Quantum teleportation and Birman–Murakami–Wenzl algebra

Abstract

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 the BMW algebra, which is generated by both the Temperley-Lieb projector and the Yang-Baxter gate. We describe quantum teleportation using the Temperley-Lieb projector and the Yang-Baxter gate, respectively, and study teleportation-based quantum computation using the Yang-Baxter gate. On the other hand, we exploit the extended Temperley-Lieb diagrammatical approach to clearly show that the tangle relations of the BMW algebra have a natural interpretation of quantum teleportation. Inspired by this interpretation, we construct a general representation of the tangle relations of the BMW algebra and obtain interesting representations of the BMW algebra. Therefore our research sheds a light on a link between quantum information science and low-dimensional topology.

Quantum nonlocality and topological quantum phase transitions in the extended Ising chain

“…It is of note that we use the twosite quantum nonlocality based on the theory of multipartite nonlocality to identify the TQPTs of the extended Ising model in this work, avoiding the cumbersome numerical calculation of handling the three-body operator of the model. It is reported that two-site correlation can undoubtedly characterize the TQPTs in the extended Ising model [54][55][56][57][58][59][60][61][62].…”

“…Fortunately, it is found that the extended Ising model is the very one of them and hosts rich topological characterizations. Many studies using quantum correlations are proposed to explore the TQPTs in the extended Ising model [54][55][56][57][58][59][60][61][62]. Although the topological phases of the extended Ising model driven by varying system parameters are completely investigated and successfully accomplished, how the nonlocality behaves when the TQPTs emerges is still an interesting issue.…”

Steered Quantum Coherence as a Signature of Topological Quantum Phase Transitions in the Extended XY Model

“…Recently, several quantum concepts, such as quantum correlations, [31][32][33][34][35] quantum deficit, [36] quantum coherence, [37,38] and quantum Fisher information (QFI), [39] have been developed to study TQPTs. We expect to find the advantage of SQC in characterizing TQPT compared to these quantum concepts.…”

Measurement Uncertainty and Its Connection to Quantum Coherence in an Inertial Unruh–DeWitt Detector

“…There has been significant progress regarding the experimental aspects of EUR, [ 11–13 ] which has promoted the development of applications in quantum information science. [ 14–17 ] Remarkably, the techniques of entanglement‐assisted EUR have been used widely in the context of quantum information and computation, such as quantum key distribution, [ 18,19 ] quantum cryptography, [ 20,21 ] EPR steering, [ 22 ] entanglement witness, [ 11,12,23 ] quantum teleportation, [ 24 ] and quantum metrology. [ 25–27 ] Additionally, the EUR can yield promising results when considering the effect of the environment.…”