title: Faster than Hermitian quantum mechanics.
abstract: Given an initial quantum state |psi(I)> and a final quantum state |psi(F)>, there exist Hamiltonians H under which |psi(I)> evolves into |psi(F)>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time tau? For Hermitian Hamiltonians tau has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, tau can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from |psi(I)> to |psi(F)> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.
authors.affiliation: Physics Department, Washington University, St. Louis, Missouri 63130, USA
authors.forename: Carl M
authors.initials: CM
authors.lastname: Bender
authors.forename: Dorje C
authors.initials: DC
authors.lastname: Brody
authors.forename: Hugh F
authors.initials: HF
authors.lastname: Jones
authors.forename: Bernhard K
authors.initials: BK
authors.lastname: Meister