Department of Mathematical Sciences
报告题目: Generalized Graph States Based on Hadamard Matrices
摘要：Graph states are widely used in quantum information theory, including entanglement theory, quantum error correction, and one-way quantum computing. Graph states have a nice structure related to a certain graph, which is given by either a stabilizer group or an encoding circuit, both can be directly given by the graph. To generalize graph states, whose stabilizer groups are abelian subgroups of the Pauli group, one approach taken is to study non-abelian stabilizers. In this work, we propose to generalize graph states based on the encoding circuit, which is completely determined by the graph and a Hadamard matrix. We study the entanglement structures of these generalized graph states, and show that they are all maximally mixed locally. We also explore the relationship between the equivalence of Hadamard matrices and local equivalence of the corresponding generalized graph states. This leads to a natural generalization of the Pauli (X,Z) pairs, which characterizes the local symmetries of these generalized graph states. Our approach is also naturally generalized to construct graph quantum codes which are beyond stabilizer codes.
报告人简介： Bei Zeng is an associate professor of mathematics at the University of Guelph. She received the B.Sc. degree in physics and mathematics in 2002 and M.Sc. degree in physics in 2004, from Tsinghua University. She received the Ph.D. degree in physics from MIT in 2009. From Sept. 2009 to Aug. 2010, she was a postdoctoral fellow at the Institute for Quantum Computing at the University of Waterloo. Her research interests include quantum information theory, coding theory, quantum computation, theory of quantum entanglement, and mathematical physics.