Related papers: Can \v{C}encov meet Petz?
In this article a notion of information is presented which stresses the contextuality of quantum objects and their measurement. Mathematically this is reached by a quantification of the quantum mechanical surplus knowledge which has been…
We extend the generic Bell inequalities suggested by Son, Lee, and Kim [Phys. Rev. Lett. 96, 060406 (2006)] to incorporate multiple observables for tripartite systems and introduce a geometric methodology for calculating classical upper…
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in…
Let $\Gamma$ be a finite group acting faithfully and linearly on a vector space $V$. Let $T(V)$ ($S(V)$) be the tensor (symmetric) algebra associated to $V$ which has a natural $\Gamma$ action. We study generalized quadratic relations on…
We identify five selected open problems in the theory of quantum information, which are rather simple to formulate, were well-studied in the literature, but are technically not easy. As these problems enjoy diverse mathematical connections,…
Different graphical calculi have been proposed to represent quantum computation. First the ZX- calculus [4], followed by the ZW-calculus [12] and then the ZH-calculus [1]. We can wonder if new Z*-calculi will continue to be proposed…
Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…
In this chapter we explore the connection between mesoscopic physics and quantum computing. After giving a bibliography providing a general introduction to the subject of quantum information processing, we review the various approaches that…
We develop a new approach to deal with qubit information systems using toric geometry and its relation to Adinkra graph theory. More precisely, we link three different subjects namely toric geometry, Adinkras and quantum information theory.…
In this project, we will develop the theory of Banach algebras and prove two celebrated theorems, the Gelfand representation theorem and the GKZ theorem. We will then proceed to develop the theory of $C^*$-algebras and prove the…
I present a method of performing geometric quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UTC). I also show that by using this method…
We propose a new methodology, called numerical canonical quantization, to solve quantum Maxwell's equations useful for mathematical modeling of quantum optics physics, and numerical experiments on arbitrary passive and lossless…
By identifying a family of corner cutting schemes as a dimension elevation process of Gelfond-Bezier curves, we give a Muntz type condition for the convergence of the generated control polygons to the underlying curve. The surprising…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
Borrowing ideas from the relation between simply laced Lie algebras and Dynkin diagrams, a weighted graph theory representation of quantum information is addressed. In this way, the density matrix of a quantum state can be interpreted as a…
We survey Weber's class number problem and its variants in the spirit of arithmetic topology; we recollect some history, present a relation to certain units and generalized Pell's equation, and overview a study of the $p$-adic limits of…
A family of skew information quantities is obtained, in which the well-known Wigner-Yanase skew information and quantum Fisher information stand as special cases. A transparent proof of convexity of the generalized skew information is…
We review some geometrical aspects pertaining to the world of monotone quantum metrics in finite dimensions. Particular emphasis is given to an unfolded perspective for quantum states that is built out of the spectral theorem and is…
We introduce and analyse the structure of C*-algebras arising from ideals in right tensor C*-precategories, which naturally generalize both relative Cuntz-Pimsner and Doplicher-Roberts algebras. We establish an explicit intrinsic…
It is shown on a simple classical model of a quantum particle at rest that information contained into the quantum state (quantum information) can be obtained by integrating the corresponding probability distribution on phase space, i.e. by…