[en] The set of pure spin states with vanishing spin expectation value can be regarded as the set of the less coherent pure spin states. This set can be divided into a finite number of nested subsets on the basis of higher order moments of the spin operators. This subdivision relies on the notion of anticoherent spin state to order t : A spin state is said to be anticoherent to order t if the moment of order k of the spin components along any directions are equal for k = 1,2, . . . ,t . Most spin states are neither coherent nor anticoherent, but can be arbitrary close to one or the other. In or- der to quantify the degree of anticoherence of pure spin states, we introduce the notion of anticoherence measures. By relying on the mapping between spin-j states and symmetric states of 2j spin 1/2 (Majorana representation), we present a systematic way of constructing anticoherence measures to any order. We briefly discuss their connection with measures of quantum coherence. Finally, we illustrate our measures on various spin states and use them to investigate the problem of the existence of anticoherent spin states with degenerated Majorana points.
Disciplines :
Physics
Author, co-author :
Baguette, Dorian ; Université de Liège > Département de physique > Optique quantique
Martin, John ; Université de Liège > Département de physique > Optique quantique
Language :
English
Title :
Anticoherence measures for pure spin states
Publication date :
September 2017
Journal title :
Physical Review. A, Atomic, molecular, and optical physics
ISSN :
1050-2947
eISSN :
1094-1622
Publisher :
American Physical Society
Volume :
96
Pages :
032304
Peer reviewed :
Peer Reviewed verified by ORBi
Tags :
CÉCI : Consortium des Équipements de Calcul Intensif
Funders :
CÉCI - Consortium des Équipements de Calcul Intensif [BE]
E. Schrödinger, Naturwissenschaften 14, 664 (1926). NATWAY 0028-1042 10.1007/BF01507634
J.-P. Gazeau, Coherent States in Quantum Physics (Wiley-VCH, Berlin, 2009).
W. Zhang, D. Feng, and R. Gilmore, Rev. Mod. Phys. 62, 867 (1990). RMPHAT 0034-6861 10.1103/RevModPhys.62.867
E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963). PRLTAO 0031-9007 10.1103/PhysRevLett.10.277
R. J. Glauber, Phys. Rev. 130, 2529 (1963). PHRVAO 0031-899X 10.1103/PhysRev.130.2529
J. Zimba, Electron. J. Theor. Phys. 3, 143 (2006).
J. Crann, R. Pereira, and D. W. Kribs, J. Phys. A 43, 255307 (2010). 1751-8113 10.1088/1751-8113/43/25/255307
D. Baguette, F. Damanet, O. Giraud, and J. Martin, Phys. Rev. A 92, 052333 (2015). PLRAAN 1050-2947 10.1103/PhysRevA.92.052333
O. Giraud, D. Braun, D. Baguette, T. Bastin, and J. Martin, Phys. Rev. Lett. 114, 080401 (2015). PRLTAO 0031-9007 10.1103/PhysRevLett.114.080401
R. Pereira and C. Paul-Paddock, J. Math. Phys. 58, 062107 (2017). JMAPAQ 0022-2488 10.1063/1.4986413
A. Klyachko, arXiv:quant-ph/0206012.
D. Baguette, T. Bastin, and J. Martin, Phys. Rev. A 90, 032314 (2014). PLRAAN 1050-2947 10.1103/PhysRevA.90.032314
A. Luis, Phys. Rev. A 66, 013806 (2002). PLRAAN 1050-2947 10.1103/PhysRevA.66.013806
A. Luis and N. Korolkova, Phys. Rev. A 74, 043817 (2006). PLRAAN 1050-2947 10.1103/PhysRevA.74.043817
G. Björk, J. Söderholm, L. L. Sanchez-Soto, A. B. Klimov, I. Ghiu, P. Marian, and T. A. Marian, Opt. Commun. 283, 4440 (2010). OPCOB8 0030-4018 10.1016/j.optcom.2010.04.088
Á. Rivas and A. Luis, Phys. Rev. A 88, 052120 (2013). PLRAAN 1050-2947 10.1103/PhysRevA.88.052120
O. Giraud, P. Braun, and D. Braun, Phys. Rev. A 78, 042112 (2008). PLRAAN 1050-2947 10.1103/PhysRevA.78.042112
O. Giraud, P. Braun, and D. Braun, New J. Phys. 12, 063005 (2010). NJOPFM 1367-2630 10.1088/1367-2630/12/6/063005
This state is also known in the literature as the tetrahedron state since in the Majorana representation, its defining four Majorana points draw a regular tetrahedron.
