Entanglement and off-diagonal long-range order of an {eta}-pairing state Heng, Fan [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080 (China)]; Lloyd, Seth [Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)] 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATION FUNCTIONS; DATA PROCESSING; ENERGY LEVELS; ENTROPY; INFORMATION THEORY; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; QUANTUM INFORMATION; QUANTUM MECHANICS; SUPERCONDUCTIVITY Off-diagonal long-range order (ODLRO) which is believed to be one characteristic of superconductivity is a quantum phenomenon not describable in classical mechanical terms. The quantum state constructed by {eta}-pairing demonstrates ODLRO. Entanglement is a key concept of the quantum information processing and has no classical counterpart. We study the entanglement property of the {eta}-pairing quantum state by concurrence and entropy which are two measures of the entanglement. We show that the concurrence of entanglement between one-site and the rest sites is exactly the correlation function of the ODLRO for the {eta}-pairing state in the thermodynamic limit. So, when the {eta}-pairing state is entangled, it demonstrates ODLRO and is thus in the superconducting phase, if it is a separable state, there is no ODLRO. In the thermodynamical limit, the entanglement between the M-site and other sites of the {eta}-pairing state does not vanish. Other types of ODLRO of the {eta}-pairing state are presented. We show that the behaviour of the ODLRO correlation functions is equivalent to that of the entanglement of the {eta}-pairing state. The scaling of the entropy of the entanglement for the {eta}-pairing state is studied. Electrical Engineering Department, University of California at Los Angeles, Los Angeles, CA 90095, USA (United States) Available online at http://stacks.iop.org/0305-4470/38/5285/a5_23_014.pdf or at the Web site for the Journal of Physics. A, Mathematical and General (ISSN 1361-6447) http://www.iop.org/;INIS United Kingdom 2005-06-10 English Journal Article Journal Name: Journal of Physics. A, Mathematical and General; Journal Volume: 38; Journal Issue: 23; Other Information: PII: S0305-4470(05)98308-X; DOI: 10.1088/0305-4470/38/23/014; Country of input: International Atomic Energy Agency (IAEA) Medium: X; Size: page(s) 5285-5292 https://doi.org/10.1088/0305-4470/38/23/014 [] 23 38 Journal ID: ISSN 0305-4470; JPHAC5; TRN: GB05P3140095903 GBN 2010-12-31 20657148