Constructing a Maximally Entangled Seven-Qubit State via Orthogonal Arrays
Xin-Wei Zha , Min-Rui Wang* , and Ruo-Xu Jiang
School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China
Abstract ：Huber et al. [Phys. Rev. Lett. 118 (2017) 200502 ] have proved that a seven-qubit state whose three-body marginal states are all maximally mixed does not exist. Here, we propose a method to build a maximally entangled state based on orthogonal arrays to construct maximally entangled seven-qubit states. Using this method, we not only determine that a seven-qubit state whose three-body marginals are all maximally mixed does not exist, but also find the condition for maximally entangled seven-qubit states. We consider that $\pi_{\rm ME} =19/140$ is a condition for maximally entangled seven-qubit states. Furthermore, we derive three forms of maximally entangled seven-qubit states via orthogonal arrays.
收稿日期: 2020-03-15
出版日期: 2020-09-01
:
03.67.-a
(Quantum information)
03.65.Ud
(Entanglement and quantum nonlocality)
03.67.Mn
(Entanglement measures, witnesses, and other characterizations)
[1] Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) [2] Ekert A K 1991 Phys. Rev. Lett. 67 661 [3] Benatti F, Liguori A M and Paluzzano G 2010 J. Phys. A 43 045304 [4] Facchi P, Marzolino U, Parisi G, Pascazio S and Scardicchio A 2008 Phys. Rev. Lett. 101 050502 [5] Higuchi A and Sudbery A 2000 Phys. Lett. A 273 213 [6] Gisin N and Bechmann-Pasquinucci H 1998 Phys. Lett. A 246 1 [7] Verstraete F, Audenaert K and De Moor B 2001 Phys. Rev. A 64 012316 [8] Acín A, Gill R and Gisin N 2005 Phys. Rev. Lett. 95 210402 [9] Ishizaka S and Hiroshima T 2000 Phys. Rev. A 62 022310 [10] Yu N K, Duan R Y and Ying M S 2012 Phys. Rev. Lett. 109 020506 [11] De Vicente J I, Spee C and Kraus B 2013 Phys. Rev. Lett. 111 110502 [12] Martin J, Giraud O, Braun P A et al. 2010 Phys. Rev. A 81 062347 [13] Facchi P, Florio G, Parisi G and Pascazio S 2008 Phys. Rev. A 77 060304 [14] Zha X W, Yuan C Z and Zhang Y P 2013 Laser Phys. Lett. 10 045201 [15] Goyeneche D and Życzkowski K 2014 Phys. Rev. A 90 022316 [16] Arnaud L and Cerf N J 2013 Phys. Rev. A 87 012319 [17] Gour G and Wallach N R 2010 J. Math. Phys. 51 112201 [18] Huber F, Gühne O and Siewert J 2017 Phys. Rev. Lett. 118 200502 [19] Giraud O 2007 J. Phys. A 40 F1053 [20] Zha X W, Ahmed I, Zhang D and Zhang Y P 2020 Laser Phys. Lett. 17 035201 [21] Zha X W, Song H Y, Qi J X et al. 2012 J. Phys. A 45 255302 [22] Yu X Y, Zha X W and Che J L 2018 Sci. Sin.-Phys. Mech. Astron. 48 020301 (in Chinese)
[1]
.
[2]
.
[3]
.
[4]
.
[5]
.
[6]
.
[7]
.
[8]
.
[9]
.
[10]
.
[11]
.
[12]
.
[13]
.
[14]
.
[15]
.
2020, Vol. 37 
