Tetrapartite entanglement features of W-Class state in uniform acceleration

doi:10.1007/s11467-019-0940-1

Front. Phys.

2020, Vol. 15

Issue (1) : 11602 https://doi.org/10.1007/s11467-019-0940-1

RESEARCH ARTICLE

Tetrapartite entanglement features of W-Class state in uniform acceleration

Qian Dong¹(

), Ariadna J. Torres-Arenas¹(

), Guo-Hua Sun²(

), Shi-Hai Dong¹(

)

¹. Laboratorio de Información Cuántica, CIDETEC, Instituto Politécnico Nacional, UPALM, CDMX 07700, Mexico
². Catedrática CONACyT, Centro de Investigación en Computación, Instituto Politécnico Nacional, UPALM, CDMX 07738, Mexico

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Abstract

Using the single-mode approximation, we first calculate entanglement measures such as negativity (1–3 and 1–1 tangles) and von Neumann entropy for a tetrapartite W-Class system in noninertial frame and then analyze the whole entanglement measures, the residual π₄ and geometric Π₄ average of tangles. Notice that the difference between π₄ and Π₄ is very small or disappears with the increasing accelerated observers. The entanglement properties are compared among the different cases from one accelerated observer to four accelerated observers. The results show that there still exists entanglement for the complete system even when acceleration r tends to infinity. The degree of entanglement is disappeared for the 1–1 tangle case when the acceleration r>0.472473. We reexamine the Unruh effect in noninertial frames. It is shown that the entanglement system in which only one qubit is accelerated is more robust than those entangled systems in which two or three or four qubits are accelerated. It is also found that the von Neumann entropy S of the total system always increases with the increasing accelerated observers, but the S_κξ and S_κζδ with two and three involved noninertial qubits first increases and then decreases with the acceleration parameter r, but they are equal to constants 1 and 0.811278 respectively for zero involved noninertial qubit.

Keywords tetrapartite W-Class state entanglement Dirac field noninertial frames

Corresponding Author(s): Qian Dong,Ariadna J. Torres-Arenas,Guo-Hua Sun,Shi-Hai Dong

Issue Date: 22 November 2019

Cite this article:

Qian Dong,Ariadna J. Torres-Arenas,Guo-Hua Sun, et al. Tetrapartite entanglement features of W-Class state in uniform acceleration[J]. Front. Phys. , 2020, 15(1): 11602.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-019-0940-1
https://academic.hep.com.cn/fop/EN/Y2020/V15/I1/11602

