Faster than Hermitian Time Evolution Export

@misc{citeulike:2426999, abstract = {For any pair of quantum states, an initial state |I\> and a final quantum state |F\>, in a Hilbert space, there are many Hamiltonians H under which |I\> evolves into |F\>. Let us impose the constraint that the difference between the largest and smallest eigenvalues of H, E\_max and E\_min, is held fixed. We can then determine the Hamiltonian H that satisfies this constraint and achieves the transformation from the initial state to the final state in the least possible 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. The minimum value of \tau can be made arbitrarily small because for PT-symmetric Hamiltonians the path from the vector |I\> to the vector |F\>, as measured using the Hilbert-space metric appropriate for this theory, can be made arbitrarily 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.}, archivePrefix = {arXiv}, author = {Bender, Carl M.}, citeulike-article-id = {2426999}, citeulike-linkout-0 = {http://arxiv.org/abs/0712.3910}, citeulike-linkout-1 = {http://arxiv.org/pdf/0712.3910}, eprint = {0712.3910}, keywords = {non-hermitian\_hamiltonians, quantum\_physics}, month = {Dec}, posted-at = {2008-02-25 20:20:31}, priority = {2}, title = {Faster than Hermitian Time Evolution}, url = {http://arxiv.org/abs/0712.3910}, year = {2007} }

TY - ELEC ID - citeulike:2426999 L3 - citeulike-article-id:2426999 N2 - For any pair of quantum states, an initial state |I> and a final quantum state |F>, in a Hilbert space, there are many Hamiltonians H under which |I> evolves into |F>. Let us impose the constraint that the difference between the largest and smallest eigenvalues of H, E_max and E_min, is held fixed. We can then determine the Hamiltonian H that satisfies this constraint and achieves the transformation from the initial state to the final state in the least possible 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. The minimum value of \tau can be made arbitrarily small because for PT-symmetric Hamiltonians the path from the vector |I> to the vector |F>, as measured using the Hilbert-space metric appropriate for this theory, can be made arbitrarily 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. TI - Faster than Hermitian Time Evolution KW - non-hermitian_hamiltonians KW - quantum_physics AU - Bender, Carl PY - 2007/Dec/27/ UR - http://arxiv.org/abs/0712.3910 ER -