Related papers: Teleportation, Braid Group and Temperley--Lieb Alg…
In this paper, we explore algebraic structures and low dimensional topology underlying quantum information and computation. We revisit quantum teleportation from the perspective of the braid group, the symmetric group and the virtual braid…
Bell states and quantum teleportation play important roles in the study of quantum information and computation. But a comprehensive theoretical research on both of them remains to be performed. This work aims to investigate important…
The braid group appears in many scientific fields and its representations are instrumental in understanding topological quantum algorithms, topological entropy, classification of manifolds and so on. In this work, we study planer diagrams…
In this paper, we revisit topological-like features in the extended Temperley--Lieb diagrammatical representation for quantum circuits including the teleportation, dense coding and entanglement swapping. We perform these quantum circuits…
This paper focuses on the study of topological features in teleportation-based quantum computation as well as aims at presenting a detailed review on teleportaiton-based quantum computation (Gottesman and Chuang, Nature 402, 390, 1999). In…
The virtual knot theory is a new interesting subject in the recent study of low dimensional topology. In this paper, we explore the algebraic structure underlying the virtual braid group and call it the virtual Temperley--Lieb algebra which…
In this paper, we investigate the relationship of quantum teleportation in quantum information science and the Birman-Murakami-Wenzl (BMW) algebra in low-dimensional topology. For simplicity, we focus on the two spin-1/2 representation of…
Quantum teleportation plays a key role in modern quantum technologies. Thus, it is of much interest to generate alternative approaches or representations aimed at allowing us a better understanding of the physics involved in the process…
Important developments in fault-tolerant quantum computation using the braiding of anyons have placed the theory of braid groups at the very foundation of topological quantum computing. Furthermore, the realization by Kauffman and Lomonaco…
We study the construction of both universal quantum computation and multi-partite entangled states in the topological diagrammatical approach to quantum teleportation. Our results show that the teleportation-based quantum circuit model…
Permutation and its partial transpose play important roles in quantum information theory. The Werner state is recognized as a rational solution of the Yang--Baxter equation, and the isotropic state with an adjustable parameter is found to…
In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particle-like excitations (quasiparticles) around one another in…
The topological model for quantum computation is an inherently fault-tolerant model built on anyons in topological phases of matter. A key role is played by the braid group, and in this survey we focus on a selection of ways that the…
Teleportation is a facet where quantum measurements can act as a powerful resource in quantum physics, as local measurements allow to steer quantum information in a non-local way. While this has long been established for a single Bell pair,…
This is a systematic introduction for physicists to the theory of algebras and groups with braid statistics, as developed over the last three years by the author. There are braided lines, braided planes, braided matrices and braided groups…
Simplest quantum teleportation algorithms can be represented in geometric terms in spaces of dimensions 3 (for real state-vectors) and 4 (for complex state-vectors). The geometric representation is based on geometric-algebra coding, a…
The topological surface code is a leading candidate for harnessing long-range entanglement to protect logical quantum information against errors, and teleportation of logical states is desirable for robust quantum information processing.…
We present two paradigms relating algebraic, topological and quantum computational statistics for the topological model for quantum computation. In particular we suggest correspondences between the computational power of topological quantum…
We determine the image of the braid groups inside the Temperley-Lieb algebras, defined over finite field, in the semisimple case, and for suitably large (but controlable) order of the defining (quantum) parameter. We also prove that, under…
Quantum Candies or Qandies provide us with a lucid way of understanding the concepts of quantum information and quantum science in the language of candies. The critical idea of qandies is intuitively depicting quantum science to the general…