Related papers: Quantum theory realises all joint measurability gr…
We discuss the notion about physical quantities as having values represented by real numbers, and its limiting to describe nature to be understood in relation to our appreciation that the quantum theory is a better theory of natural…
Quantum supermaps are higher-order maps transforming quantum operations into quantum operations. Here we extend the theory of quantum supermaps, originally formulated in the finite dimensional setting, to the case of higher-order maps…
In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…
In any given experimental scenario, the rules of quantum theory provide statistical distributions that the observed outcomes are expected to follow. The set formed by all these distributions contains the imprint of quantum theory, capturing…
The ordinary linear quantum theory predicts the quantum correlations at any distance (the universal superposition principle). It creates the decoherence problem since quantum interactions entangle states into non-separable combination. On…
We consider the question whether electromagnetism can be derived from quantum physics of measurements. It turns out that this is possible, both for quantum and classical electromagnetism, if we use more recent innovations such as smearing…
We develop a quantum effective action for scalar-tensor theories of gravity which is both spacetime diffeomorphism invariant and field reparameterisation (frame) invariant beyond the classical approximation. We achieve this by extending the…
Ernst Specker considered a particular feature of quantum theory to be especially fundamental, namely that pairwise joint measurability of sharp measurements implies their global joint measurability (https://vimeo.com/52923835). To date,…
We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the…
Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of…
We introduce a notion of curvature on finite, combinatorial graphs. It can be easily computed by solving a linear system of equations. We show that graphs with curvature bounded below by $K>0$ have diameter bounded by $\mbox{diam}(G) \leq…
Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters \lambda_{ij}. The deformations for which the…
The fact that quantum theory is non-differentiable, while general relativity is built on the assumption of differentiability sources an incompatibility between quantum theory and gravity. Higher order geometry addresses this issue directly…
The aim of this paper is to give a simple, geometric proof of Wigner's theorem on the realization of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several proofs exist already, it seems that…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
It is shown that any theory that has certain properties has a measurement problem, in the sense that it makes predictions that are incompatible with measurement outcomes being absolute (that is, unique and non-relational). These properties…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…
We present a rigorous proof of the convergence theorem for the Feynman graphs in arbitrary massive Euclidean quantum field theories on non-commutative R^d (NQFT). We give a detailed classification of divergent graphs in some massive NQFT…
Joint or simultaneous measurements of non-commuting quantum observables are possible at the cost of increased unsharpness or measurement uncertainty. Many different criteria exist for defining what an "optimal" joint measurement is, with…