Related papers: Quantum theory realises all joint measurability gr…
We study the compatibility (or joint measurability) of quantum observables in a setting where the experimenter has access to multiple copies of a given quantum system, rather than performing the experiments on each individual copy…
Quantum tomography approaches typically consider a set of observables which we wish to measure, design a measurement scheme which measures each of the observables and then repeats the measurements as many times as necessary. We show that…
A relation algebra is called measurable when its identity is the sum of measurable atoms, and an atom is called measurable if its square is the sum of functional elements. In this paper we show that atomic measurable relation algebras have…
Non-Abelian Gauss law is interpreted in terms of area bits described in a local frame which fit together into closed surfaces and the Non-Abelian Stokes law in terms of length bits described in a local frame which fit together into closed…
We show that any two Hadamard graphs on the same number of vertices are quantum isomorphic. This follows from a more general recipe for showing quantum isomorphism of graphs arising from certain association schemes. The main result is built…
Joint measurements of non-commuting observables are characterized by unavoidable measurement uncertainties that can be described in terms of the error statistics for input states with well-defined values for the target observables. However,…
Let $M$ be a graph manifold such that each piece of its JSJ decomposition has the $\Bbb H^2 \times \Bbb R$ geometry. Assume that the pieces are glued by isometries. Then, there exists a complete Riemannian metric on $\Bbb R \times M$ which…
Predictions for measurement outcomes in physical theories are usually computed by combining two distinct notions: a state, describing the physical system, and an observable, describing the measurement which is performed. In quantum theory,…
We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…
Classical and quantum measurement theories are usually held to be different because the algebra of classical measurements is commutative, however the Poisson bracket allows noncommutativity to be added naturally. After we introduce…
In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. It concerns the…
Despite the unparalleled accuracy of quantum-theoretical predictions across an enormous range of phenomena, the theory's foundations are still in doubt. The theory deviates radically from classical physics, predicts counterintuitive…
We introduce a notion of measuring scales for quantum abelian gauge systems. At each measuring scale a finite dimensional affine space stores information about the evaluation of the curvature on a discrete family of surfaces. Affine maps…
We present a conceptually new approach to describe state-of-the-art photonic quantum experiments using Graph Theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that…
The proper resolution of the so-called measurement problem requires a "top-down" conception of the quantum world that is opposed to the usual "bottom-up" conception, which builds on an intrinsically and maximally differentiated manifold.…
We establish a connection between measurement-based quantum computation and the field of mathematical logic. We show that the computational power of an important class of quantum states called graph states, representing resources for…
Quantum algebraic observables representing localization in space-time of a Dirac electron are defined. Inertial motion of the electron is represented in the quantum algebra with electron mass acting as the generator of motion. Since…
In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which is an algebra generated by…
Observed physical phenomena can be described well by quantum mechanics or general relativity. People may try to find an unified fundamental theory which mainly aims to merge gravity with quantum theory. However, difficulty in merging those…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…