Related papers: Quantum Conditional Probabilities and New Measures…
It is argued that Feynman's rules for evaluating probabilities, combined with von Neumann's principle of psycho-physical parallelism, help avoid inconsistencies, often associated with quantum theory. The former allows one to assign…
For many-particle systems, quantum information in base n can be defined by partitioning the set of states according to the outcomes of n-ary (joint) observables. Thereby, k particles can carry k nits. With regards to the randomness of…
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
Classical and quantum information theory are simply explained. To be more specific it is clarified why Shannon entropy is used as measure of classical information and after a brief review of quantum mechanics it is possible to demonstrate…
We study the contextuality of a three-level quantum system using classical conditional entropy of measurement outcomes. First, we analytically construct the minimal configuration of measurements required to reveal contextuality. Next, an…
Our aim is to make a step towards clarification of foundations for the notion of entanglement (both physical and mathematical) by representing it in the conditional probability framework. In Schr\"odinger's words, this is entanglement of…
For noncomposite systems in classical and quantum domains, we obtain new inequalities such as the subadditivity and strong subadditivity conditions for Shannon entropies and information determined by the probability distributions and for…
We consider the analysis of probability distributions through their associated covariance operators from reproducing kernel Hilbert spaces. We show that the von Neumann entropy and relative entropy of these operators are intimately related…
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…
Uncertainty principle plays a crucial role in quantum mechanics, because it captures the essence of the inevitable randomness associated with the outcomes of two incompatible quantum measurements. Information entropy can perfectly describe…
An essential quantity in quantum information theory is the von Neumann entropy which depends entirely on the quantum density operator. Once known, the density operator reveals the statistics of observables in a quantum process, and the…
It is observed that the entropy reduction (the information gain in the initial terminology) of an efficient (ideal or pure) quantum measurement coincides with the generalized quantum mutual information of a q-c channel mapping an a priori…
Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized measurement results. In this article, a…
This work develops a conceptual framework for the foundations of quantum physics, linking two main approaches: the algebraic formulation and quantum probability. Rather than proposing new axioms or theories, the text reorganizes and…
The concept of causality is fundamental to numerous scientific explanations; however, its extension to the quantum regime has yet to be rigorously explored. This letter introduces the development of a quantum causal index, a novel extension…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
Observational entropy is interpreted as the uncertainty an observer making measurements associates with a system. So far, properties that make such an interpretation possible rely on the assumption of ideal projective measurements. We show…
We show that the so-called quantum probabilistic rule, usually presented in the physical literature as an argument of the essential distinction between the probability relations under quantum and classical measurements, is not, as it is…
In this paper, we characterize the saturation of four universal inequalities in quantum information theory, including a variant version of strong subadditivity inequality for von Neumann entropy, the coherent information inequality, the…