Related papers: A combined-probability space and (un)certainty rel…
We show that probabilities of results of all possible measurements performing on a quantum system depend on the system's state only through its density matrix. Therefore all experimentally available information about the state contains in…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
In ordinary situations involving a small part of the universe, Born's rule seems to work well for calculating probabilities of observations in quantum theory. However, there are a number of reasons for believing that it is not adequate for…
Conventional quantum mechanics with a complex Hilbert space and the Born Rule is derived from five axioms describing properties of probability distributions for the outcome of measurements. Axioms I,II,III are common to quantum mechanics…
QBism regards quantum mechanics as an addition to probability theory. The addition provides an extra normative rule for decision-making agents concerned with gambling across experimental contexts, somewhat in analogy to the double-slit…
Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum…
A new geometric representation of qubit and qutrit states based on probability simplexes is used to describe the separability and entanglement properties of density matrices of two qubits. The Peres--Horodecki positive partial transpose…
Uncertainty quantification (UQ) is essential for deploying machine learning models in safety-critical physical systems, yet classical Bayesian approaches incur substantial computational overhead. We establish a formal connection between…
The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…
Projective measurement is used as a fundamental axiom in quantum mechanics, even though it is discontinuous and cannot predict which measured operator eigenstate will be observed in which experimental run. The probabilistic Born rule gives…
For a given pure state of a composite quantum system we analyze the product of its projections onto a set of locally orthogonal separable pure states. We derive a bound for this product analogous to the entropic uncertainty relations. For…
We show that the uncertainty relation as expressed in the Robertson-Schrodinger generalized form can be used to detect the mixedness of three-level quantum systems in terms of measureable expectation values of suitably chosen observables…
We introduce a hierarchy of conditions necessarily satisfied by any distribution P(ab) representing the probabilities for two separate observers to obtain outcomes a and b when making local measurements on a shared quantum state. Each…
In this paper we develop a new technique to model joint distributions of signals. Our technique is based on quantum mechanical conjugate variables. We show that the transition probability of quantum states leads to a distance function on…
Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet…
Constrained quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with a finite number of supporting points lying on a specific set. The specific set is known as the…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
The auxiliary rules of quantum mechanics have always included the Born rule that connects probability with square modulus. This need not be the case, for it is possible to introduce probability into the theory through probability current…
The expectation values of operators drawn from a single quantum state cannot be outside of a particular region, called their allowed region or the joint numerical range of the operators. Basically, the allowed region is an image of the…
It is argued from several points of view that quantum probabilities might play a role in statistical settings. New approaches toward quantum foundations have postulates that appear to be equally valid in macroscopic settings. One such…