Related papers: A quantum framework for likelihood ratios
As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges…
The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones: this leads to a frame in which two kinds of correlations emerge: the classical…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
A new formulation of quantum mechanics is developed which does not require the concept of the wave-particle duality. Rather than assigning probabilities to outcomes, probabilities are instead assigned to entire fine-grained histories. The…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
In statistical practice, a realistic Bayesian model for a given data set can be defined by a likelihood function that is analytically or computationally intractable, due to large data sample size, high parameter dimensionality, or complex…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
Statistical prediction plays an important role in many decision processes such as university budgeting (depending on the number of students who will enroll), capital budgeting (depending on the remaining lifetime of a fleet of systems), the…
This work develops analytic methods to quantitatively demarcate quantum reality from its subset of classical phenomenon, as well as from the superset of general probabilistic theories. Regarding quantum nonlocality, we discuss how to…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the…
A quantum probability measure is a function on a sigma-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but whose values are positive operators acting on a complex…
In a Cox model, the partial likelihood, as the product of a series of conditional probabilities, is used to estimate the regression coefficients. In practice, those conditional probabilities are approximated by risk score ratios based on a…
The ability to efficiently infer system parameters is essential in any signal-processing task that requires fast operation. Dealing with quantum systems, a serious challenge arises due to substantial growth of the underlying Hilbert space…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
Quantum estimation theory is a reformulation of random statistical theory with the modern language of quantum mechanics. In fact, the density operator plays a role similar to that of probability distribution functions in classical…
Any physical theory aims to establish the relationship between physical systems in terms of the interaction between these systems. However, any known approach in the literature to infer this interaction is dependent on the particular…
Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions…
Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability…