Absolute-separability witnesses for symmetric multiqubit states

[en] The persistent separability of certain quantum states, known as symmetric absolutely separable (SAS), under symmetry-preserving global unitary transformations is of key significance in the context of quantum resources for bosonic systems. In this paper, we develop criteria for detecting SAS states of any number of qubits. Our approach is based on the Glauber-Sudarshan P representation for finite-dimensional quantum systems. We introduce three families of SAS witnesses, one linear and two nonlinear in the eigenvalues of the state, formulated respectively as an algebraic inequality or a quadratic optimization problem. These witnesses are capable of identifying more SAS states than previously known counterparts. We also explore the geometric properties of the subsets of SAS states detected by our witnesses, shedding light on their distinctions.

Disciplines :

Physics

Author, co-author :

Serrano Ensástiga, Eduardo ; Université de Liège - ULiège > Complex and Entangled Systems from Atoms to Materials (CESAM)

Denis, Jérôme ; Université de Liège - ULiège > Département de physique > Optique quantique

Martin, John ; Université de Liège - ULiège > Département de physique

Language :

English

Title :

Absolute-separability witnesses for symmetric multiqubit states

Publication date :

22 February 2024

Journal title :

Physical Review. A

ISSN :

2469-9926

eISSN :

2469-9934

Publisher :

American Physical Society (APS)

Volume :

109

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://link.aps.org/article/10.1103/PhysRevA.109.022430

Funders :

ULiège - Université de Liège [BE]
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]

Available on ORBi :

