Quantum states far from the energy eigenstates of any local Hamiltonian.

@article{Haselgrove2003QuantumSF,
  title={Quantum states far from the energy eigenstates of any local Hamiltonian.},
  author={Henry L. Haselgrove and Michael A. Nielsen and Tobias J. Osborne},
  journal={Physical review letters},
  year={2003},
  volume={91 21},
  pages={
          210401
        }
}
What quantum states are possible energy eigenstates of a many-body Hamiltonian? Suppose the Hamiltonian is nontrivial, 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 psi which are "far away" from all the eigenstates E of any nontrivial L-local Hamiltonian, in the sense that ||psi-E|| is greater than some constant lower bound, independent of the form of the Hamiltonian. 

References

Publications referenced by this paper.
SHOWING 1-10 OF 12 REFERENCES

Phys

  • P. W. Shor
  • Rev. A 52, 2493
  • 1995
Highly Influential
7 Excerpts

Nature 416

  • A. Osterloh, L. Amico, G. Falci, R. Fazio
  • 608
  • 2002
1 Excerpt

Phys

  • T. J. Osborne, M. A. Nielsen
  • Rev. A 66, 032110
  • 2002

Sci

  • M. A. Nielsen
  • Am. 287, 66
  • 2002
1 Excerpt

and A

  • G. Vidal, J. I. Latorre, E. Rico
  • Kitaev, arXiv:quant-ph/0211074
  • 2002
1 Excerpt

Phys

  • D. Gunlycke, S. Bose, V. M. Kendon, V. Vedral
  • Rev. A 64, 042302
  • 2001

Opt

  • J. Preskill, J. Mod
  • 47, 127
  • 2000
1 Excerpt

Phys

  • A. R. Calderbank, E. M. Rains, P. W. Shor, N.J.A. Sloane
  • Rev. Lett. 78, 405
  • 1997

Similar Papers

Loading similar papers…