相关论文: Commutation Groups and State-Independent Contextua…
Quantum fields are shown to provide an example of infinite-dimensional quantum groups. A dictionary is established between quantum field and quantum group concepts: the expectation value over the vacuum is the counit, Wick's theorem is the…
In standard quantum mechanics, reference frames are treated as abstract entities. We can think of them as idealized, infinite-mass subsystems which decouple from the rest of the system. In nature, however, all reference frames are realized…
$p$-Mechanics is a consistent physical theory which describes both classical and quantum mechanics simultaneously through the representation theory of the Heisenberg group. In this paper we describe how non-linear canonical transformations…
Contextuality is a key characteristic that separates quantum from classical phenomena and an important tool in understanding the potential advantage of quantum computation. However, when assessing the quantum resources available for quantum…
In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in…
For a family of unital free *-algebras with a family of states on them, we construct a sequence of noncommutative probability spaces, which are tensor product algebras with tensor product states and which approximate the free product of…
The algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider structure groups taking values in the quantum groups and…
In this version small mistakes are corrected and the exposition is changed as suggested by the referee (to appear in Canadian Journal of Mathematics). The first main result of the paper is a criterion for a partially commutative group $\GG$…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
Properties of group coherent states can be derived "effectively" without knowing full wave functions. The procedure is detailed in this article as an example of general methods for effective constraints. The role of constraints in the…
The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements cannot be viewed as revealing pre-existing properties of…
Contextuality is a fundamental feature of quantum theory and is necessary for quantum computation and communication. Serious steps have therefore been taken towards a formal framework for contextuality as an operational resource. However,…
In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. We, then, unearth the structure of the convex set of covariant…
The authors previously found a model of universal quantum computation by making use of the coset structure of subgroups of a free group $G$ with relations. A valid subgroup $H$ of index $d$ in $G$ leads to a 'magic' state…
We study subsets $E$ of finitely generated groups where the set of all words over a given finite generating set that lie in $E$ forms a context-free language. We call these sets recognisably context-free. They are invariant of the choice of…
In this thesis we shall demonstrate that a measurement of position alone in non-commutative space cannot yield complete information about the quantum state of a particle. Indeed, the formalism used entails a description that is non-local in…
Non-classical probability (along with its underlying logic) is a defining feature of quantum mechanics. A formulation that incorporates them, inherently and directly, would promise a unified description of seemingly different prescriptions…
Contextuality is a central feature distinguishing quantum from classical probability theories, but its operational meaning is often stated only qualitatively. In this Letter, we study a simple information-theoretic question: how much…
The ability to understand and generate languages sets human cognition apart from other known life forms'. We study a way of combing two of the most successful routes to meaning of language--statistical language models and symbolic semantics…
Graph-theoretic structures play a central role in the description and analysis of quantum systems. In this work, we introduce a new class of quantum states, called $A_\alpha$-graph states, which are constructed from either unweighted or…