Faster than Hermitian Time Evolution - High Energy Physics - TheoryReport as inadecuate

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Abstract: For any pair of quantum states, an initial state |I> and a final quantumstate |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 thelargest and smallest eigenvalues of H, E max and E min, is held fixed. We canthen determine the Hamiltonian H that satisfies this constraint and achievesthe transformation from the initial state to the final state in the leastpossible time \tau. For Hermitian Hamiltonians, \tau has a nonzero lower bound.However, among non-Hermitian PT-symmetric Hamiltonians satisfying the sameenergy constraint, \tau can be made arbitrarily small without violating thetime-energy uncertainty principle. The minimum value of \tau can be madearbitrarily small because for PT-symmetric Hamiltonians the path from thevector |I> to the vector |F>, as measured using the Hilbert-space metricappropriate for this theory, can be made arbitrarily short. The mechanismdescribed here is similar to that in general relativity in which the distancebetween two space-time points can be made small if they are connected by awormhole. This result may have applications in quantum computing.

Author: Carl M. Bender


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