Quantum states far from the energy eigenstates of any local Hamiltonian
arXiv:quant-ph/0303022 · doi:10.1103/PhysRevLett.91.210401
Abstract
What quantum states are possible energy eigenstates of a many-body Hamiltonian? Suppose the Hamiltonian is non-trivial, i.e., not a multiple of the identity, and L-local, in the sense of containing interaction terms involving at most L bodies, for some fixed L. We construct quantum states ψwhich are ``far away'' from all the eigenstates E of any non-trivial L-local Hamiltonian, in the sense that |ψ-E| is greater than some constant lower bound, independent of the form of the Hamiltonian.
arXiv comment4 pages
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