Quantum states far from the energy eigenstates of any local Hamiltonian

Henry L. Haselgrove; Michael A. Nielsen; Tobias J. Osborne

doi:10.1103/physrevlett.91.210401

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Quantum states far from the energy eigenstates of any local Hamiltonian

Henry L. Haselgrove·Michael A. Nielsen·Tobias J. Osborne

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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.

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Henry L. Haselgrove, Michael A. Nielsen, Tobias J. Osborne. 2003-03-04. Quantum states far from the energy eigenstates of any local Hamiltonian. https://doi.org/10.1103/physrevlett.91.210401

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