Related papers: Quantum teleportation and Birman-Murakami-Wenzl al…
Quantum state teleportation is a protocol where a shared entangled state is used as a quantum channel to transmit quantum information between distinct locations. Here we consider the task of estimating entanglement in teleportation…
A method of constructing Temperley-Lieb algebras(TLA) representations has been introduced in [Xue \emph{et.al} arXiv:0903.3711]. Using this method, we can obtain another series of $n^{2}\times n^{2}$ matrices $U$ which satisfy the TLA with…
Quantum computers are constantly growing in their number of qubits, but continue to suffer from restrictions such as the limited pairs of qubits that may interact with each other. Thus far, this problem is addressed by mapping and moving…
In this work we introduce the concept of Modular Framization or simply Framization. We construct a framization $F_{d,n}$ of the Birman--Wenzl--Murakami algebra, also known as BMW algebra, and start a systematic study of this framization. We…
In this manuscript we analyse generalised port-based teleportation (PBT) schemes, allowing for transmitting more than one unknown quantum state (or a composite quantum state) in one go, where the state ends up in several ports at Bob's…
We consider quantum teleportation using the thermally entangled state of a three-qubit Heisenberg XX ring as a resource. Our investigation reveals interesting aspects of quantum entanglement not reflected by the pairwise thermal concurrence…
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…
The cyclotomic Birman-Wenzl-Murakami algebras are quotients of the affine BMW algebras in which the affine generator satisfies a polynomial relation. We show that the cyclotomic BMW algebras are free modules over any (admissible, integral)…
It is crucial to design quantum circuits as small as possible and as shallow as possible for quantum information processing tasks. We design quantum circuits with simplified gate-count, cost, and depth for implementing quantum teleportation…
Quantum geometry may enable the development of quantum phases ranging from superconductivity to correlated topological states. One powerful probe of quantum geometry is the nonlinear Hall response which detects Berry curvature dipole in…
This paper presents results on the framization of some knot algebras, defined by the authors. We explain the motivations of the concept of framization, coming from the Yokonuma--Hecke algebras, as well as recent results on the framization…
We study a class of quantum channels arising from the representation theory of compact quantum groups that we call Temperley-Lieb quantum channels. These channels simultaneously extend those introduced in [BC18], [AN14], and [LS14].…
Quantum teleportation and quantum memory are two crucial elements for large-scale quantum networks. With the help of prior distributed entanglement as a "quantum channel", quantum teleportation provides an intriguing means to faithfully…
We consider multiple teleportation in the Knill-Laflamme-Milburn (KLM) scheme. We introduce adaptive teleportation, i.e., such that the choice of entangled state used in the next teleportation depends on the results of the measurements…
We show that quantum entanglement states are associated with multilinear polynomials that cannot be factored. By using these multilinear polynomials, we propose a geometric representation for entanglement states. In particular, we show that…
Motived by the study of motion in a random environment we introduce and investigate a variant of the Temperley-Lieb algebra. This algebra is very rich, providing us three classes of solutions of the Yang-Baxter equation. This allows us to…
In this thesis, we have proposed some novel thought experiments involving foundations of quantum mechanics and quantum information theory, using quantum entanglement property. Concerning foundations of quantum mechanics, we have suggested…
Connections between set-theoretic Yang-Baxter and reflection equations and quantum integrable systems are investigated. We show that set-theoretic $R$-matrices are expressed as twists of known solutions. We then focus on reflection and…
Here a finite-Lieb-lattice quantum computing circuit consisting of spin-1/2 quantum bits (qubits) and triplet couplers is designed. Important gradient - quantum entanglement - is analysed. This type of design could be realised in a vast…
We introduce a BMW type algebra for every Coxeter group. These new algebras are introduced as deformations of the Brauer type algebras introduced by the author, they have the corresponding Hecke algebras as quotients.