Related papers: A Quantum Canonical Embedding
The present thesis shows that Quantum Information concepts can be used to better understand the quantum-to-classical boundary in mesoscopic and macroscopic systems. Our findings suggest a way to push this boundary towards the macroscopic…
The algebra of generalized linear quantum canonical transformations is examined in the prespective of Schwinger's unitary-canonical basis. Formulation of the quantum phase problem within the theory of quantum canonical transformations and…
This is a brief, popular-level introduction to holographic entanglement. It was published in the newsletter of the International Centre for Theoretical Sciences, Bangalore.
We introduce a modified quantum enveloping algebra as well as a (modified) covering quantum algebra for the ortho-symplectic Lie superalgebra osp(1|2). Then we formulate and compute the corresponding canonical bases, and relate them to the…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
The dual basis of the canonical basis of the modified quantized enveloping algebra is studied, in particular for type $A$. The construction of a basis for the coordinate algebra of the $n\times n$ quantum matrices is appropriate for the…
In this paper we define canonical sine and cosine transform, convolution operations, prove convolution theorems in space of integrable functions on real space. Further, obtain some results require to construct the spaces of integrable…
Short review article on quantum computation accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM
A formulation of Covariant Canonical Quantization is discussed, which works on an extended Hilbert space and reduces to conventional canonical quantization when constraining to the solution of the field equation a priori. From the formal…
Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties more complex than tractable at present on classical architectures. Here, we discuss…
Some filtrations of the tensor product of a highest weight module and a lowest weight module over quantum group $U_q(\mathfrak g)$ are constructed in \cite{LZ:2009} and one can use them to define some ideals of the modified quantized…
We provide some necessary details to several arguments appearing in our previous paper ``Canonical bases for quantum generalized Kac-Moody algebras''. We also make the link with some other work on the same subject.
We investigate an entangled deformation of the deterministic quantum cloning process, called enscription, that can be applied to (certain) sets of distinct quantum states which are not necessarily orthogonal, called texts. Some basic…
A certain notion of canonical equivalence in quantum mechanics is proposed. It is used to relate quantal systems with discrete ones. Discrete systems canonically equivalent to the celebrated harmonic oscillator as well as the quartic and…
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…
We prove some infinitesimal analogs of classical results of Menger, Schoenberg and Blumenthal giving the existence conditions for isometric embeddings of metric spaces in the finite-dimensional Euclidean spaces.
This is a review of the aspirations and disappointments of the canonical quantization of geometry. I compare the two chief ways of looking at canonical gravity, geometrodynamics and connection dynamics. I capture as much of the classical…
This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…
A common theme in mathematics is the evaluation of Gauss integrals. This, coupled with the fact that they are used in different branches of science, makes the topic always actual and interesting. In these notes we shall analyze a particular…
Quantum embedding theories are powerful tools for approximately solving large-scale strongly correlated quantum many-body problems. The main idea of quantum embedding is to glue together a highly accurate quantum theory at the local scale…