Nonlinear entanglement witnesses based on continuous-variable local orthogonal observables for bipartite systems. (English) Zbl 1333.81042
Summary: In this paper, a nonlinear entanglement witness criterion based on continuous-variable local orthogonal observables for bipartite states is established, which is strictly stronger than the the linear entanglement witnesses criterion introduced by C. Zhang et al. [“Detecting and estimating continuous-variable entanglement by local orthogonal observables”, Phys. Rev. Lett. 111, No. 19, Article ID 190501, 11 p. (2013; doi:10.1103/PhysRevLett.111.190501)]. This criterion is particularly applied to two-mode Gaussian states yielding a criterion in terms of the covariance matrix. Comparison with CCNR criterion is discussed.
MSC:
| 81P40 | Quantum coherence, entanglement, quantum correlations |
References:
| [1] | Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000) · Zbl 1049.81015 |
| [2] | Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009) · Zbl 1205.81012 · doi:10.1103/RevModPhys.81.865 |
| [3] | Gühne, O., Tóth, G.: Entanglement detection. Phys. Rep. 474, 1-75 (2009) · doi:10.1016/j.physrep.2009.02.004 |
| [4] | Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413 (1996) · Zbl 0947.81003 · doi:10.1103/PhysRevLett.77.1413 |
| [5] | Hou, J.-C.: A characterization of positive linear maps and criteria for entangled quantum states. J. Phys. A Math. Theor. 43, 385201 (2010) · Zbl 1198.81055 · doi:10.1088/1751-8113/43/38/385201 |
| [6] | Qi, X.-F., Hou, J.-C.: Positive finite rank elementary operators and characterizing entanglement of states. J. Phys. A Math. Theor. 44, 215305 (2011) · Zbl 1218.81019 · doi:10.1088/1751-8113/44/21/215305 |
| [7] | Horodecki, M., Horodecki, P., Horodecki, R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1-8 (1996) · Zbl 1037.81501 · doi:10.1016/S0375-9601(96)00706-2 |
| [8] | Chen, K., Wu, L.-A.: A matrix realignment method for recognizing entanglement. Quant. Inf. Comput. 3, 193-202 (2003) · Zbl 1152.81692 |
| [9] | Rodolph, O.: Computable cross-norm criterion for separability. Lett. Math. Phys. 70, 57-64 (2004) · Zbl 1059.81030 · doi:10.1007/s11005-004-0767-7 |
| [10] | Gühne, O.: Characterizing entanglement via uncertainty relations. Phys. Rev. Lett. 92, 117903 (2004) · doi:10.1103/PhysRevLett.92.117903 |
| [11] | Tóth, G., Gühne, O.: Entanglement detection in the stabilizer formalism. Phys. Rev. A 72, 022340 (2005) · doi:10.1103/PhysRevA.72.022340 |
| [12] | Duan, L.-M., Giedke, G., Cirac, J.I., Zoller, P.: Inseparability criterion for continuous variable systems. Phys. Rev. Lett. 84, 2722 (2000) · Zbl 1004.81503 · doi:10.1103/PhysRevLett.84.2722 |
| [13] | Hillery, M., Zubairy, M.S.: Entanglement conditions for two-mode states. Phys. Rev. Lett. 96, 050503 (2006) · doi:10.1103/PhysRevLett.96.050503 |
| [14] | Nha, H., Zubairy, M.S.: Uncertainty inequalities as entanglement criteria for negative partial-transpose states. Phys. Rev. Lett. 101, 130402 (2008) · doi:10.1103/PhysRevLett.101.130402 |
| [15] | Shchukin, E., Vogel, W.: Inseparability criteria for continuous bipartite quantum states. Phys. Rev. Lett. 95, 230502 (2005) · doi:10.1103/PhysRevLett.95.230502 |
