Related papers: Generalized Multiplicative Domains and Quantum Err…
We fully classify completely multiplicative sequences which are given by generalised polynomial formulae, and obtain a similar result for (not necessarily completely) multiplicative sequences under the additional restriction that the…
Three extensions and reinterpretations of nonclassical probabilities are reviewed. (i) We propose to generalize the probability axiom of quantum mechanics to self-adjoint positive operators of trace one. Furthermore, we discuss the…
Generalised observables (POM observables) are necessary for representing all possible measurements on a quantum system. Useful algebraic operations such as addition and multiplication are defined for these observables, recovering many…
Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…
We show that quantum subdynamics of an open quantum system can always be described by a Hermitian map, irrespective of the form of the initial total system state. Since the theory of quantum error correction was developed based on the…
We obtain generalisations of some inequalities for positive unital linear maps on matrix algebra. This also provides several positive semidefinite matrices and we get some old and new inequalities involving the eigenvalues of a Hermitian…
In this article, we establish the duality between the generalised Drinfeld double and generalised quantum codouble within the framework of modular or manageable (not necessarily regular) multiplicative unitaries, and discuss several…
We elaborate on the notion of generalized tomograms, both in the classical and quantum domains. We construct a scheme of star-products of thick tomographic symbols and obtain in explicit form the kernels of classical and quantum generalized…
We construct differential algebras in which spaces of (one-dimensional) periodic ultradistributions are embedded. By proving a Schwartz impossibility type result, we show that our embeddings are optimal in the sense of being consistent with…
We compare two known methods of extending a complex, unital, commutative normed algebra so as to include solutions to sets of monic polynomials over the original algebra. (One of these is a generalisation of a construction from the thesis…
We analyze bipartite matrices and linear maps between matrix algebras, which are respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' actions. By presenting an expansive list of examples from the…
We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable, c) completely positive, d) extended by identity impose…
Left and right "generalized Schur algebras", previously introduced by the author, are defined and analyzed. Filtrations of these algebras lead, in most cases, to parameterizations of the their irreducible representations over fields of…
We establish operator structure identities for quantum channels and their error-correcting and private codes, emphasizing the complementarity relationship between the two perspectives. Relevant structures include correctable and private…
Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching…
We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…
We present a new application of harmonic analysis to quantum information by constructing intriguing classes of quantum channels stemming from specific representations of multiplier algebras over locally compact groups $G$. Beginning with a…
We investigate quantum corrections to the effective action of the universal hypermultiplet in the language of projective superspace. We rederive the recently found one-loop correction to the universal hypermultiplet moduli space geometry.…
An interesting concept in quantum computation is that of global control (GC), where there is no need to manipulate qubits individually. One can implement a universal set of quantum gates on a one-dimensional array purely via signals that…
We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of…