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The dynamics of two entangled qubits exposed to classical noise: role of spatial and temporal noise correlations. (English) Zbl 1325.81022

Summary: We investigate the decay of two-qubit entanglement caused by the influence of classical noise. We consider the whole spectrum of cases ranging from independent to fully correlated noise affecting each qubit. We take into account different spatial symmetries of noises, and the regimes of noise autocorrelation time. The latter can be either much shorter than the characteristic qubit decoherence time (Markovian decoherence), or much longer (approaching the quasi-static bath limit). We express the entanglement of two-qubit states in terms of expectation values of spherical tensor operators which allows for transparent insight into the role of the symmetry of both the two-qubit state and the noise for entanglement dynamics.

MSC:

81P40 Quantum coherence, entanglement, quantum correlations
81S22 Open systems, reduced dynamics, master equations, decoherence
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[1] Steane, A.: Quantum computing. Rep. Prog. Phys. 61, 117 (1998) · doi:10.1088/0034-4885/61/2/002
[2] Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865-942 (2009) · Zbl 1205.81012 · doi:10.1103/RevModPhys.81.865
[3] Leggett, A.J., Chakravarty, S., Dorsey, A.T., Fisher, M.P.A., Garg, A., Zwerger, W.: Dynamics of the dissipative two-state system. Rev. Mod. Phys. 59, 1 (1987) · doi:10.1103/RevModPhys.59.1
[4] Weiss, U.: Quantum Dissipative Systems. World Scientific, Singapore (1999) · Zbl 1137.81301 · doi:10.1142/4239
[5] Shimshoni, E., Gefen, Y.: Onset of dissipation in zener dynamics: relaxation versus dephasing. Ann. Phys. (NY) 210, 16 (1991) · doi:10.1016/0003-4916(91)90275-D
[6] Shimshoni, E., Stern, A.: Dephasing of interference in Landau-Zener transitions. Phys. Rev. B 47, 9523-9536 (1993) · doi:10.1103/PhysRevB.47.9523
[7] Zurek, W.H.: Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715 (2003) · Zbl 1205.81031 · doi:10.1103/RevModPhys.75.715
[8] Aolita, L., de Melo, F., Davidovich, L.: Open-system dynamics of entanglement (2014). arXiv:1402.3713
[9] Schoelkopf, RJ; Clerk, AA; Girvin, SM; Lehnert, KW; Devoret, MH; Nazarov, YV (ed.), Qubits as spectrometers of quantum noise, 175-203 (2003), Dordrecht · doi:10.1007/978-94-010-0089-5_9
[10] Paladino, E., Galperin, Y.M., Falci, G., Altshuler, B.L.: \[1/f1\]/f noise: implications for solid-state quantum information. Rev. Mod. Phys. 86, 361 (2014) · doi:10.1103/RevModPhys.86.361
[11] Fischer, J., Trif, M., Coish, W.A., Loss, D.: Spin interactions, relaxation and decoherence in quantum dots. Solid State Commun. 149, 1443 (2009) · doi:10.1016/j.ssc.2009.04.033
[12] Cywiński, Ł.: Dephasing of electron spin qubits due to their interaction with nuclei in quantum dots. Acta Phys. Pol. A 119, 576 (2011)
[13] Monz, T., Schindler, P., Barreiro, J.T., Chwalla, M., Nigg, D., Coish, W.A., Harlander, M., Hänsel, W., Hennrich, M., Blatt, R.: 14-Qubit entanglement: creation and coherence. Phys. Rev. Lett. 106, 130506 (2011) · doi:10.1103/PhysRevLett.106.130506
[14] Schindler, P., Nigg, D., Monz, T., Barreiro, J.T., Martinez, E., Wang, S.X., Quint, S., Brandl, M.F., Nebendahl, V., Roos, C.F., Chwalla, M., Hennrich, M., Blatt, R.: A quantum information processor with trapped ions. New J. Phys. 15, 123012 (2013) · doi:10.1088/1367-2630/15/12/123012
[15] Makhlin, Y., Schön, G., Shnirman, A.: Dephasing of solid-state qubits at optimal points. Chem. Phys. 296, 315 (2004) · doi:10.1016/j.chemphys.2003.09.025
[16] Pokrovsky, V.L., Sun, D.: Fast quantum noise in the Landau-Zener transition. Phys. Rev. B 76, 024310 (2007) · doi:10.1103/PhysRevB.76.024310
[17] Duan, L.-M., Guo, G.-C.: Reducing decoherence in quantum-computer memory with all quantum bits coupling to the same environment. Phys. Rev. A 57, 737 (1998) · doi:10.1103/PhysRevA.57.737
[18] Burkard, G.: Non-Markovian qubit dynamics in the presence of \[1/f1\]/f noise. Phys. Rev. B 79, 125317 (2009) · doi:10.1103/PhysRevB.79.125317
