Related papers: Conjugates, Filters and Quantum Mechanics
Using a result of H. Hanche-Olsen, we show that (subject to fairly natural constraints on what constitutes a system, and on what constitutes a composite system), orthodox finite-dimensional complex quantum mechanics with superselection…
I discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. Stated informally, these require that systems appear completely classical as…
Quantum theory's Hilbert space apparatus in its finite-dimensional version is nearly reconstructed from four simple and quantum-mechanically motivated postulates for a quantum logic. The reconstruction process is not complete, since it…
Symmetry postulates play a crucial role in various approaches to reconstruct quantum theory from a few basic principles. Discrete and continuous symmetries are under consideration. The continuous case better matches the physical needs for…
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…
In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…
Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…
Starting from an abstract setting for the Lueders - von Neumann quantum measurement process and its interpretation as a probability conditionalization rule in a non-Boolean event structure, the author derived a certain generalization of…
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…
Adrian Kent has recently presented a critique [arXiv:2307.06191] of our paper [Nat. Comms. 10, 1361 (2019)] in which he claims to refute our main result: the measurement postulates of quantum mechanics can be derived from the rest of…
I explore several related routes to deriving the Jordan-algebraic structure of finite-dimensional quantum theory from more transparent operational or physical principles, mainly involving ideas about the symmetries of, and the correlations…
We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically…
It is shown that the quantum theory can be formulated on homogeneous spaces of generalized coherent states in a manner that accounts for interference, entanglement, and the linearity of dynamics without using the superposition principle.…
There is a natural equivalence relation on representations of the states of a given quantum system in a Hilbert space, two representations being equivalent iff they are related by a unitary transformation. There are two equivalence classes,…
We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras (EJAs), satisfying some reasonable additional constraints motivated by the desire to construct dagger-compact categories of such…
The interplay between the algebraic structure (operator algebras) for the quantum observables and the convex structure of the state space has been explored for a long time and most advanced results are due to Alfsen and Shultz. Here we…
This note adds to the recent spate of derivations of the probabilistic apparatus of finite-dimensional quantum theory from various axiomatic packages. We offer two different axiomatic packages that lead easily to the Jordan algebraic…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the…
We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…