Related papers: Characterizing common cause closedness of quantum …
We introduce a quantum generalisation of the notion of coupling in probability theory. Several interesting examples and basic properties of quantum couplings are presented. In particular, we prove a quantum extension of Strassen theorem for…
In the following we revisit the frequency interpretation of probability of Richard von Mises, in order to bring the essential implicit notions in focus. Following von Mises, we argue that probability can only be defined for events that can…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume…
We analyze a family of measures of general quantum correlations for composite systems, defined in terms of the bipartite entanglement necessarily created between systems and apparatuses during local measurements. For every entanglement…
A Newtonian approach to quantum gravity is studied. At least for weak gravitational fields it should be a valid approximation. Such an approach could be used to point out problems and prospects inherent in a more exact theory of quantum…
We analyze the possible results of the most general measurement on two copies of a quantum state. We show that $\mu$ can label a set of outcomes of such measurement if and only if there is a family of completely co--positive (ccP) maps…
The main principle of affine quantum gravity is the strict positivity of the matrix \{\hat g_{ab}(x)\} composed of the spatial components of the local metric operator. Canonical commutation relations are incompatible with this principle,…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
We show that quantum theory (QT) is a substructure of classical probabilistic physics. The central quantity of the classical theory is Hamilton's function, which determines canonical equations, a corresponding flow, and a Liouville equation…
One of the main problems in any quantum resource theory is the characterization of the conversions between resources by means of the free operations of the theory. In this work, we advance on this characterization within the quantum…
The probability operator is derived from first principles for an equilibrium quantum system. It is also shown that the superposition states collapse into a mixture of states giving the conventional von Neumann trace form for the quantum…
We extend Einstein's hole argument into the quantum domain, and argue that quantum observables for quasiclassical superpositional states of gravitational fields require additional information to be well-defined, namely, relative positions…
Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which…
Correlation self-testing of quantum theory involves identifying a task or set of tasks whose optimal performance can be achieved only by theories that can realise the same set of correlations as quantum theory in every causal structure.…
Motivated by Popescu's example of hidden nonlocality, we elaborate on the conjecture that quantum states that are intuitively nonlocal, i.e., entangled, do not admit a local causal hidden variables model. We exhibit quantum states which…
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
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…
In the operator formalism of quantum mechanics, the density operator describes the complete statistics of a quantum state in terms of d^2 independent elements, where d is the number of possible outcomes for a precise measurement of an…