Abstract
Given an initial quantum state and a final quantum state , there exist Hamiltonians under which evolves into . Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of is held fixed, which achieves this transformation in the least time ? For Hermitian Hamiltonians has a nonzero lower bound. However, among non-Hermitian -symmetric Hamiltonians satisfying the same energy constraint, can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from to 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.
- Received 5 September 2006
DOI:https://doi.org/10.1103/PhysRevLett.98.040403
©2007 American Physical Society