We investigate how equilibrium entanglement is manifested in the nonlinear response of an N-qubit system. We show that in the thermodynamic limit the irreducible part of the nth-order nonlinear susceptibility indicates that the eigenstates of the system contain entangled (n + 1)-qubit clusters. This opens the way to a directly observable multiqubit entanglement signature. We show that the irreducible part of the static cubic susceptibility of a system of four flux qubits, as a function of external parameters, behaves as a global 4-qubit entanglement measure introduced in Ref. (20). We discuss the possibility of extracting purely-entanglement-generated contribution from the general multipoint correlators in a multiqubit system.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Osborne T.J., Nielsen M.A. (2002). Phys. Rev. A 66, 32110
Osterloh A., Amico L., Falci G., Fazio R. (2002). Nature (London) 416, 608
M. A. Martin-Delgado, quant-ph/0207026.
Ghosh S., Rosenbaum T.F., Aeppli G., Coppersmith S.N. (2003). Nature (London) 425, 48
Vidal G., Latorre J.I., Rico E., Kitaev A. (2003). Phys. Rev. Lett. 90, 227902
Verstraete F., Martin-Delgado M.A., Cirac J.I. (2004). Phys. Rev. Lett. 92, 087201
Brandão F.G.S.L. (2005). New J. Phys. 7, 254
Liu Y., Wei L.F., Nori F. (2004). Europhys. Lett. 67, 874
Liu Y., Wei L.F., Nori F. (2005). Phys. Rev. B 72, 014547
Glaser U., Büttner H., Fehske H. (2003). Phys. Rev. A 68, 032318
Wu L.-A., Bandyopadhyay S., Sarandy M.S., Lidar D.A. (2005). Phys. Rev. A 72, 032309
Roscilde T., Verrucchi P., Fubini A., Haas S. Tognetti V. (2004). Phys. Rev. Lett. 93, 167203
E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, quant-ph/0001106.
D. Aharonov, W. van Dam, J. Kempe, Z. Landau, S. Lloyd, and O. Regev, quant-ph/0405098.
A. Mizel, D. A. Lidar, and M. Mitchell, quant-ph/0609067.
Vidal G. (2003). Phys. Rev. Lett. 91, 147902
S. Bandyopadhyay and D. Lidar, Phys. Rev. A 70, 010301(R) (2004).
Izmalkov A., Grajcar M., Il’ichev E., Wagner Th., Meyer H.-G., Smirnov A.Yu., Amin M.H.S., van den Brink A.M., Zagoskin A.M. (2004). Phys. Rev. Lett. 93, 037003
Grajcar M., Izmalkov A., van der Ploeg S.H.W., Linzen S., Plecenik T., Wagner Th., Huebner U., Il’ichev E., Meyer H.-G., Smirnov A.Yu., Love P.J., Maassen van den Brink A., Amin M.H.S., Uchaikin S., Zagoskin A.M. (2006). Phys. Rev. Lett. 96, 047006
Love P.J., van den Brink A.M., Smirnov A.Yu., Amin M.H.S., Grajcar M., Il’ichev E., Izmalkov A., Zagoskin A.M. (2007). Quantum. Inf. Process. 6, 187
A. Yu. Smirnov, cond-mat/0312635.
Gühne O., Tóth G., Briegel H.J. (2005). New J. Phys. 7, 229
Strictly speaking, what can be measured is \(\langle\chi_{0B}\rangle = \sum_{n=0}^{2^M-1}\rho_n \chi_{0B}^n\) , the average over the stationary state of the system, but for low enough effective temperature we’ll be close to the ground state value, \(\chi_{0B}^0\) .
D.A. Meyer, N. Wallach, J. Math. Phys. 43, 4273 (2002); G. K. Brennen, Quantum. Inf. Comput. 3, 616 (2003).
Scott A.J. (2004). Phys. Rev. A 69, 052330
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zagoskin, A.M., Smirnov, A.Y., Gupta, S.K. et al. Nonlinear Response and Observable Signatures of Equilibrium Entanglement. Quantum Inf Process 6, 381–399 (2007). https://doi.org/10.1007/s11128-007-0065-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11128-007-0065-2