PIRSA:11020102 Scientific Series Quantum Information

DOI10.48660/11020102

Series: Perimeter Institute Quantum Discussions

Ocko, S. (2011). Quantum codes give counterexamples to the unique pre-image conjecture of the N-representability problem. Perimeter Institute. https://pirsa.org/11020102

Ocko, Sam. Quantum codes give counterexamples to the unique pre-image conjecture of the N-representability problem. Perimeter Institute, Feb. 16, 2011, https://pirsa.org/11020102 

@misc{ pirsa_PIRSA:11020102,
  doi = {10.48660/11020102},
  url = {https://pirsa.org/11020102},
  author = {Ocko, Sam},
  keywords = {Quantum Information},
  language = {en},
  title = {Quantum codes give counterexamples to the unique pre-image conjecture of the N-representability problem},
  publisher = {Perimeter Institute},
  year = {2011},
  month = {feb},
  note = {PIRSA:11020102 see, \url{https://pirsa.org}}
}

Abstract

It is well known that the ground state energy of many-particle Hamiltonians involving only 2- body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While determining which 2-particle density matrices are 'N-representable' is a computationally hard problem, all known extreme N-representable 2-particle reduced density matrices arise from a unique N-particle pre-image, satisfying a conjecture established in 1972. We present explicit counterexamples to this conjecture through giving Hamiltonians with 2-body interactions which have degenerate ground states that cannot be distinguished by any 2-body operator. We relate the existence of such counterexamples to quantum error correction codes and topologically ordered spin systems.

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