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Published in: Quantum Information Processing 6/2020

01-06-2020

Separability of heterogeneous multipartite quantum systems using Bloch Vectors

Authors: Andrei Tănăsescu, Pantelimon George Popescu

Published in: Quantum Information Processing | Issue 6/2020

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Abstract

Refining recent results, we propose an upper bound for the norms of Bloch Vectors for heterogeneous quantum systems containing an arbitrary number of qudits with possibly different numbers of levels. We also generalize recent approaches for tripartite and four-partite heterogeneous systems and for multipartite homogeneous systems. Our results imply a necessary algebraic condition for separability of a general multipartite heterogeneous quantum system under arbitrary partitioning.

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Literature
2.
go back to reference Horodecki, Pawel: Separability criterion and inseparable mixed states with positive partial transposition. Phys. Lett. A 232(5), 333–339 (1997)ADSMathSciNetCrossRef Horodecki, Pawel: Separability criterion and inseparable mixed states with positive partial transposition. Phys. Lett. A 232(5), 333–339 (1997)ADSMathSciNetCrossRef
3.
4.
go back to reference Rudolph, Oliver: Further results on the cross norm criterion for separability. Quantum Inf. Process. 4, 219–239 (2005)MathSciNetCrossRef Rudolph, Oliver: Further results on the cross norm criterion for separability. Quantum Inf. Process. 4, 219–239 (2005)MathSciNetCrossRef
5.
go back to reference Chen, Kai, Ling-An, Wu: A matrix realignment method for recognizing entanglement. Quantum Inf. Comput. 3(3), 193–202 (2003)MathSciNetMATH Chen, Kai, Ling-An, Wu: A matrix realignment method for recognizing entanglement. Quantum Inf. Comput. 3(3), 193–202 (2003)MathSciNetMATH
6.
go back to reference Liu, Bi-Heng, Xiao-Min, Hu, Chen, Jiang-Shan, Zhang, Chao, Huang, Yun-Feng, Li, Chuan-Feng, Guo, Guang-Can, Karpat, Göktug, Fanchini, Felipe F., Piilo, Jyrki, Maniscalco, Sabrina: Time-invariant entanglement and sudden death of nonlocality. Phys. Rev. A 94, 062107 (2016)ADSCrossRef Liu, Bi-Heng, Xiao-Min, Hu, Chen, Jiang-Shan, Zhang, Chao, Huang, Yun-Feng, Li, Chuan-Feng, Guo, Guang-Can, Karpat, Göktug, Fanchini, Felipe F., Piilo, Jyrki, Maniscalco, Sabrina: Time-invariant entanglement and sudden death of nonlocality. Phys. Rev. A 94, 062107 (2016)ADSCrossRef
7.
go back to reference Lewenstein, M., Kraus, B., Cirac, J.I., Horodecki, P.: Optimization of entanglement witnesses. Phys. Rev. A 62, 052310 (2000)ADSCrossRef Lewenstein, M., Kraus, B., Cirac, J.I., Horodecki, P.: Optimization of entanglement witnesses. Phys. Rev. A 62, 052310 (2000)ADSCrossRef
8.
go back to reference Marcus, H., de Vicente, J.I.: Structure of multidimensional entanglement in multipartite systems. Phys. Rev. Lett. 110(3), 030501 (2013)CrossRef Marcus, H., de Vicente, J.I.: Structure of multidimensional entanglement in multipartite systems. Phys. Rev. Lett. 110(3), 030501 (2013)CrossRef
9.
go back to reference Hassan, Ali Saif M, Joag, Pramod S: Experimentally accessible geometric measure for entanglement in n-qubit pure states. Phys. Rev. A 77(6), 062334 (2008)ADSCrossRef Hassan, Ali Saif M, Joag, Pramod S: Experimentally accessible geometric measure for entanglement in n-qubit pure states. Phys. Rev. A 77(6), 062334 (2008)ADSCrossRef
10.
go back to reference Hassan, Ali Saif M, Joag, Pramod S: Geometric measure for entanglement in n-qudit pure stat. Phys. Rev. 80(4), 042302 (2009)MathSciNetCrossRef Hassan, Ali Saif M, Joag, Pramod S: Geometric measure for entanglement in n-qudit pure stat. Phys. Rev. 80(4), 042302 (2009)MathSciNetCrossRef
11.
go back to reference Santos, M.F., Carvalho, A.R.R.: Observing different quantum trajectories in cavity QED. EPL 94(6), 64003 (2011)ADSCrossRef Santos, M.F., Carvalho, A.R.R.: Observing different quantum trajectories in cavity QED. EPL 94(6), 64003 (2011)ADSCrossRef
12.
go back to reference Ho, C.-L., Deguchi, T.: Multi-qudit states generated by unitary braid quantum gates based on temperley-lieb algebra. EPL 118(4), 40001 (2017)ADSCrossRef Ho, C.-L., Deguchi, T.: Multi-qudit states generated by unitary braid quantum gates based on temperley-lieb algebra. EPL 118(4), 40001 (2017)ADSCrossRef
13.
go back to reference Yun Shang, Yu., Wang, Meng Li, Ruqian, Lu: Quantum communication protocols by quantum walks with two coins. EPL 124(6), 60009 (2019)CrossRef Yun Shang, Yu., Wang, Meng Li, Ruqian, Lu: Quantum communication protocols by quantum walks with two coins. EPL 124(6), 60009 (2019)CrossRef
