Related papers: Included-row exchange principle for quantum minors
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
We introduce a definition of admissibility for subintervals in interval exchange transformations. Using this notion, we prove a property of the natural codings of interval exchange transformations, namely that any derived set of a regular…
The characterization of quantum correlations is crucial to the development of new quantum technologies and to understand how dramatically quantum theory departs from classical physics. Here we systematically study single- and multiparticle…
We introduce the notions of quantum characteristic and quantum flatness for arbitrary rings. More generally, we develop the theory of quantum integers in a ring and show that the hypothesis of quantum flatness together with positive quantum…
In this paper a nonlocal generalization of field quantization is suggested. This quantization principle presupposes the assumption that the commutator between a field operator an the operator of the canonical conjugated variable referring…
We establish a quantum Galois correspondence for compact Lie groups of automorphisms acting on a simple vertex operator algebra.
Let $R$ be a commutative ring with identity. For an $R$-module $M$, the notion of strongly prime submodule of $M$ is defined. It is shown that this notion of prime submodule inherits most of the essential properties of the usual notion of…
Building large-scale quantum communication networks has its unique challenges. Here, we demonstrate that a network-wide synergistic usage of quantum memories distributed in a quantum communication network offers a fundamental advantage. We…
Let $\FF$ be a finite field and $(Q,\bfd)$ an acyclic valued quiver with associated exchange matrix $\tilde{B}$. We follow Hubery's approach \cite{hub1} to prove our main conjecture of \cite{rupel}: the quantum cluster character gives a…
We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state…
It is well-known that the Pl\"ucker relations generate the ideal of relations of the maximal minors of a generic matrix. In this paper we discuss the relations between minors of a (non-maximal) fixed size. We will exhibit minimal relations…
Using a suitably noncommutative flat matrix model, it is shown that the quantum permutation group has free orbitals: that is, a monomial in the generators of the algebra of functions can be zero for trivial reasons only. It is shown that…
The transfer or exchange of multipartite quantum states is critical to the realization of large-scale quantum information processing and quantum communication. A challenging question in this context is: What is the minimum resource required…
We develop theory of multiplicity maps for compact quantum groups, as an application, we obtain a complete classification of right coideal $C^*$-algebras of $C(SU_q(2))$ for $q\in [-1,1]\setminus \{0\}$. They are labeled with Dynkin…
The key requirement for quantum networking is the distribution of entanglement between nodes. Surprisingly, entanglement can be generated across a network without direct transfer - or communication - of entanglement. In contrast to…
Recently there has been much effort in developing a quantum generalisation of reference frame transformations. Despite important progress, a complete understanding of their principles is still lacking. In particular, we argue that previous…
We present a theory of "quantum references", similar to lenses in classical functional programming, that allow to point to a subsystem of a larger quantum system, and to mutate/measure that part. Mutable classical variables, quantum…
In perturbative quantum field theory the maintenance of classical symmetries is quite often investigated by means of algebraic renormalization, which is based on the Quantum Action Principle. We formulate and prove this principle in a new…
A new formulation of quantum mechanics is proposed based on a new principle that can be considered a generalization of the Born rule. The principle is composed of a mathematical expression and an associated interpretation, and establishes a…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…