[19] Yu, T., Eberly, J.H.: Qubit disentanglement and decoherence via dephasing. Phys. Rev. B 68, 165322 (2003) · doi:10.1103/PhysRevB.68.165322
[20] Ting, Y., Eberly, J.H.: Sudden death of entanglement: classical noise effects. Opt. Commun. 264, 393 (2006) · doi:10.1016/j.optcom.2006.01.061
[21] Ann, K., Jaeger, G.: Disentanglement and decoherence in two-spin and three-spin systems under dephasing. Phys. Rev. B 75, 115307 (2007) · doi:10.1103/PhysRevB.75.115307
[22] Ting, Y., Eberly, J.H.: Entanglement evolution in a non-Markovian environment. Opt. Commun. 283, 676 (2010) · doi:10.1016/j.optcom.2009.10.042
[23] Benedetti, C., Buscemi, F., Bordone, P., Paris, M.G.A.: Dynamics of quantum correlations in colored-noise environments. Phys. Rev. A 87, 052328 (2013) · doi:10.1103/PhysRevA.87.052328
[24] Zhou, D., Lang, A., Joynt, R.: Disentanglement and decoherence from classical non-Markovian noise: random telegraph noise. Quantum Inf. Process. 9, 727 (2010) · Zbl 1209.81143 · doi:10.1007/s11128-010-0165-2
[25] Bellomo, B., Compagno, G., D’Arrigo, A., Falci, G., Lo Franco, R., Paladino, E.: Entanglement dynamics of two independent qubits in environments with and without memory. Phys. Rev. A 81, 062309 (2010) · doi:10.1103/PhysRevA.81.062309
[26] Ban, M.: Entanglement, phase correlation and dephasing of two-qubit states. Opt. Commun. 281, 3943 (2008) · doi:10.1016/j.optcom.2008.03.058
[27] Corn, B., Ting, Y.: Modulated entanglement evolution via correlated noises. Quantum Inf. Process. 8, 565 (2009) · Zbl 1180.81085 · doi:10.1007/s11128-009-0138-5
[28] De, A., Lang, A., Zhou, D., Joynt, R.: Suppression of decoherence and disentanglement by the exchange interaction. Phys. Rev. A 83, 042331 (2011) · doi:10.1103/PhysRevA.83.042331
[29] Brox, H., Bergli, J., Galperin, Y.M.: Bloch-sphere approach to correlated noise in coupled qubits. J. Phys. A Math. Theor. 45, 455302 (2012) · Zbl 1267.81053 · doi:10.1088/1751-8113/45/45/455302
[30] Budimir, J., Skinner, J.L.: On the relationship between \[t_1\] t1 and \[t_2\] t2 for stochastic relaxation models. J. Stat. Phys. 49, 1029 (1987) · doi:10.1007/BF01017558
[31] Aihara, M., Sevian, H.M., Skinner, J.L.: Non-markovian relaxation of a spin-\[ \frac{1}{2}12\] particle in a fluctuating transverse field: cumulant expansion and stochastic simulation results. Phys. Rev. A 41, 6596 (1990) · doi:10.1103/PhysRevA.41.6596
[32] Szańkowski, P., Trippenbach, M., Band, Y.B.: Spin decoherence due to fluctuating fields. Phys. Rev. E 87, 052112 (2013) · doi:10.1103/PhysRevE.87.052112
[33] de Lange, G., Wang, Z.H., Ristè, D., Dobrovitski, V.V., Hanson, R.: Universal dynamical decoupling of a single solid-state spin from a spin bath. Science 330, 60 (2010) · doi:10.1126/science.1192739
[34] Fox, R.F.: Application of cumulant techniques to multiplicative stochastic processes. J. Math. Phys. 15, 1479 (1974) · doi:10.1063/1.1666835
[35] Falci, G., D’Arrigo, A., Mastellone, A., Paladino, E.: Initial decoherence in solid state qubits. Phys. Rev. Lett. 94, 167002 (2005) · Zbl 1175.81060 · doi:10.1103/PhysRevLett.94.167002
[36] Taylor, J.M., Lukin, M.D.: Dephasing of quantum bits by a quasi-static mesoscopic environment. Quantum Inf. Process. 5, 503 (2006) · Zbl 1112.81316 · doi:10.1007/s11128-006-0036-z
[37] Makhlin, Y., Shnirman, A.: Dephasing of solid-state qubits at optimal points. Phys. Rev. Lett. 92, 178301 (2004) · doi:10.1103/PhysRevLett.92.178301
[38] Cywiński, Ł.: Dynamical-decoupling noise spectroscopy at an optimal working point of a qubit. Phys. Rev. A 90, 042307 (2014) · doi:10.1103/PhysRevA.90.042307
[39] Życzkowski, K., Horodecki, P., Horodecki, M., Horodecki, R.: Dynamics of quantum entanglement. Phys. Rev. A 65, 012101 (2001) · Zbl 0984.81007 · doi:10.1103/PhysRevA.65.012101
[40] Ting, Y., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004) · doi:10.1103/PhysRevLett.93.140404
[41] Ting, Y., Eberly, J.H.: Sudden death of entanglement. Science 323, 598 (2009) · Zbl 1226.81024 · doi:10.1126/science.1167343
