Related papers: Quantum teleportation and Birman-Murakami-Wenzl al…
In this article we consider conditions under which projection operators in multiplicity free semi-simple tensor categories satisfy Temperley-Lieb like relations. This is then used as a stepping stone to prove sufficient conditions for…
In this expository paper we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and ZX-calculus,…
Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of…
The topological basis associated with Birman-Wenzl-Murakami algebra (BWMA) is constructed and the three dimensional forms of braiding matrices S have been found for both $S^+=S$ and $S^+=S^{-1}$. A familiar spin-1 model related to braiding…
A generalization of the Kauffman tangle algebra is given for Coxeter type Dn. The tangles involve a pole or order 2. The algebra is shown to be isomorphic to the Birman-Murakami-Wenzl algebra of the same type. This result extends the…
A new link between tetrahedra and the group SU(2) is pointed out: by associating to each face of a tetrahedron an irreducible unitary SU(2) representation and by imposing that the faces close, the concept of quantum tetrahedron is seen to…
We study various aspects of the topological quantum computation scheme based on the non-Abelian anyons corresponding to fractional quantum hall effect states at filling fraction 5/2 using the Temperley-Lieb recoupling theory. Unitary…
We uncover a connection between two seemingly separate subjects in integrable models: the representation theory of the affine Temperley-Lieb algebra, and the algebraic structure of solutions to the Bethe equations of the XXZ spin chain. We…
We apply covert quantum communication based on entanglement generated from the Minkowski vacuum to the setting of quantum computation and quantum networks. Our approach hides the generation and distribution of entanglement in quantum…
Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solution-generating technique to solve the $(d,m,l)$-generalized Yang-Baxter equation, for $m/2\leq l \leq m$, which allows to systematically…
In [1] we discussed how quantum gravity may be simulated using quantum devices and gave a specific proposal -- teleportation by size and the phenomenon of size-winding. Here we elaborate on what it means to do 'Quantum Gravity in the Lab'…
This paper explores the fundamental relationship between the geometry of entanglement and von Neumann entropy, shedding light on the intricate nature of quantum correlations. We provide a comprehensive overview of entanglement, highlighting…
If a photon interacts with a member of an entangled photon pair via a so-called Bell-state measurement (BSM), its state is teleported over principally arbitrary distances onto the second member of the pair. Starting in 1997, this puzzling…
We extend the Framization of the Temperley-Lieb algebra to Coxeter systems of type $\mathtt{B}$. We first define a natural extension of the classical Temperley-Lieb algebra to Coxeter systems of type $\mathtt{B}$ and prove that such an…
Many of the known solutions of the Yang-Baxter equation, which are related to solvable lattice models of vertex- and IRF-type, yield representations of the Birman-Wenzl-Murakami algebra. From these, representations of a two-colour…
Quantum teleportation provides a way to transfer unknown quantum states from one system to another via an entangled state as a quantum channel without physical transmission of the object itself. The entangled channel, measurement performed…
Quantum teleportation -- the transmission and reconstruction over arbitrary distances of the state of a quantum system -- is demonstrated experimentally. During teleportation, an initial photon which carries the polarization that is to be…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…
We introduce tangles of type $E_n$ and construct a representation of the Birman-Murakami-Wenzl algebra (BMW algebra) of type $E_6$. As a representation of the Artin group of type $E_6$, this representation is equivalent to the faithful…
With the long-term goal of studying models of quantum gravity in the lab, we propose holographic teleportation protocols that can be readily executed in table-top experiments. These protocols exhibit similar behavior to that seen in the…