C. Chryssomalakos and H. Hernández-Coronado, Phys. Rev. A 95, 052125 (2017). 1050-2947 10.1103/PhysRevA.95.052125
P. Kolenderski and R. Demkowicz-Dobrzanski, Phys. Rev. A 78, 052333 (2008). PLRAAN 1050-2947 10.1103/PhysRevA.78.052333
D. Baguette and J. Martin (unpublished).
A. A. Klyachko and A. S. Shumovsky, J. Opt. B: Quantum Semiclass. Opt. 5, S322 (2003). JOBOFD 1464-4266 10.1088/1464-4266/5/3/364
S. BinicioÇlu, M. A. Can, A. A. Klyachko, and A. S. Shumovsky, Found. Phys. 37, 1253 (2007). FNDPA4 0015-9018 10.1007/s10701-007-9149-1
A. A. Klyachko, B. Öztop, and A. S. Shumovsky, Phys. Rev. A 75, 032315 (2007). PLRAAN 1050-2947 10.1103/PhysRevA.75.032315
A. Sawicki, M. Oszmaniec, and M. Kuś, Phys. Rev. A 86, 040304 (R) (2012). PLRAAN 1050-2947 10.1103/PhysRevA.86.040304
M. Blasone, F. Dell'Anno, S. De Siena, and F. Illuminati, J. Phys. Conf. Ser. 237, 012007 (2010). 1742-6596 10.1088/1742-6596/237/1/012007
M. Erementchouk and M. N. Leuenberger, ISRN Math. Phys. 2014, 264956 (2014). 10.1155/2014/264956
J. Lozada-Vera, V. S. Bagnato, and M. C. de Oliveira, New J. Phys. 15, 113012 (2013). NJOPFM 1367-2630 10.1088/1367-2630/15/11/113012
M. Kitagawa and M. Ueda, Phys. Rev. A 47, 5138 (1993) PLRAAN 1050-2947 10.1103/PhysRevA.47.5138;
J. H. Hannay, J. Phys. A 31, L53 (1998) JPHAC5 0305-4470 10.1088/0305-4470/31/2/002;
H. Mäkelä and K.-A. Suominen, Phys. Rev. Lett. 99, 190408 (2007) PRLTAO 0031-9007 10.1103/PhysRevLett.99.190408;
J. Martin, O. Giraud, P. A. Braun, D. Braun, and T. Bastin, Phys. Rev. A 81, 062347 (2010) PLRAAN 1050-2947 10.1103/PhysRevA.81.062347;
M. Aulbach, D. Markham, and M. Murao, New J. Phys. 12, 073025 (2010) NJOPFM 1367-2630 10.1088/1367-2630/12/7/073025;
P. Ribeiro and R. Mosseri, Phys. Rev. Lett. 106, 180502 (2011) PRLTAO 0031-9007 10.1103/PhysRevLett.106.180502;
E. Bannai and M. Tagami, J. Phys. A 44, 342002 (2011) 1751-8113 10.1088/1751-8113/44/34/342002;
S. Tamate, K. Ogawa, and M. Kitano, Phys. Rev. A 84, 052114 (2011) PLRAAN 1050-2947 10.1103/PhysRevA.84.052114;
P. Bruno, Phys. Rev. Lett. 108, 240402 (2012) PRLTAO 0031-9007 10.1103/PhysRevLett.108.240402;
W. Ganczarek, M. Kuś, and K. Zyczkowski, Phys. Rev. A 85, 032314 (2012) PLRAAN 1050-2947 10.1103/PhysRevA.85.032314;
H. D. Liu and L. B. Fu, Phys. Rev. Lett. 113, 240403 (2014) PRLTAO 0031-9007 10.1103/PhysRevLett.113.240403;
C. Yang, H. Guo, L.-B. Fu, and S. Chen, Phys. Rev. B 91, 125132 (2015) PRBMDO 1098-0121 10.1103/PhysRevB.91.125132;
Q. Guo, H. Liu, T. Zhou, X.-Z. Chen, and B. Wu, Eur. Phys. J. D 70, 128 (2016) EPJDF6 1434-6060 10.1140/epjd/e2016-70059-y;
F. Bohnet-Waldraff, D. Braun, and O. Giraud, Phys. Rev. A 93, 012104 (2016) 1050-2947 10.1103/PhysRevA.93.012104;
M. Cormann and Y. Caudano, J. Phys. A: Math. Theor. 50, 305302 (2017). 1751-8113 10.1088/1751-8121/aa7639
Z. Wang and D. Markham, Phys. Rev. Lett. 108, 210407 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.210407
E. Majorana, Nuovo Cimento 9, 43 (1932). NUCIAD 0029-6341 10.1007/BF02960953
I. Bengtsson and K. Zyczkowski, Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd ed. (Cambridge University Press, Cambridge, UK, 2008).
T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.113.140401
A. Streltsov, H. Kampermann, S. Wölk, M. Gessner, and D. Bruß, arXiv:1612.07570.
Note that Fig. 3 in Ref. [12] shows the geometric entanglement of the states (5) as a function of (Equation presented). The geometric entanglement is related to the Fubini-Study distance of the states (5) to the set of separable states, whereas the Bures measure of 2 anticoherence is related to the Bures distance between the 2 spin-(Equation presented) reduced state and the maximally mixed state. Interestingly, there is a certain degree of similarity between this figure and Fig. 2 of the present paper.
W. Dür, C. Simon, and J. I. Cirac, Phys. Rev. Lett. 89, 210402 (2002). PRLTAO 0031-9007 10.1103/PhysRevLett.89.210402
G. Björk, M. Grassl, P. de la Hoz, G. Leuchs, and L. L. Sánchez-Soto, Phys. Scr. 90, 108008 (2015). PHSTBO 0031-8949 10.1088/0031-8949/90/10/108008
T. Bastin, S. Krins, P. Mathonet, M. Godefroid, L. Lamata, and E. Solano, Phys. Rev. Lett. 103, 070503 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.070503
M. Aulbach, Int. J. Quantum Inform. 10, 1230004 (2012). 0219-7499 10.1142/S0219749912300045
P. de la Hoz, A. B. Klimov, G. Björk, Y.-H. Kim, C. Müller, C. Marquardt, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 88, 063803 (2013). PLRAAN 1050-2947 10.1103/PhysRevA.88.063803