Abstract
Quantum entanglement is one of the fields in quantum mechanics. Recently, quantum entanglement becomes the heart of many tasks in quantum information such as quantum cryptography, quantum teleportation and quantum computing due to the capability it to compute data more efficient compare classical computer. Therefore, the measurement of entanglement become important to determine either the state is entangled or separable. The aim of this paper is to view all possible methods of measurement in term of detection and quantification for multipartite entanglement cases. The outcome of this paper is to classify the method of detection and quantification including summarize the criteria and advantage or disadvantage of each method.
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References
Abaffy M (2011) Multipartite entanglement. Bachelor. Masaryk university, Brno
Amico L, Fazio R, Osterloh A, Vedral V (2008) Entanglement in many-body systems. Rev Mod Phys 80(2):517–576
Barnum H, Linden N (2001) Monotones and invariants for multi-particle quantum states. J Phys A: Math Gen 34(35):6787
Bruß D (2002) Characterizing entanglement. J Math Phys 43(9):4237–4251. doi:10.1063/1.1494474
Carteret HA, Higuchi A, Sudbery A (2000) Multipartite generalization of the Schmidt decomposition. J Math Phys 41(12):7932–7939. doi:10.1063/1.1319516
Chuang IL, Neilsen MA (2000) Quantum computation and quantum information. Cambridge University Press, Cambridge
Eisert J, Briegel HJ (2001) Schmidt measure as a tool for quantifying multiparticle entanglement. Phys Rev A 64(2):022306
Eltschka C, Siewert J (2014a) Practical method to obtain a lower bound to the three-tangle. Phys Rev A 89(2):022312
Eltschka C, Siewert J (2014b) Quantifying entanglement resources, arXiv:quant-ph/1402.6710v
Guhne O, Toth G (2009) Entanglement detection. J Phys Rep 1–75. doi:10.1016/j.physrep.2009.02.2004
Guo Y, Fan H (2013) Generalized Schmidt number for multipartite states, arXiv:quant-ph/1304.1950v2
Hiesmayr BC, Huber M, Krammer P (2009) Two computable sets of multipartite entanglement measures. Phys Rev A 79(6):062308
Horodecki M, Horodecki P, Horodecki R (1996) Separability of mixed states: necessary and sufficient conditions. Phys Lett A 223(1–2):1–8
Idrus B, Konstadopoulou A, Vourdas A (2010) Correlations in a chain of three oscillators with nearest neighbour coupling. J Mod Opt 57(7):1–6. doi:10.1080/09500341003789926
Jiao-Jiao L, Zhi-Xi W (2010) Monogamy relations in tripartite quantum system. Chin Phys B 19(10):100310–100310. doi:10.1088/1674-1056/19/10/100310
Jingshui Y, Wenbo X (2011) Calculation of quantum entanglement. In: Paper presented at the tenth international symposium on distributed computing and applications to business, engineering and science (DCABES), 2011
Jurkowski J, Chruściński D (2010) Estimating concurrence via entanglement witnesses. Phys Rev A 81(5):052308
Kinsella S (2006) Online measurement of entanglement of a quantum state (D. o. I. Technology, Trans). National University of Ireland, Galway, pp 1–50
Krammer P (2005) Quantum entanglement: detection, classification, and quantification Master University of Vienna. Austria, Wien
Lanyon BP, Jurcevic P, Zwerger M, Hempel C, Martinez EA, Dür W, Roos CF (2013) Measurement-based quantum computation with trapped ions. Phys Rev Lett 111(21):210501
Lewenstein M, Kraus B, Cirac JI, Horodecki P (2000) Optimization of entanglement witnesses. Phys Rev A 62(5):052310
Li H, Wang S, Cui J, Long G (2013) Quantifying entanglement of arbitrary-dimensional multipartite pure states in terms of the singular values of coefficient matrices. Phys Rev A 87(4):042335
Liu D, Zhao X, Long G-L (2010) Multiple entropy measures for multi-particle pure quantum state. Commun Theor Phys 54(5):825
Ma Z-H, Chen Z-H, Chen J-L, Spengler C, Gabriel A, Huber M (2011) Measure of genuine multipartite entanglement with computable lower bounds. Phys Rev A 83(6):062325
Ryszard H, Paweł H, Michał H, Karol H (2009) Quantum entanglement. Rev Mod Phys 81(2):865–942
Sheikholeslam SA, Gulliver TA (2012) Classification and measurement of multipartite quantum entanglements. arXiv:quant-ph/1205.2339v1
Sperling J, Vogel W (2011) The Schmidt number as a universal entanglement measure. Phys Scr 83(4):045002
Terhal BM (2000) Bell inequalities and the separability criterion. Phys Lett A 271(5):319–326
Wei T-C, Goldbart PM (2003) Geometric measure of entanglement and applications to bipartite and multipartite quantum states. Phys Rev A 68(4):042307
Yu C-S, Song H-S (2005) Multipartite entanglement measure. Phys Rev A 71(4):042331
Zhu X-N, Fei S-M (2013) Lower bound of concurrence for qubit systems. In: Quantum information processing, pp 1–9. doi:10.1007/s11128-013-0693-7
Zhu X-N, Zhao M-J, Fei S-M (2012) Lower bound of multipartite concurrence based on subquantum state decomposition. Phys Rev A 86(2):022307
Zulkarnain ZA, Konstadopoulou A, Vourdas A (2006) Measurements and correlations in tri-partite systems. Int J Mod Phys B 20:1551–1563
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This work is supported by the research grant provided by Malaysian Ministry of Higher Education code: FGRS/1/2011/SG/UKM/03/5.
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Mohd, S.M., Idrus, B., Mukhtar, M., Zainuddin, H. (2016). Critical Review of Measurement for Multipartite Entanglement: Detection and Quantification. In: Yacob, N., Mohamed, M., Megat Hanafiah, M. (eds) Regional Conference on Science, Technology and Social Sciences (RCSTSS 2014). Springer, Singapore. https://doi.org/10.1007/978-981-10-0534-3_32
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DOI: https://doi.org/10.1007/978-981-10-0534-3_32
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