A discrete and finite approach to past physical reality.
A new approach to representation of observables on fuzzy quantum posets
We give a representation of an observable on a fuzzy quantum poset of type II by a pointwise defined real-valued function. This method is inspired by that of Kolesárová [6] and Mesiar [7], and our results extend representations given by the author and Dvurečenskij [4]. Moreover, we show that in this model, the converse representation fails, in general.
An order for quantum observables
Consistent histories: Description of a world with increasing entropy.
Decay times in quantum mechanics.
Decoherence in pre-symmetric spaces.
Dilations of positive operator measures and bimeasures related to quantum mechanics
Facial structures of separable and PPT states
A positive semi-definite block matrix (a state if it is normalized) is said to be separable if it is the sum of simple tensors of positive semi-definite matrices. A state is said to be entangled if it is not separable. It is very difficult to detect the border between separable and entangled states. The PPT (positive partial transpose) criterion tells us that the partial transpose of a separable state is again positive semi-definite, as was observed by M. D. Choi in 1982 from...
Instruments and mutual entropies in quantum information
General quantum measurements are represented by instruments. In this paper the mathematical formalization is given of the idea that an instrument is a channel which accepts a quantum state as input and produces a probability and an a posteriori state as output. Then, by using mutual entropies on von Neumann algebras and the identification of instruments and channels, many old and new informational inequalities are obtained in a unified manner. Such inequalities involve various quantities which characterize...
Markov chains approximation of jump–diffusion stochastic master equations
Quantum trajectories are solutions of stochastic differential equations obtained when describing the random phenomena associated to quantum continuous measurement of open quantum system. These equations, also called Belavkin equations or Stochastic Master equations, are usually of two different types: diffusive and of Poisson-type. In this article, we consider more advanced models in which jump–diffusion equations appear. These equations are obtained as a continuous time limit of martingale problems...
Matrix representation of finite effect algebras
In this paper we present representation of finite effect algebras by matrices. For each non-trivial finite effect algebra we construct set of matrices in such a way that effect algebras and are isomorphic if and only if . The paper also contains the full list of matrices representing all nontrivial finite effect algebras of cardinality at most .
Maximum entropy wave functions.
Möbius gyrovector spaces in quantum information and computation
Hyperbolic vectors, called gyrovectors, share analogies with vectors in Euclidean geometry. It is emphasized that the Bloch vector of Quantum Information and Computation (QIC) is, in fact, a gyrovector related to Möbius addition rather than a vector. The decomplexification of Möbius addition in the complex open unit disc of a complex plane into an equivalent real Möbius addition in the open unit ball of a Euclidean 2-space is presented. This decomplexification proves useful, enabling the resulting...
Notes on the essential system to acquire information.
Observables on -MV algebras and -lattice effect algebras
Effect algebras were introduced as abstract models of the set of quantum effects which represent sharp and unsharp properties of physical systems and play a basic role in the foundations of quantum mechanics. In the present paper, observables on lattice ordered -effect algebras and their “smearings” with respect to (weak) Markov kernels are studied. It is shown that the range of any observable is contained in a block, which is a -MV algebra, and every observable is defined by a smearing of a sharp...
On a characterization of probability measures on Boolean algebras and some orthomodular lattices
On the factorization criterion for quantum statistics
Positive linear maps of matrix algebras
A characterization of the structure of positive maps is presented. This sheds some more light on the old open problem studied both in Quantum Information and Operator Algebras. Our arguments are based on the concept of exposed points, links between tensor products and mapping spaces and convex analysis.
Pure Jauch-Piron states on von Neumann algebras
Quantum entanglement and projective ring geometry.