14.
go back to reference Imany, P., Jaramillo-Villegas, J.A., Alshaykh, M.S., Lukens, J.M., Odele, O.D., Moore, A.J., Leaird, D.E., Qi, M., Weiner, A.M.: High-dimensional optical quantum logic in large operational spaces. NPJ Quantum Inf. 5(1), 1–10 (2019)CrossRef Imany, P., Jaramillo-Villegas, J.A., Alshaykh, M.S., Lukens, J.M., Odele, O.D., Moore, A.J., Leaird, D.E., Qi, M., Weiner, A.M.: High-dimensional optical quantum logic in large operational spaces. NPJ Quantum Inf. 5(1), 1–10 (2019)CrossRef
17.
go back to reference de Vicente, J.I.: Separability criteria based on the bloch representation of density matrices. Quantum Inf. Comput. 7, 624 (2007)MathSciNetMATH de Vicente, J.I.: Separability criteria based on the bloch representation of density matrices. Quantum Inf. Comput. 7, 624 (2007)MathSciNetMATH
18.
go back to reference de Vicente, Julio I: Further results on entanglement detection and quantification from the correlation matrix criterion. J. Phys. A Math. Theor 41(6), 065309 (2008)ADSMathSciNetCrossRef de Vicente, Julio I: Further results on entanglement detection and quantification from the correlation matrix criterion. J. Phys. A Math. Theor 41(6), 065309 (2008)ADSMathSciNetCrossRef
19.
go back to reference Li, Ming, Wang, Jing, Fei, Shao-Ming, Li-Jost, Xianqing: Quantum separability criteria for arbitrary-dimensional multipartite states. Phys. Rev. A 89(2), 022325 (2014)ADSCrossRef Li, Ming, Wang, Jing, Fei, Shao-Ming, Li-Jost, Xianqing: Quantum separability criteria for arbitrary-dimensional multipartite states. Phys. Rev. A 89(2), 022325 (2014)ADSCrossRef
20.
go back to reference de Vicente, Julio I, Huber, Marcus: Multipartite entanglement detection from correlation tensors. Phys. Rev. A 84(6), 062306 (2011)ADSCrossRef de Vicente, Julio I, Huber, Marcus: Multipartite entanglement detection from correlation tensors. Phys. Rev. A 84(6), 062306 (2011)ADSCrossRef
21.
go back to reference Shen, Shu-Qian, Juan, Yu., Li, Ming, Fei, Shao-Ming: Improved separability criteria based on bloch representation of density matrices. Sci. Rep. 6, 28850 (2016)ADSCrossRef Shen, Shu-Qian, Juan, Yu., Li, Ming, Fei, Shao-Ming: Improved separability criteria based on bloch representation of density matrices. Sci. Rep. 6, 28850 (2016)ADSCrossRef
22.
go back to reference Li, Ming, Wang, Zong, Wang, Jing, Shen, Shuqian, Fei, Shao-ming: The norms of bloch vectors and classification of four-qudits quantum states. EPL 125(2), 20006 (2019)ADSCrossRef Li, Ming, Wang, Zong, Wang, Jing, Shen, Shuqian, Fei, Shao-ming: The norms of bloch vectors and classification of four-qudits quantum states. EPL 125(2), 20006 (2019)ADSCrossRef
23.
go back to reference Tănăsescu, Andrei, Popescu, Pantelimon-George: Bloch vector norms of separable multi-partite quantum systems. EPL (Europhys. Lett.) 126(6), 60003 (2019)CrossRef Tănăsescu, Andrei, Popescu, Pantelimon-George: Bloch vector norms of separable multi-partite quantum systems. EPL (Europhys. Lett.) 126(6), 60003 (2019)CrossRef
24.
go back to reference Zhao, Hui, Zhang, Mei-Ming, Jing, NaiHuan, Wang, Zhi-Xi: Separability criteria based on bloch representation of density matrices. Quantum Inf. Process. 19(1), 14 (2020)ADSMathSciNetCrossRef Zhao, Hui, Zhang, Mei-Ming, Jing, NaiHuan, Wang, Zhi-Xi: Separability criteria based on bloch representation of density matrices. Quantum Inf. Process. 19(1), 14 (2020)ADSMathSciNetCrossRef
25.
go back to reference Harriman, John E: Geometry of density matrices I. definitions, n matrices and 1 matrices. Phys. Rev. A 17(4), 1249 (1978)ADSCrossRef Harriman, John E: Geometry of density matrices I. definitions, n matrices and 1 matrices. Phys. Rev. A 17(4), 1249 (1978)ADSCrossRef
26.
go back to reference Goyeneche, Dardo, Bielawski, Jakub, Życzkowski, Karol: Multipartite entanglement in heterogeneous systems. Phys. Rev. A 94, 012346 (2016)ADSCrossRef Goyeneche, Dardo, Bielawski, Jakub, Życzkowski, Karol: Multipartite entanglement in heterogeneous systems. Phys. Rev. A 94, 012346 (2016)ADSCrossRef
Metadata
Title
Separability of heterogeneous multipartite quantum systems using Bloch Vectors
Authors
Andrei Tănăsescu
Pantelimon George Popescu
Publication date
01-06-2020
Publisher
Springer US
Published in
Quantum Information Processing / Issue 6/2020
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-020-02668-8

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