相关论文: A remark on manageable multiplicative unitaries

We give a classification of unitary representations of certain Polish, not necessarily locally compact, groups: the groups of all measurable functions with values in the circle and the groups of all continuous functions on compact, second…

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…

Let v be the right regular representation of a compact quantum group G. Then (S.L.Woronowicz, "Compact quantum groups") v contains all irreducible representations of G and each irreducible representation enters v with the multiplicity equal…

Z.-J. Ruan has shown that several amenability conditions are all equivalent in the case of discrete Kac algebras. In this paper, we extend this work to the case of discrete quantum groups. That is, we show that a discrete quantum group,…

Maximally entangled bipartite unitary operators or gates find various applications from quantum information to being building blocks of minimal models of many-body quantum chaos, and have been referred to as "dual unitaries". Dual unitary…

According to a fundamental result in quantum computing, any unitary transformation on a composite system can be generated using so-called 2-local unitaries that act only on two subsystems. Beyond its importance in quantum computing, this…

We have written down a set of notes on compact quantum groups from which all the different aspects can be learned in an easy way and such that a lot of insight can be obtained without too much effort. Compact quantum groups have been…

We construct quantum mechanical observables and unitary operators which, if implemented in physical systems as measurements and dynamical evolutions, would contradict the Church-Turing thesis which lies at the foundation of computer…

We study actions of compact quantum groups on type I factors, which may be interpreted as projective representations of compact quantum groups. We generalize to this setting some of Woronowicz' results concerning Peter-Weyl theory for…

We outline a simple proof of Hulanicki's theorem, that a locally compact group is amenable if and only if the left regular representation weakly contains all unitary representations. This combines some elements of the literature which have…

In this paper, we provide several characterisations for uniform amenability concerning a family of finitely generated groups. More precisely, we show that the Hulanicki-Reiter condition for uniform amenability can be weakened in several…

We define concepts of amenability and co-amenability for algebraic quantum groups in the sense of A. Van Daele. We show that co-amenability of an algebraic quantum group always implies amenability of its dual. Various necessary and/or…

Boundedness and compactness properties of multiplication operators on quantum (non-commutative) function spaces are investigated. For endomorphic multiplication operators these properties can be characterized in the setting of quantum…

In this short note, further to Ng's study, we extend Bekka amenability and weak Bekka amenability to general locally compact quantum groups. We generalize some Ng's results to the general case. In particular, we show that, a locally compact…

Motivated by the recent rapid development of complexity theory applied to quantum mechanical processes we present the complete derivation of Nielsen's complexity of unitaries belonging to the representations of oscillator group. Our…

In unitary property testing a quantum algorithm, also known as a tester, is given query access to a black-box unitary and has to decide whether it satisfies some property. We propose a new technique for proving lower bounds on the quantum…

We show that the joint behaviour of an arbitrary pair of quantum observables can be described by quasi-probabilities, which are extensions of the standard probabilities used for describing the behaviour of a single observable. The physical…

Physical interpretations of the time-symmetric formulation of quantum mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of weak values. The most direct, yet somewhat naive, interpretation uses the time-symmetric…

The controllability property of the unitary propagator of an N-level quantum mechanical system subject to a single control field is described using the structure theory of semisimple Lie algebras. Sufficient conditions are provided for the…

During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…