Related papers: The Operational Choi-Jamiolkowski Isomorphism
The Hilbert space formalism of quantum theory manifests a map between bipartite states and time evolutions, known as Jamiolkowski isomorphism. We extend this map in a physical setting to prove the equality of spatial correlations in…
The role of operational quantum mechanics, quantum axiomatics and quantum structures in general is presented as a contribution to a compendium on quantum physics, its history and philosophy.
We develop a possibilistic semantic formalism for quantum phenomena from an operational perspective. This semantic system is based on a Chu duality between preparation processes and yes/no tests, the target space being a three-valued set…
The quasiprobability representation of quantum states addresses two main concerns, the identification of nonclassical features and the decomposition of the density operator. While the former aspect is a main focus of current research, the…
Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations,…
Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical…
Although the present paper looks upon the formal apparatus of quantum mechanics as a calculus of correlations, it goes beyond a purely operationalist interpretation. Having established the consistency of the correlations with the existence…
This article, addressed to a general audience of functional analysts, is intended to be an illustration of a few basic principles from `noncommutative functional analysis', more specifically the new field of {\em operator spaces.} In our…
Quasiprobability representations are well-established tools in quantum information science, with applications ranging from the classical simulability of quantum computation to quantum process tomography, quantum error correction, and…
It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schr\"odinger equation are derived from the causal action principle. The…
The standard operational probabilistic framework (within which we can formulate Operational Quantum Theory) is time asymmetric. This is clear because the conditions on allowed operations are time asymmetric. It is odd, though, because…
The ontological aspect of Bohmian mechanics, as a hidden-variable theory that provides us with an objective description of a quantum world without observers, is widely known. Yet its practicality is getting more and more acceptance and…
We introduce a family of relativistic non-rigid non-inertial frames as a gauge fixing of the description of N positive energy particles in the framework of parametrized Minkowski theories. Then we define a multi-temporal quantization scheme…
The aim of this work is to firstly demonstrate the efficacy of the recently proposed Orlicz space formalism for Quantum theory \cite{ML}, and secondly to show how noncommutative differential structures may naturally be incorporated into…
We introduce a class of probabilistic theories, termed Minimal Strongly Causal Operational Probabilistic Theories, where system dynamics are constrained to the minimal set of operations consistent with the set of states and permitting…
This paper offers a brief introduction to the framework of "general probabilistic theories", otherwise known as the "convex-operational" approach the foundations of quantum mechanics. Broadly speaking, the goal of research in this vein is…
Non-classical states that are characterized by their non-positive quasi-probabilities in phase space are known to be the basis for various quantum effects. In this work, we investigate the interrelation between the non-classicality and…
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…