title: Local PT symmetry violates the no-signaling principle.
abstract: Bender et al. [Phys. Rev. Lett. 80, 5243 (1998)] have developed PT-symmetric quantum theory as an extension of quantum theory to non-Hermitian Hamiltonians. We show that when this model has a local PT symmetry acting on composite systems, it violates the nonsignaling principle of relativity. Since the case of global PT symmetry is known to reduce to standard quantum mechanics A. Mostafazadeh [J. Math. Phys. 43, 205 (2001)], this shows that the PT-symmetric theory is either a trivial extension or likely false as a fundamental theory.
authors.affiliation: Physics Department, National Tsing-Hua University, Hsinchu City 300, Taiwan and Centre for Quantum Computation & Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology, Sydney, New South Wales 2007, Australia.
authors.forename: Yi-Chan
authors.initials: YC
authors.lastname: Lee
authors.affiliation: Centre for Quantum Computation & Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology, Sydney, New South Wales 2007, Australia.
authors.forename: Min-Hsiu
authors.initials: MH
authors.lastname: Hsieh
authors.affiliation: School of Physics, University of Sydney, Sydney, New South Wales 2006, Australia.
authors.forename: Steven T
authors.initials: ST
authors.lastname: Flammia
authors.affiliation: Physics Department, National Tsing-Hua University, Hsinchu City 300, Taiwan and Institute of Photonics Technologies, National Tsing-Hua University, Hsinchu City 300, Taiwan.
authors.forename: Ray-Kuang
authors.initials: RK
authors.lastname: Lee