Related papers: The quantum de Finetti representation for the Baye…
The subjective Bayesian interpretation of probability asserts that the rules of the probability calculus follow from the normative principle of Dutch-book coherence: A decision-making agent should not assign probabilities such that a series…
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…
A number of phenomena generally believed characteristic of quantum mechanics and seen as interpretively problematic--the incompatibility and value-indeterminacy of variables, the non-existence of dispersion-free states, the failure of the…
Does the notion of a quantum randomized or nondeterministic algorithm make sense, and if so, does quantum randomness or nondeterminism add power? Although reasonable quantum random sources do not add computational power, the discussion of…
Single-world unitary quantum theories imply that some measurements have results whose probabilities can not be calculated by the Born rule.
In previous articles we presented a derivation of Born's rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization. Physically, the structure of QM results of an…
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In…
Quantum decision theory is introduced here, and new basis for this theory is proposed. It is first based upon the author's general arguments for the Hilbert space formalism in quantum theory, next on arguments for the Born rule, that is,…
The original definition of quantum discord of bipartite states was defined over projective measurements, in this paper we discuss some generalizations of it. These generalizations are defined over general measurements, rank-one general…
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
The problem of construction of irreducible representations of quantum $A^q_n$ algebras is solved at the level of explicit integration of the linear (inhomogeneous) system in finite differences in the n-dimensional space. The general…
The Born rule provides a probability vector (distribution) with a quantum state for a measurement setting. For two settings, we have a pair of vectors from the same quantum state. Each pair forms a combined-probability vector that obeys…
According to the Born rule, the probability density in quantum theory is determined by the square of the wave function. A generally accepted derivation of this rule has not yet been proposed. In the given work, a simple physical picture is…
The lack of the Max Born interpretation of the wave function as a probability density describing the localization of a quantum system in configuration space is pointed out related to the recent category based model of quantum mechanics…
This paper presents a series of results on the interplay between quantum estimation, cloning and finite de Finetti theorems. First, we consider the measure-and-prepare channel that uses optimal estimation to convert M copies into k…
Objective probability in quantum mechanics is often thought to involve a stochastic process whereby an actual future is selected from a range of possibilities. Everett's seminal idea is that all possible definite futures on the pointer…
We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the…
We introduce the notion of quantum dissension for a three-qubit system as a measure of quantum correlations. We use three equivalent expressions of three-variable mutual information. Their differences can be zero classically but not so in…
This paper is dedicated to present model independent results for noncommutative quantum mechanics. We determine sufficient conditions for the convergence of the Born series and, in the sequel, unitarity is proved in full generality.
We argue that in quantum gravity there is no Born rule. The quantum-gravity regime, described by a non-normalisable Wheeler-DeWitt wave functional $\Psi$, must be in quantum nonequilibrium with a probability distribution $P\neq\left\vert…