[42] Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998) · Zbl 1368.81047 · doi:10.1103/PhysRevLett.80.2245
[43] Ashm, R.B.: Basic Probability Theory. Dover, New York (2008)
[44] Sakurai, J.J.: Modern Quantum Mechanics. Addison Wesley, London (1994)
[45] Ting, Y., Eberly, J.H.: Evolution from entanglement to decoherence of bipartite mixed “x” states. Quantum Inf. Comput. 7, 459 (2007)
[46] Horodecki, R., Horodecki, M.: Information-theoretic aspects of inseparability of mixed states. Phys. Rev. A 54, 1838-1843 (1996) · doi:10.1103/PhysRevA.54.1838
[47] Hill, S., Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022 (1997) · doi:10.1103/PhysRevLett.78.5022
[48] Aolita, L., de Melo, F., Davidovich, L.: Open-system dynamics of entanglement. Rep. Prog. Phys. 78, 042001 (2015) · doi:10.1088/0034-4885/78/4/042001
[49] Szańkowski, P., Trippenbach, M., Chwedeńczuk, J.: Parameter estimation in memory-assisted noisy quantum interferometry. Phys. Rev. A 90(6), 063619 (2014) · doi:10.1103/PhysRevA.90.063619
[50] Feynman, R.P.: An operator calculus having applications in quantum electrodynamics. Phys. Rev. 84, 108 (1951) · Zbl 0044.23304 · doi:10.1103/PhysRev.84.108
[51] Kubo, R.: Generalized cumulant expansion method. J. Phys. Soc. Jpn. 17, 1100 (1962) · Zbl 0118.45203 · doi:10.1143/JPSJ.17.1100
[52] Van Kampen, N.G.: A cumulant expansion for stochastic linear differential equations. I. Physica 74, 215 (1974) · doi:10.1016/0031-8914(74)90121-9
[53] Van Kampen, N.G.: A cumulant expansion for stochastic linear differential equations. II. Physica 74, 239 (1974) · doi:10.1016/0031-8914(74)90122-0
[54] Fox, R.F.: Critique of the generalized cumulant expansion method. J. Math. Phys. 17, 1148 (1976) · doi:10.1063/1.523041
[55] Zhou, D., Chern, G.-W., Fei, J., Joynt, R.: Topology of entanglement evolution of two qubits. Int. J. Mod. Phys. B 26, 1250054 (2012) · Zbl 1247.81061 · doi:10.1142/S0217979212500543
[56] Blum, K.: Density Matrix Theory and Applications. Plenum Press, New York (1981) · Zbl 1234.81008 · doi:10.1007/978-1-4615-6808-7
[57] Wang, M.C., Uhlenbeck, G.E.: On the theory of the Brownian motion II. Rev. Mod. Phys. 17, 323 (1945) · Zbl 0063.08172 · doi:10.1103/RevModPhys.17.323
[58] Lidar, D.A.: Review of decoherence free subspaces, noiseless subsystems, and dynamical decoupling. Adv. Chem. Phys. 154, 295-354 (2014) · Zbl 1291.81101
[59] Bergli, J., Galperin, Y.M., Altshuler, B.L.: Decoherence of a qubit by a non-Gaussian noise at an arbitrary working point. Phys. Rev. B 74, 024509 (2006) · doi:10.1103/PhysRevB.74.024509
[60] Benedetti, C., Paris, M.G.A.: Effective dephasing for a qubit interacting with a transverse classical field. Int. J. Quantum Inf. 12, 1461004 (2014) · Zbl 1294.81069 · doi:10.1142/S0219749914610048
[61] Cucchietti, F.M., Paz, J.P., Zurek, W.H.: Decoherence from spin environments. Phys. Rev. A 72, 052113 (2005) · doi:10.1103/PhysRevA.72.052113
[62] Dobrovitski, V.V., Feiguin, A.E., Hanson, R., Awschalom, D.D.: Decay of rabi oscillations by dipolar-coupled dynamical spin environments. Phys. Rev. Lett. 102, 237601 (2009) · doi:10.1103/PhysRevLett.102.237601
[63] Bragar, I., Cywiński, Ł.: Dynamics of entanglement of two electron spins interacting with nuclear spin baths in quantum dots. Phys. Rev. B 91, 155310 (2015) · doi:10.1103/PhysRevB.91.155310
[64] Shulman, M.D., Harvey, S.P., Nichol, J.M., Bartlett, S.D., Doherty, A.C., Umansky, V., Yacoby, A.: Suppressing qubit dephasing using real-time hamiltonian estimation. Nat. Commun. 5, 5156 (2014) · doi:10.1038/ncomms6156
[65] Hung, J.-T., Cywiński, Ł., Xuedong, H., Das Sarma, S.: Hyperfine interaction induced dephasing of coupled spin qubits in semiconductor double quantum dots. Phys. Rev. B 88, 085314 (2013) · doi:10.1103/PhysRevB.88.085314
[66] DArrigo, A., Mastellone, A., Paladino, E., Falci, G.: Effects of low-frequency noise cross-correlations in coupled superconducting qubits. New J. Phys. 10, 115006 (2008) · Zbl 1175.81060 · doi:10.1088/1367-2630/10/11/115006
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