Quantum Codes Give Counterexamples to the Unique Preimage Conjecture of the N-Representability Problem
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Ocko-2011-Quantum Codes Give C.pdf
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Checksum (MD5)
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Author(s)
Ocko, Samuel Alan
Chen, Xie
Zeng, Bei
Yoshida, Beni
Ji, Zhengfeng
Ruskai, Mary Beth
Chung, Isaac L.
Date Issued
March 2011
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Ocko, Samuel et al. “Quantum Codes Give Counterexamples to the Unique Preimage Conjecture of the N-Representability Problem.” Physical Review Letters 106 (2011). © 2011 American Physical Society.
Version
Final published version
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 preimage, 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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.106.110501
