events, requires the use of positive operator-valued measure that is a generalization of the projection-valued measure. The latter is…