Quantum Codes Give Counterexamples to the Unique Preimage Conjecture of the N-Representability Problem

作     者：Samuel A. Ocko Xie Chen Bei Zeng Beni Yoshida Zhengfeng Ji Mary Beth Ruskai Isaac L. Chuang 

作者机构：Department of Physics Massachusetts Institute of Technology Cambridge Massachusetts USA Department of Mathematics and Statistics University of Guelph Guelph Ontario Canada Institute for Quantum Computing University of Waterloo Waterloo Ontario Canada Perimeter Institute for Theoretical Physics Waterloo Ontario Canada Department of Electrical and Computer Engineering Tufts University Medford Massachusetts USA 

出 版 物：《Physical Review Letters》 (Phys Rev Lett)

年 卷 期：2011年第106卷第11期

页      面：110501-110501页

核心收录：

学科分类：07[理学] 0702[理学-物理学] 

基　　金：National Science Foundation  NSF 

主　　题：Hamiltonians 

摘      要：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.