Chin. Phys. Lett.  2013, Vol. 30 Issue (9): 090303    DOI: 10.1088/0256-307X/30/9/090303
GENERAL |
Separability of Generalized Graph Product States
ZHAO Hui**, FAN Jiao
College of Applied Science, Beijing University of Technology, Beijing 100124
Cite this article:   
ZHAO Hui, FAN Jiao 2013 Chin. Phys. Lett. 30 090303
Download: PDF(441KB)  
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

We construct two classes of generalized graph product states and study the entanglement of these states. It is first presented that the density matrices of complex edge-weighted digraphs associated with the generalized graph product in mn systems are positive partial transformation and separable states. Then we prove that the density matrices of the vertex-weighted digraphs associated with another generalized graph product are entangled states.

Received: 27 June 2013      Published: 21 November 2013
PACS:  03.67.Mn (Entanglement measures, witnesses, and other characterizations)  
  03.65.Ud (Entanglement and quantum nonlocality)  
  02.10.Ox (Combinatorics; graph theory)  
TRENDMD:   
URL:  
https://cpl.iphy.ac.cn/10.1088/0256-307X/30/9/090303       OR      https://cpl.iphy.ac.cn/Y2013/V30/I9/090303
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
ZHAO Hui
FAN Jiao

[1] Nielsen M and Chuang I 2000 Quantum Computation and Quantum Information (New York: Cambridge University Press) chap 7 p 277
[2] Bapat R B 2001 Graphs Matrices (New Delhi: Hindustan Book Agency) chap 1 p 9
[3] Newman M E J 2010 Networks: An Introduction (New York: Oxford University Press) chap 6 p 142
[4] Parsonage E, Nguyen H X, Bowden R, Knight S, Falkner M and Roughan M 2011 IEEE International Conference on Network Protocols (Vancouver Canada 17–20 October 2011) p 79
[5] Even S and Even G 2011 Graph Algorithms (New York: Cambridge University Press) chap 6 p 117
[6] Kocay W and Kreher D L 2005 Graphs Algorithms Optimization (Boca Raton: CRC Press) chap 14 p 387
[7] Werner R F 1989 Phys. Rev. A 40 4277
[8] Ostlund S and Rommer S 1995 Phys. Rev. Lett. 75 3537
[9] Fannes M, Nachtergaele B and Werner R 1992 Commun. Math. Phys. 144 443
[10] Eisert J and Plenio M B 2003 Int. J. Quantum Inf. 1 479
[11] Braunstein S L and Van Loock P 2005 Rev. Mod. Phys. 77 513
[12] Braunst S L, Ghosh S and Severini S 2006 Ann. Comb. 10 291
[13] Braunst S L et al 2006 Phys. Rev. A 73 012320
[14] Chen L B 2002 Chin. Phys. B 11 999
[15] Huang Y X and Zhan M S 2004 Chin. Phys. B 13 2021
[16] Xu J, Chen X Y and Li H T 2012 Acta Phys. Sin. 61 220304 (in Chinese)
[17] West D B 2001 Introduction to Graph Theory (Upper Saddle River: Prentice Hall) chap 1 p 20
[18] Diestel R 2005 Graph Theory (New York: Springer-Verlag) vol 173 chap 1 p 5
[19] Horn R A and Johnson C R 1985 Matrix Analysis (Cambridge: Cambridge University Press) chap 7 p 369
[20] Wu C W 2006 Phys. Lett. A 351 18
[21] Adhikari B, Adhikari S and Banerjee S 2012 arXiv:1205.2747 [quant-ph]
[22] Solomon Ivan J, Mukunda N and Simon R 2012 Quantum Inf. Process. 11 873

