Related papers: Comparison of Information Structures and Completel…
The concepts of `conditional entropy' and `information' retain their validity for quantum systems, but their properties differ somewhat from those of their classical counterparts; specifically, some equalities and inequalities of classical…
The graphs induced by partition logics allow a dual probabilistic interpretation: a classical one for which probabilities lie on the convex hull of the dispersion-free weights, and another one, suggested independently from the quantum Born…
We explain the quantum structure as due to the presence of two effects, (a) a real change of state of the entity under influence of the measurement and, (b) a lack of knowledge about a deeper deterministic reality of the measurement…
The usual formulation of quantum theory is based on rather obscure axioms (employing complex Hilbert spaces, Hermitean operators, and the trace rule for calculating probabilities). In this paper it is shown that quantum theory can be…
Cryptography plays a pivotal role in safeguarding sensitive information and facilitating secure communication. Classical cryptography relies on mathematical computations, whereas quantum cryptography operates on the principles of quantum…
A simple mapping procedure is presented by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed directly into those in curved space with torsion. Our procedure evolved from…
The probabilistic description of the time evolution of a physical system can take two conceptually distinct forms: a trajectory of probabilities, which specifies how probabilities evolve over time, and a probability on trajectories, which…
We investigate a two-qubit system to understand the relationship between concurrence and mutual information, where the former determines the amount of quantum entanglement, whereas the latter is its classical residue after performing local…
This paper presents a new proof of the renewal theorem by bijecting a general point process to a deterministic one (where the time between events is always fixed). It also provides insight into the workings of the renewal theorem.
Quantum machine learning is often motivated by the idea that quantum systems can expose useful high-dimensional structure that is difficult to access with classical models. We isolate one central component of this claim: the fixed…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
According to the probability ranking principle, the document set with the highest values of probability of relevance optimizes information retrieval effectiveness given the probabilities are estimated as accurately as possible. The key…
In this work we examine quantum states which have non-negative amplitudes (in a fixed basis) and the channels which preserve them. These states include the ground states of stoquastic Hamiltonians and they are of interest since they avoid…
In complete analogy with the classical situation (which is briefly reviewed) it is possible to define bi-Hamiltonian descriptions for Quantum systems. We also analyze compatible Hermitian structures in full analogy with compatible Poisson…
Information spreads in time. For example, correlations dissipate when the correlated system locally couples to a third party, such as the environment. This simple but important fact forms the known quantum data-processing inequality. Here…
The probability simplex is the set of all probability distributions on a finite set and is the most fundamental object in the finite probability theory. In this paper we give a characterization of statistical models on finite sets which are…
The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are operational, i.e., phenomenal, probabilistic correlations that lie outside the polytope…
Assuming that quantum states, including pure states, represent subjective degrees of belief rather than objective properties of systems, the question of what other elements of the quantum formalism must also be taken as subjective is…
It is shown that a normalisable probability density can be defined for the entire complex plane in the modified de Broglie-Bohm quantum mechanics, which gives complex quantum trajectories. This work is in continuation of a previous one that…
We review some connections between quantum information and statistical mechanics. We focus on three sets of results for classical spin models. First, we show that the partition function of all classical spin models (including models in…