2010/10/31 by Samuel A. Ocko, Xie Chen, Bei Zeng +4 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Conjecture #Counterexample #Discrete mathematics #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Theoretical physics #physics.chem-ph #quant-ph
paper · pdf · doi:10.1103/physrevlett.106.110501
published as Phys. Rev. Lett. 106, 110501 (2011) · 4 pages, 1 figure
arxiv created 2011/03/14 · openalex publication_date 2011/03/14 · arxiv updated 2013/05/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.