Related papers: Tsirelson's Problem
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
One obtains Bell's inequalities if one posits a hypothetical joint probability distribution, or {\it measure}, whose marginals yield the probabilities produced by the spin measurements in question. The existence of a joint measure is in…
A review is given of recent work aimed at constructing a quantum theory of cosmology in which all observables refer to information measurable by observers inside the universe. At the classical level the algebra of observables should be…
Quantum theory has the intriguing feature that is inconsistent with noncontextual hidden variable models, for which the outcome of a measurement does not depend on which other compatible measurements are being performed concurrently. While…
Bell's theorem renders quantum correlations distinct from those of any local-realistic model. Although being stronger than classical correlations, quantum correlations are limited by the Tsirelson bound. This bound, however, applies for…
The existence of contextuality in quantum mechanics is a fundamental departure from the classical description of the world. Currently, the quest to identify scenarios which cannot be more contextual than quantum theory is at the forefront…
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…
In this note, we develop a framework to describe open quantum systems in the Heisenberg picture, i.e., via time evolving operator algebras. We point out the incompleteness of the previous proposals in this regard. We argue that a complete…
In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify…
A measurement model is a framework that describes a quantum measurement process. In this article we restrict attention to $MM$s on finite-dimensional Hilbert spaces. Suppose we want to measure an observable $A$ whose outcomes $A_x$ are…
Quantum measurement is a physical process. What physical resources and constraints does quantum mechanics require for measurement to produce the classical world we observe? Treating measurement as a fully unitary quantum process, our goal…
We derive several uncertainty relations for two arbitrary unitary operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using the…
Whether an almost-commuting pair of operators must be close to a commuting pair is a central question in operator and matrix theory. We investigate this problem for pairs of $C^*$-subalgebras $\mathcal{A}$ and $\mathcal{B}$ of…
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 derive an exact uncertainty relation for arbitrary quantum states of finite-dimensional Hilbert spaces. For any given $k$-partition of a $d$-dimensional multipartite system, we introduce the total uncertainty as the sum of the…
Quantum theory introduces a cut between the observer and the observed system, but does not provide a definition of what is an observer. Based on an informational definition of observer, Grinbaum has recently predicted an upper bound on…
We study the problem when an almost commuting $n$-tuple self-adjoint operators in an infinite dimensional separable Hilbert space $H$ is close to an $n$-tuple of commuting self-adjoint operators on $H.$ We give an affirmative answer to the…
The state space structure for a composite quantum system is postulated among several mathematically consistent possibilities that are compatible with local quantum description. For instance, unentangled Gleason's theorem allows a state…
The quantum measurement problem considered for measuring system (MS) consist of measured state S (particle), detector D and information processing device (observer) O. It's shown that O states selfreference structure results in principal…
In a parametrized and constrained Hamiltonian system, an observable is an operator which commutes with all (first-class) constraints, including the super-Hamiltonian. The problem of the frozen formalism is to explain how dynamics is…