Related papers: Generalized Holevo theorem and distinguishability …
The notion of distance between a global Maxwellian function and an arbitrary solution $f$ (with the same total density $\rho$ at the fixed moment $t$) of Boltzmann equation is introduced. In this way we essentially generalize the important…
A new necessary separability criterion that relates the structures of the total density matrix and its reductions is given. The method used is based on the realignment method [K. Chen and L.A. Wu, Quant. Inf. Comput. 3, 193 (2003)]. The new…
We introduce the concept of cloning for classes of observables and classify cloning machines for qubit systems according to the number of parameters needed to describe the class under investigation. A no-cloning theorem for observables is…
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…
We establish connections between the requirement of measurability of a probability space and the principle of complimentarity in quantum mechanics. It is shown that measurability of a probability space implies the dependence of results of…
In a pre-selected Hilbert space of quantum states the unitarity of the evolution is usually guaranteed via a pre-selection of the generator (i.e., of the Hamiltonian operator) in self-adjoint form. In fact, the simultaneous use of both of…
General wisdom tells us that if two quantum states are ``macroscopically distinguishable'' then their superposition should be hard to observe. We make this intuition precise and general by quantifying the difficulty to observe the quantum…
Our everyday reality is characterized by objective information$\unicode{x2013}$information that is selected and amplified by the environment that interacts with quantum systems. Many observers can accurately infer that information…
General relativity may seem very different from quantum theory, but work on quantum gravity has revealed a deep analogy between the two. General relativity makes heavy use of the category nCob, whose objects are (n-1)-dimensional manifolds…
We consider some generalization of the theory of quantum states, which is based on the analysis of long standing problems and unsatisfactory situation with the possible interpretations of quantum mechanics. We demonstrate that the…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
Every topological space has a Kolmogorov quotient that is obtained by identifying topologically indistinguishable points, that is, points that are contained in exactly the same open sets. In this survey, we look at the relationship between…
Most of the standard proofs of the Bell theorem are based on the Kolmogorov axioms of probability theory. We show that these proofs contain mathematical steps that cannot be reconciled with the Kolmogorov axioms. Specifically we demonstrate…
We introduce the concept of mutual independence -- correlations shared between distant parties which are independent of the environment. This notion is more general than the standard idea of a secret key -- it is a fully quantum and more…
Motivated by the notions of $k$-extendability and complete extendability of the state of a finite level quantum system as described by Doherty et al (Phys. Rev. A, 69:022308), we introduce parallel definitions in the context of Gaussian…
The projected ensemble -- an ensemble of pure states on a subsystem conditioned on projective measurement outcomes on its complement -- provides a finer probe of ergodicity and information structure than the reduced density matrix of the…
We show how one can solve the problem of discriminating between qubit states. We use the quantum state discrimination duality theorem and the Bloch sphere representation of qubits which allows for an easy geometric and analytical…
Standard quantum mechanics undeniably violates the notion of separability that classical physics accustomed us to consider as valid. By relating the phenomenon of quantum nonseparability to the all-important concept of potentiality, we…
The characterization of the quantum ensemble is a fundamental issue in quantum information theory and foundations. The ensemble is also useful for various quantum information processing. To characterize the quantum ensemble, in this…
Quantum theory has the property of "local tomography": the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We…