Related articles from Frontiers Journals
[1] Shaowei Li, Daojin Fan, Ming Gong, Yangsen Ye, Xiawei Chen, Yulin Wu, Huijie Guan, Hui Deng, Hao Rong, He-Liang Huang, Chen Zha, Kai Yan, Shaojun Guo, Haoran Qian, Haibin Zhang, Fusheng Chen, Qingling Zhu, Youwei Zhao, Shiyu Wang, Chong Ying, Sirui Cao, Jiale Yu, Futian Liang, Yu Xu, Jin Lin, Cheng Guo, Lihua Sun, Na Li, Lianchen Han, Cheng-Zhi Peng, Xiaobo Zhu, and Jian-Wei Pan. Realization of Fast All-Microwave Controlled-Z Gates with a Tunable Coupler[J]. Chin. Phys. Lett., 2022, 39(3): 090303
[2] Xin-Wei Zha , Min-Rui Wang, and Ruo-Xu Jiang . Constructing a Maximally Entangled Seven-Qubit State via Orthogonal Arrays[J]. Chin. Phys. Lett., 2020, 37(9): 090303
[3] Qian Dong, M. A. Mercado Sanchez, Guo-Hua Sun, Mohamad Toutounji, Shi-Hai Dong. Tripartite Entanglement Measures of Generalized GHZ State in Uniform Acceleration[J]. Chin. Phys. Lett., 2019, 36(10): 090303
[4] Sheng-Li Zhang, Song Yang. Methods for Derivation of Density Matrix of Arbitrary Multi-Mode Gaussian States from Its Phase Space Representation[J]. Chin. Phys. Lett., 2019, 36(9): 090303
[5] Jie Zhou, Hui-Xian Meng, Jing-Ling Chen. Detecting Quantumness in the $n$-cycle Exclusivity Graphs[J]. Chin. Phys. Lett., 2019, 36(8): 090303
[6] Feng-Lin Wu, Si-Yuan Liu, Wen-Li Yang, Heng Fan. Construction of Complete Orthogonal Genuine Multipartite Entanglement State[J]. Chin. Phys. Lett., 2019, 36(6): 090303
[7] Bing-Bing Chai, Jin-Liang Guo. Distillability of Sudden Death in Qutrit-Qutrit Systems under Global Mixed Noise[J]. Chin. Phys. Lett., 2019, 36(5): 090303
[8] Meng Qin, Li Wang, Bili Wang, Xiao Wang, Zhong Bai, Yanbiao Li. Renormalization of Tripartite Entanglement in Spin Systems with Dzyaloshinskii–Moriya Interaction[J]. Chin. Phys. Lett., 2018, 35(10): 090303
[9] Sheng-Li Zhang, Chen-Hui Jin, Jian-Hong Shi , Jian-Sheng Guo, Xu-Bo Zou, Guang-Can Guo. Continuous Variable Quantum Teleportation in Beam-Wandering Modeled Atmosphere Channel[J]. Chin. Phys. Lett., 2017, 34(4): 090303
[10] Sheng-Li Zhang, Chen-Hui Jin, Jian-Sheng Guo, Jian-Hong Shi, Xu-Bo Zou, Guang-Can Guo. Decoy State Quantum Key Distribution via Beam-Wandering Modeled Atmosphere Channel[J]. Chin. Phys. Lett., 2016, 33(12): 090303
[11] Yong-Gang Tan, Qiang Liu. Measurement-Device-Independent Quantum Key Distribution with Two-Way Local Operations and Classical Communications[J]. Chin. Phys. Lett., 2016, 33(09): 090303
[12] Jin-Tao Tan, Yun-Rong Luo, Zheng Zhou, Wen-Hua Hai. Combined Effect of Classical Chaos and Quantum Resonance on Entanglement Dynamics[J]. Chin. Phys. Lett., 2016, 33(07): 090303
[13] Sheng-Li Zhang, Jian-Sheng Guo, Jian-Hong Shi, Xu-Bo Zou. Distillation of Atmospherically Disturbed Continuous Variable Quantum Entanglement with Photon Subtraction[J]. Chin. Phys. Lett., 2016, 33(07): 090303
[14] Hong-Mei Zou, Mao-Fa Fang. Controlling Entropic Uncertainty in the Presence of Quantum Memory by Non-Markovian Effects and Atom–Cavity Couplings[J]. Chin. Phys. Lett., 2016, 33(07): 090303
[15] Da-Chuang Li, Xian-Ping Wang, Hu Li, Xiao-Man Li, Ming Yang, Zhuo-Liang Cao. Effects of Pure Dzyaloshinskii–Moriya Interaction with Magnetic Field on Entanglement in Intrinsic Decoherence[J]. Chin. Phys. Lett., 2016, 33(05): 090303
Viewed
Full text


Abstract