Quantum Codes Give Counterexamples to the Unique Preimage Conjecture of the N-Representability Problem
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...
| Main Authors: | , , , , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Physical Society
2011
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| Online Access: | http://hdl.handle.net/1721.1/66149 https://orcid.org/0000-0001-7296-523X https://orcid.org/0000-0002-1069-008X |
| Summary: | 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. |
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