since 06 March 2024

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Bibliography

D. Deutsch and R. Jozsa, Proc. R. Soc. A 439, 553 (1992) 0962-8444 10.1098/rspa.1992.0167.
C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993) 0031-9007 10.1103/PhysRevLett.70.1895.
L. K. Grover, Phys. Rev. Lett. 79, 325 (1997) 0031-9007 10.1103/PhysRevLett.79.325.
P. W. Shor, SIAM Rev. 41, 303 (1999) 0036-1445 10.1137/S0036144598347011.
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, New York, 2010).
I. Bengtsson and K. Zyczkowski, Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd ed. (Cambridge University Press, New York, 2017).
R. F. Werner, Phys. Rev. A 40, 4277 (1989) 0556-2791 10.1103/PhysRevA.40.4277.
M. Kuś and K. Zyczkowski, Phys. Rev. A 63, 032307 (2001) 1050-2947 10.1103/PhysRevA.63.032307.
K. Zyczkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, Phys. Rev. A 58, 883 (1998) 1050-2947 10.1103/PhysRevA.58.883.
L. Gurvits and H. Barnum, Phys. Rev. A 66, 062311 (2002) 1050-2947 10.1103/PhysRevA.66.062311.
R. Hildebrand, Phys. Rev. A 75, 062330 (2007) 1050-2947 10.1103/PhysRevA.75.062330.
S. Adhikari, Eur. Phys. J. D 75, 92 (2021) 1434-6060 10.1140/epjd/s10053-021-00103-w.
S. Halder, S. Mal, and A. Sen(De), Phys. Rev. A 103, 052431 (2021) 2469-9926 10.1103/PhysRevA.103.052431.
S. N. Filippov, A. A. Melnikov, and M. Ziman, Phys. Rev. A 88, 062328 (2013) 1050-2947 10.1103/PhysRevA.88.062328.
S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, Phys. Rev. Lett. 83, 1054 (1999) 0031-9007 10.1103/PhysRevLett.83.1054.
J. A. Jones, Prog. Nucl. Magn. Reson. Spectrosc. 59, 91 (2011) 0079-6565 10.1016/j.pnmrs.2010.11.001.
L. Gurvits, in Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing (Association for Computing Machinery, New York, 2003), pp. 10-19.
O. Gühne and G. Tóth, Phys. Rep. 474, 1 (2009) 0370-1573 10.1016/j.physrep.2009.02.004.
F. Verstraete, K. Audenaert, and B. De Moor, Phys. Rev. A 64, 012316 (2001) 1050-2947 10.1103/PhysRevA.64.012316.
R. Hildebrand, Phys. Rev. A 76, 052325 (2007) 1050-2947 10.1103/PhysRevA.76.052325.
N. Johnston, Phys. Rev. A 88, 062330 (2013) 1050-2947 10.1103/PhysRevA.88.062330.
A. Patra, S. Mal, and A. Sen(De), Phys. Rev. A 104, 032427 (2021) 2469-9926 10.1103/PhysRevA.104.032427.
W. Thirring, R. A. Bertlmann, P. Köhler, and H. Narnhofer, Eur. Phys. J. D 64, 181 (2011) 1434-6060 10.1140/epjd/e2011-20452-1.
B. Leggio, A. Napoli, H. Nakazato, and A. Messina, Entropy 22, 62 (2020) 1099-4300 10.3390/e22010062.
P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Rev. Mod. Phys. 79, 135 (2007) 0034-6861 10.1103/RevModPhys.79.135.
J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Zukowski, Rev. Mod. Phys. 84, 777 (2012) 0034-6861 10.1103/RevModPhys.84.777.
B. Morris, B. Yadin, M. Fadel, T. Zibold, P. Treutlein, and G. Adesso, Phys. Rev. X 10, 041012 (2020) 2160-3308 10.1103/PhysRevX.10.041012.
G. Champagne, N. Johnston, M. MacDonald, and L. Pipes, Linear Algebra and its Applications 649, 273 (2022) 0024-3795 10.1016/j.laa.2022.05.004.
E. Serrano-Ensástiga and J. Martin, SciPost Phys. 15, 120 (2023) 2542-4653 10.21468/SciPostPhys.15.3.120.
F. Bohnet-Waldraff, O. Giraud, and D. Braun, Phys. Rev. A 95, 012318 (2017) 2469-9926 10.1103/PhysRevA.95.012318.
F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972) 0556-2791 10.1103/PhysRevA.6.2211.
O. Giraud, P. Braun, and D. Braun, Phys. Rev. A 78, 042112 (2008) 1050-2947 10.1103/PhysRevA.78.042112.
E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963) 0031-9007 10.1103/PhysRevLett.10.277.
R. J. Glauber, Phys. Rev. 131, 2766 (1963) 0031-899X 10.1103/PhysRev.131.2766.
N. Abbasli, V. Abgaryan, M. Bures, A. Khvedelidze, I. Rogojin, and A. Torosyan, Phys. Part. Nuclei 51, 443 (2020) 1063-7796 10.1134/S1063779620040024.
V. Abgaryan, A. Khvedelidze, and A. Torosyan, J. Math. Sci. 251, 301 (2020) 1072-3374 10.1007/s10958-020-05092-6.
J. Denis, J. Davis, R. B. Mann, and J. Martin, arXiv:2304.09006.
A. Peres, Phys. Rev. Lett. 77, 1413 (1996) 0031-9007 10.1103/PhysRevLett.77.1413.
R. H. Dicke, Phys. Rev. 93, 99 (1954) 0031-899X 10.1103/PhysRev.93.99.
J. M. Radcliffe, J. Phys. A 4, 313 (1971) 0022-3689 10.1088/0305-4470/4/3/009.
D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).
U. Fano, Phys. Rev. 90, 577 (1953) 0031-899X 10.1103/PhysRev.90.577.
J. K. Korbicz, J. I. Cirac, and M. Lewenstein, Phys. Rev. Lett. 95, 120502 (2005) 0031-9007 10.1103/PhysRevLett.95.120502.
F. Bohnet-Waldraff, D. Braun, and O. Giraud, Phys. Rev. A 94, 042343 (2016) 2469-9926 10.1103/PhysRevA.94.042343.
A. B. Klimov, J. L. Romero, and H. De Guise, J. Phys. A 50, 323001 (2017) 1751-8113 10.1088/1751-8121/50/32/323001.
E. Serrano-Ensástiga and D. Braun, Phys. Rev. A 101, 022332 (2020) 2469-9926 10.1103/PhysRevA.101.022332.
J. Denis and J. Martin, Phys. Rev. Res. 4, 013178 (2022) 2643-1564 10.1103/PhysRevResearch.4.013178.
Here, we use the term witness for both linear and nonlinear functionals. This generalization has already been used in the literature (see, e.g., [64,65]).
A. W. Marshall, I. Olkin, and B. C. Arnold, Inequalities: Theory of Majorization and its Applications, 2nd ed. (Springer, New York, 2010).
C. Dunkl and K. Zyczkowski, J. Math. Phys. 50, 123521 (2009) 0022-2488 10.1063/1.3272543.
P. Diţǎ, J. Math. Phys. 47, 083510 (2006) 0022-2488 10.1063/1.2229424.
A. C. Smith, in Mathematics and Computing, edited by R. N. Mohapatra, D. R. Chowdhury, and D. Giri (Springer, New York, 2015), pp. 239-250.
I. Bengtsson, Å. Ericsson, M. Kuś, W. Tadej, and K. Zyczkowski, Commun. Math. Phys. 259, 307 (2005) 0010-3616 10.1007/s00220-005-1392-8.
G. Rajchel-Mieldzioć, K. Korzekwa, Z. Puchała, and K. Zyczkowski, J. Math. Phys. 63, 012202 (2022) 0022-2488 10.1063/5.0046581.
G. Rajchel, A. Gąsiorowski, and K. Zyczkowski, Math. Comput. Sci. 12, 473 (2018) 1661-8270 10.1007/s11786-018-0384-y.
R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University Press, New York, 2012).
In fact, for any product of a vector and a bistochastic matrix (Equation presented), one can find an orthostochastic matrix (Equation presented), i.e., that comes from an orthogonal matrix, such that (Equation presented) (see Theorem B.6 of Ref. [49]).
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevA.109.022430 for video by E. Serrano-Ensástiga, J. Denis, and J. Martin (2023).
The proof of the convexity of the set of symmetric absolutely separable states is a special case of the convexity of the absolutely separable case [66].
A. K. Ekert, C. M. Alves, D. K. L. Oi, M. Horodecki, P. Horodecki, and L. C. Kwek, Phys. Rev. Lett. 88, 217901 (2002) 0031-9007 10.1103/PhysRevLett.88.217901.
G. Ghirardi, L. Marinatto, and T. Weber, J. Stat. Phys. 108, 49 (2002) 0022-4715 10.1023/A:1015439502289.
È. L. Akim and A. Levin, Dokl. Akad. Nauk. SSSR 138, 503 (1961).
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York, 2014).
O. Gühne and N. Lütkenhaus, Phys. Rev. Lett. 96, 170502 (2006) 0031-9007 10.1103/PhysRevLett.96.170502.
C.-J. Zhang, Y.-S. Zhang, S. Zhang, and G.-C. Guo, Phys. Rev. A 76, 012334 (2007) 1050-2947 10.1103/PhysRevA.76.012334.
N. Ganguly, J. Chatterjee, and A. S. Majumdar, Phys. Rev. A 89, 052304 (2014) 1050-2947 10.1103/PhysRevA.89.052304.