1	A. Einstein, B. Podolsky, and N. Rosen, Can quantummechanical description of physical reality be considered complete? Phys. Rev. 47(10), 777 (1935) https://doi.org/10.1103/PhysRev.47.777
2	E. Schrödinger, Discussion of probability relations between separated systems, Math. Proc. Camb. Philos. Soc. 31(4), 555 (1935) https://doi.org/10.1017/S0305004100013554
3	E. Schrödinger, Die gegenwärtige Situation in der Quantenmechanik, Naturwissenschaften 23(48), 807 (1935) https://doi.org/10.1007/BF01491891
4	E. Schrödinger, Probability relations between separated systems, Math. Proc. Camb. Philos. Soc. 32(3), 446 (1936) https://doi.org/10.1017/S0305004100019137
5	R. F. Werner, Quantum states with Einstein–Podolsky– Rosen correlations admitting a hidden-variable model, Phys. Rev. A 54(8), 4277 (1989) https://doi.org/10.1103/PhysRevA.40.4277
6	R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81(2), 865 (2009) https://doi.org/10.1103/RevModPhys.81.865
7	O. Gühne and G. Tóth, Entanglement detection, Phys. Rep. 474, 1 (2009) https://doi.org/10.1016/j.physrep.2009.02.004
8	J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, Cambridge, 1987
9	A. Peres, Separability Criterion for density matrices, Phys. Rev. Lett. 77(8), 1413 (1996) https://doi.org/10.1103/PhysRevLett.77.1413
10	K. Życzkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, Volume of the set of separable states, Phys. Rev. A 58(2), 883 (1998) https://doi.org/10.1103/PhysRevA.58.883
11	Y. Li, C. Liu, Q. Wang, H. Zhang, and L. Hu, Tetrapartite entanglement of fermionic systems in noninertial frames, Optik (Stuttg.) 127(20), 9788 (2016) https://doi.org/10.1016/j.ijleo.2016.07.069
12	V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, Quantifying Entanglement, Phys. Rev. Lett. 78(12), 2275 (1997) https://doi.org/10.1103/PhysRevLett.78.2275
13	V. Vedral and M. B. Plenio, Entanglement measures and purification procedures, Phys. Rev. A 57(3), 1619 (1998) https://doi.org/10.1103/PhysRevA.57.1619
14	V. Vedral, M. B. Plenio, K. Jacobs, and P. L. Knight, Statistical inference, distinguishability of quantum states, and quantum entanglement, Phys. Rev. A 56(6), 4452 (1997) https://doi.org/10.1103/PhysRevA.56.4452
15	M. Murao, M. B. Plenio, S. Popescu, V. Vedral, and P. L. Knight, Multiparticle entanglement purification protocols, Phys. Rev. A 57(6), R4075 (1998) https://doi.org/10.1103/PhysRevA.57.R4075
16	W. Dür, J. I. Cirac, and R. Tarrach, Separability and distillability of multiparticle quantum systems, Phys. Rev. Lett. 83(17), 3562 (1999) https://doi.org/10.1103/PhysRevLett.83.3562
17	C. H. Bennett, D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal, Unextendible product bases and bound entanglement, Phys. Rev. Lett. 82(26), 5385 (1999) https://doi.org/10.1103/PhysRevLett.82.5385
18	K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, The classical-quantum boundary for correlations: Discord and related measures, Rev. Mod. Phys. 84(4), 1655 (2012) https://doi.org/10.1103/RevModPhys.84.1655
19	P. M. Alsing, I. Fuentes-Schuller, R. B. Mann, and T. E. Tessier, Entanglement of Dirac fields in noninertial frames, Phys. Rev. A 74(3), 032326 (2006) https://doi.org/10.1103/PhysRevA.74.032326
20	M. Montero, J. León, and E. Martín-Martínez, Fermionic entanglement extinction in noninertial frames, Phys. Rev. A 84(4), 042320 (2011) https://doi.org/10.1103/PhysRevA.84.042320
21	M. Shamirzaie, B. N. Esfahani, and M. Soltani, Tripartite entanglements in noninertial frames, Int. J. Theor. Phys. 51(3), 787 (2012) https://doi.org/10.1007/s10773-011-0958-9
22	N. Metwally, Usefulness classes of traveling entangled channels in noninertial frames, Int. J. Mod. Phys. B 27(28), 1350155 (2013) https://doi.org/10.1142/S0217979213501555