| [16] | Simon, R.: Peres-Horodecki separability criterion for continuous variable systems. Phys. Rev. Lett. 84, 2726 (2000) · doi:10.1103/PhysRevLett.84.2726 |
| [17] | Chen, X.-Y., Jiang, L.-Z., Yu, P., Tian, M.-Z.: Realignment entanglement criterion for continuous bipartite symmetric quantum states. Phys. Rev. A 89, 012332 (2014) · doi:10.1103/PhysRevA.89.012332 |
| [18] | Werner, R.F., Wolf, M.M.: Bound entangled Gaussian states. Phys. Rev. Lett. 86, 3658 (2001) · doi:10.1103/PhysRevLett.86.3658 |
| [19] | DiGuglielmo, J., Samblowski, A., Hage, B., Pineda, C., Eisert, J., Schnabel, R.: Experimental unconditional preparation and detection of a continuous bound entangled state of light. Phys. Rev. Lett. 107, 240503 (2011) · doi:10.1103/PhysRevLett.107.240503 |
| [20] | Zhang, C.-J., Nha, H., Zhang, Y.-S., Guo, G.-C.: Entanglement detection via tighter local uncertainty relations. Phys. Rev. A 81, 012324 (2010) · doi:10.1103/PhysRevA.81.012324 |
| [21] | Bru, D.: Characterizing entanglement. J. Math. Phys. 43, 4237-4251 (2002) · Zbl 1060.81505 · doi:10.1063/1.1494474 |
| [22] | Chruściński, D., Kossakowski, A.: On the structure of entanglement witnesses and new class of positive indecomposable maps. Open Syst. Inf. Dyn. 14, 275-294 (2007) · Zbl 1129.81019 · doi:10.1007/s11080-007-9052-4 |
| [23] | Hou, J.-C., Qi, X.-F.: Constructing entanglement witnesses for infinite-dimensional systems. Phys. Rev. A 81, 062351 (2010) · doi:10.1103/PhysRevA.81.062351 |
| [24] | Tóth, G., Gühne, O.: Detecting genuine multipartite entanglement with two local measurements. Phys. Rev. Lett. 94, 060501 (2005) · Zbl 1249.68066 · doi:10.1103/PhysRevLett.94.060501 |
| [25] | Yu, S., Liu, N.-L.: Entanglement detection by local orthogonal observables. Phys. Rev. Lett. 95, 150504 (2005) · Zbl 1255.81041 · doi:10.1103/PhysRevLett.95.150504 |
| [26] | Hou, J.-C., Guo, Y.: Constructing entanglement witnesses for states in infinite-dimensional bipartite quantum systems. Int. J. Theor. Phys. 50, 1245-1254 (2011) · Zbl 1214.81043 · doi:10.1007/s10773-010-0534-8 |
| [27] | Gühne, O., Mechler, M., Tóth, G., Adam, P.: Entanglement criteria based on local uncertainty relations are strictly stronger than the computable cross norm criterion. Phys. Rev. A 74, 010301(R) (2006) · doi:10.1103/PhysRevA.74.010301 |
| [28] | Zhang, C.J., Yu, S.-X., Chen, Q., Oh, C.H.: Detecting and estimating continuous-variable entanglement by local orthogonal observables. Phys. Rev. Lett. 111, 190501 (2013) · doi:10.1103/PhysRevLett.111.190501 |
| [29] | Luo, S.L.: Wigner-Yanase skew information and uncertainty relations. Phys. Rev. Lett. 91, 180403 (2003) · doi:10.1103/PhysRevLett.91.180403 |
| [30] | Dakić, B., Vedral, V., Brukner, C̆.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010) · Zbl 1255.81213 · doi:10.1103/PhysRevLett.105.190502 |
| [31] | Braunstein, S.L., van Loock, P.: Quantum information with continuous variables. Rev. Mod. Phys. 77, 513 (2005) · Zbl 1205.81010 · doi:10.1103/RevModPhys.77.513 |
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