QUANTUM TELEPORTATION IN THE COMMUTING OPERATOR FRAMEWORK

作     者：Conlon, Alexandre Crann, Jason Kribs, David W. Levene, Rupert H. 

作者机构：School of Mathematics & Statistics Carleton University OttawaONH1S 5B6 Canada Department of Mathematics & Statistics University of Guelph GuelphONN1G 2W1 Canada Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada School of Mathematics and Statistics University College Dublin Dublin 4 Belfield Ireland Centre for Quantum Engineering Science and Technology University College Dublin Dublin 4 Belfield Ireland 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2022年

核心收录：

摘      要：We introduce a notion of teleportation scheme between subalgebras of semi-finite von Neumann algebras in the commuting operator model of locality. Using techniques from subfactor theory, we present unbiased teleportation schemes for relative commutants N′ ∩ M of a large class of finite-index inclusions N ⊆ M of tracial von Neumann algebras, where the unbiased condition means that no information about the teleported observables are contained in the classical communication sent between the parties. For a large class of subalgebras N of matrix algebras Mn(ℂ), including those relevant to hybrid classical/quantum codes, we show that any tight teleportation scheme for N necessarily arises from an orthonormal unitary Pimsner-Popa basis of Mn(ℂ) over N′, generalising work of Werner [94]. Combining our techniques with those of Brannan-Ganesan-Harris [22], we compute quantum chromatic numbers for a variety of quantum graphs arising from finite-dimensional inclusions N ⊆ M. Copyright © 2022, The Authors. All rights reserved.