23	C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein–Podolsky– Rosen channels, Phys. Rev. Lett. 70(13), 1895 (1993) https://doi.org/10.1103/PhysRevLett.70.1895
24	E. Bernstein and U. Vazirani, Quantum complexity theory, SIAM J. Comput. 26(5), 1411 (1997) https://doi.org/10.1137/S0097539796300921
25	D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information, Springer-Verlag, Berlin, 2000 https://doi.org/10.1007/978-3-662-04209-0
26	N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Quantum cryptography, Rev. Mod. Phys. 74(1), 145 (2002) https://doi.org/10.1103/RevModPhys.74.145
27	B. M. Terhal, Is entanglement monogamous? IBM J. Res. Develop. 48(1), 71 (2004) https://doi.org/10.1147/rd.481.0071
28	A. Sen De and U. Sen, Quantum advantage in communication networks, Phys. News 40(4), 17 (2010)
29	P. Y. Xiong, X. T. Yu, H. T. Zhan, and Z. C. Zhang, Multiple teleportation via partially entangled GHZ state, Front. Phys. 11(4), 110303 (2016) https://doi.org/10.1007/s11467-016-0553-x
30	P. Y. Xiong, X. T. Yu, Z. C. Zhang, H. T. Zhan, and J. Y. Hua, Routing protocol for wireless quantum multihop mesh backbone network based on partially entangled GHZ state, Front. Phys. 12(4), 120302 (2017) https://doi.org/10.1007/s11467-016-0617-y
31	K. Wang, X. T. Yu, and Z. C. Zhang, Two-qubit entangled state teleportation via optimal POVM and partially entangled GHZ state, Front. Phys. 13(5), 130320 (2018) https://doi.org/10.1007/s11467-018-0832-9
32	R. Raussendorf and H. J. Briegel, A one-way quantum computer, Phys. Rev. Lett. 86, 5188 (2001) https://doi.org/10.1103/PhysRevLett.86.5188
33	H. J. Briegel, D. E. Browne, W. Dür, R. Raussendorf, and M. Van den Nest, Measurement-based quantum computation, Nat. Phys. 5, 19 (2009) https://doi.org/10.1038/nphys1157
34	M. R. Hwang, D. Park, and E. Jung, Tripartite entanglement in a noninertial frame, Phys. Rev. A 83, 012111 (2011) https://doi.org/10.1103/PhysRevA.83.012111
35	J. Wang and J. Jing, Multipartite entanglement of fermionic systems in noninertial frames, Phys. Rev. A 83, 022314(2011) https://doi.org/10.1103/PhysRevA.83.022314
36	Y. C. Ou and H. Fan, Monogamy inequality in terms of negativity for three-qubit states, Phys. Rev. A 75, 062308(2007) https://doi.org/10.1103/PhysRevA.75.062308
37	R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, New York, 1985, p. 205, 415–441
38	S. Gartzke and A. Osterloh, Generalized W state of four qubits with exclusively the three-tangle, Phys. Rev. A 98(5), 052307 (2018) https://doi.org/10.1103/PhysRevA.98.052307
39	D. K. Park, Tripartite entanglement dynamics in the presence of Markovian or non-Markovian environment, Quantum Inform. Process. 15(8), 3189 (2016) https://doi.org/10.1007/s11128-016-1331-y
40	A. J. Torres-Arenas, Q. Dong, G. H. Sun, W. C. Qiang, and S. H. Dong, Entanglement measures of W-state in noninertial frames, Phys. Lett. B 789, 93 (2019) https://doi.org/10.1016/j.physletb.2018.12.010
41	X. H. Peng and D. Suter, Spin qubits for quantum simulations, Front. Phys. China 5(1), 1 (2010) https://doi.org/10.1007/s11467-009-0067-x
42	S. Takagi, Vacuum noise and stress induced by uniform acceleration, Prog. Theor. Phys. Suppl. 88, 1 (1986) https://doi.org/10.1143/PTPS.88.1
43	E. Martín-Martínez, L. J. Garay, and J. León, Unveiling quantum entanglement degradation near a Schwarzschild black hole, Phys. Rev. D 82(6), 064006 (2010) https://doi.org/10.1103/PhysRevD.82.064006
44	E. Martín-Martínez, L. J. Garay, and J. León, Quantum entanglement produced in the formation of a black hole, Phys. Rev. D 82(6), 064028 (2010) https://doi.org/10.1103/PhysRevD.82.064028
45	W. Dür, G. Vidal, and J. I. Cirac, Three qubits can be entangled in two inequivalent ways, Phys. Rev. A 62(6), 062314 (2000) https://doi.org/10.1103/PhysRevA.62.062314
46	M. Socolovsky, Rindler space and Unruh effect, arXiv: 1304.2833v2 [gr-qc]
47	M. Nakahara, Y. Wan, and Y. Sasaki, Diversities in Quantum Computation and Quantum Information, World Scientific, Singapore, 2013
48	N. D. Birrel and P. C. W. Davies, Quantum Fields in Curved Space, Cambridge University, Cambridge, England, 1982 https://doi.org/10.1017/CBO9780511622632
49	A. Smith and R. B. Mann, Persistence of tripartite nonlocality for noninertial observers, Phys. Rev. A 86(1), 012306 (2012) https://doi.org/10.1103/PhysRevA.86.012306
50	W. C. Qiang, G. H. Sun, Q. Dong, and S. H. Dong, Genuine multipartite concurrence for entanglement of Dirac fields in noninertial frames, Phys. Rev. A 98(2), 022320 (2018) https://doi.org/10.1103/PhysRevA.98.022320
51	W. C. Qiang and L. Zhang, Geometric measure of quantum discord for entanglement of Dirac fields in noninertial frames, Phys. Lett. B 742, 383 (2015) https://doi.org/10.1016/j.physletb.2015.02.001
52	Q. Dong, A. J. Torres-Arenas, G. H. Sun, W. C. Qiang, and S. H. Dong, Entanglement measures of a new type pseudo-pure state in accelerated frames, Front. Phys. 14(2), 21603 (2019) https://doi.org/10.1007/s11467-018-0876-x
53	H. Mehri-Dehnavi, B. Mirza, H. Mohammadzadeh, and R. Rahimi, Pseudo-entanglement evaluated in noninertial frames, Ann. Phys. 326(5), 1320 (2011) https://doi.org/10.1016/j.aop.2011.02.001
54	D. E. Bruschi, J. Louko, E. Martín-Martínez, A. Dragan, and I. Fuentes, Unruh effect in quantum information beyond the single-mode approximation, Phys. Rev. A 82(4), 042332 (2010) https://doi.org/10.1103/PhysRevA.82.042332
55	E. Martín-Martínez, D. Hosler, and M. Montero, Fundamental limitations to information transfer in accelerated frames, Phys. Rev. A 86(6), 062307 (2012) https://doi.org/10.1103/PhysRevA.86.062307
56	N. Friis, A. R. Lee, and D. E. Bruschi, Fermionic-mode entanglement in quantum information, Phys. Rev. A 87(2), 022338 (2013) https://doi.org/10.1103/PhysRevA.87.022338
57	A. Dragan, J. Doukas, E. Martín-Martínez, and D. E. Bruschi, Localized projective measurement of a quantum field in non-inertial frames, Class. Quantum Gravity 30(23), 235006 (2013) https://doi.org/10.1088/0264-9381/30/23/235006
58	J. Doukas, E. G. Brown, A. Dragan, and R. B. Mann, Entanglement and discord: Accelerated observations of local and global modes, Phys. Rev. A 87(1), 012306 (2013) https://doi.org/10.1103/PhysRevA.87.012306
59	A. Dragan, J. Doukas, and E. Martín-Martínez, Localized detection of quantum entanglement through the event horizon, Phys. Rev. A 87(5), 052326 (2013) https://doi.org/10.1103/PhysRevA.87.052326
60	C. P. Williams, Explorations in Quantum Computing, Springer Science and Business Media, New York, 2010
61	D. S. Oliveira and R. V. Ramos, Residual entanglement with negativity for pure four-qubit quantum states, Quantum Inform. Process. 9(4), 497 (2010) https://doi.org/10.1007/s11128-009-0154-5
62	C. Sabín and G. García-Alcaine, A classification of entanglement in three-qubit systems, Eur. Phys. J. D 48(3), 435 (2008) https://doi.org/10.1140/epjd/e2008-00112-5
63	J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, New Jersey, 1996
64	B. Lari and H. Hassanabadi, Thermal entanglement, specific heat and quantum discord in open quantum systems including non-markovian processes, Mod. Phys. Lett. A 34(11), 1950059 (2019), arXiv: 1704.02811 https://doi.org/10.1142/S0217732319500597
65	W. S. Chung and H. Hassanabadi, Black hole temperature and Unruh effect from the extended uncertainty principle, Phys. Lett. B 793, 451 (2019) https://doi.org/10.1016/j.physletb.2019.04.063

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