# Noise effects on entanglement distribution by separable state

- 44 Downloads

## Abstract

We investigate noise effects on the performance of entanglement distribution by separable state. We consider a realistic situation in which the mediating particle between two distant nodes of the network goes through a noisy channel. For a large class of noise models, we show that the average value of distributed entanglement between two parties is equal to entanglement between particular bipartite partitions of target qubits and exchange qubit in intermediate steps of the protocol. This result is valid for distributing two-qubit/qudit and three-qubit entangled states. In explicit examples of the noise family, we show that there exists a critical value of noise parameter beyond which distribution of distillable entanglement is not possible. Furthermore, we determine how this critical value increases in terms of Hilbert space dimension, when distributing *d*-dimensional Bell states.

### Keywords

Entanglement Entanglement generation Distribution Quantum noise Quantum communication channels## Notes

### Acknowledgements

We acknowledge financial support by Sharif University of Technology’s Office of Vice President for Research under Grant No. G950223. L. M acknowledges hospitality of the Abdus Salam International Centre for Theoretical Physics (ICTP) where parts of this work were completed.

### References

- 1.Zurek, W.H.: Decoherence and the transition from quantum to classical-revisited. Phys. Today
**44**, 36–44 (1991)CrossRefGoogle Scholar - 2.Knill, E., Laflamme, R.: Theory of quantum error-correcting codes. Phys. Rev. A
**55**, 900–911 (1997)ADSMathSciNetCrossRefGoogle Scholar - 3.Wiseman, H.M., Milburn, G.J.: Quantum Measurement and Control. Cambridge University Press, New York (2010)MATHGoogle Scholar
- 4.Gregoratti, M., Werner, R.F.: Quantum lost and found. J. Mod. Opt.
**50**, 915–933 (2003)ADSMathSciNetCrossRefMATHGoogle Scholar - 5.Memarzadeh, L., Macchiavello, C., Mancini, S.: Recovering quantum information through partial access to the environment. N. J. Phys.
**13**, 103031-1–103031-16 (2011)Google Scholar - 6.Kimble, H.J.: The quantum internet. Nature
**453**, 1023–1030 (2008)ADSCrossRefGoogle Scholar - 7.Bose, S., Vedral, V., Knight, P.L.: Multiparticle generalization of entanglement swapping. Phys. Rev. A
**57**, 822–829 (1998)ADSCrossRefGoogle Scholar - 8.Bennett, C.H., DiVincenzo, D.P., Smolin, J.A., Wootters, William K.: Mixed-state entanglement and quantum error correction. Phys. Rev. A
**54**, 3824–3851 (1996)ADSMathSciNetCrossRefMATHGoogle Scholar - 9.Cirac, J.I., Dür, W., Kraus, B., Lewenstein, M.: Entangling operations and their implementation using a small amount of entanglement. Phys. Rev. Lett.
**86**, 544–547 (2001)ADSCrossRefGoogle Scholar - 10.Kraus, B., Cirac, J.I.: Optimal creation of entanglement using a two-qubit gate. Phys. Rev. A
**63**, 062309-1–062309-8 (2001)ADSCrossRefGoogle Scholar - 11.Cirac, J.I., Zoller, P.: Preparation of macroscopic superpositions in many-atom systems. Phys. Rev. A
**50**, R2799–R2802(R) (1994)ADSCrossRefGoogle Scholar - 12.Braun, D.: Creation of entanglement by interaction with a common heat bath. Phys. Rev. Lett.
**89**, 277901–277904 (2002)CrossRefGoogle Scholar - 13.Benatti, F., Floreanini, R., Piani, M.: Environment induced entanglement in Markovian dissipative dynamics. Phys. Rev. Lett.
**91**, 070402–070404 (2003)ADSCrossRefGoogle Scholar - 14.Memarzadeh, L., Mancini, S.: Stationary entanglement achievable by environment-induced chain links. Phys. Rev. A
**83**, 042329-1–042329-5 (2011)ADSCrossRefGoogle Scholar - 15.Memarzadeh, L., Mancini, S.: Entanglement dynamics for qubits dissipating into a common environment. Phys. Rev. A
**87**, 032303-1–032303-6 (2013)ADSCrossRefGoogle Scholar - 16.Kwiat, P.G., Mattle, K., Weinfurter, H., Zeilinger, A., Sergienko, A.V., Shih, Y.: New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett.
**75**, 4337–4341 (1995)ADSCrossRefGoogle Scholar - 17.Spee, C., de Vicente, J.I., Kraus, B.: Remote entanglement preparation. Phys. Rev. A
**88**, 010305(R)-1–010305(R)-4 (2013)ADSCrossRefGoogle Scholar - 18.Cubitt, T.S., Verstraete, F., Dür, W., Cirac, J.I.: Separable states can be used to distribute entanglement. Phys. Rev. Lett.
**91**, 037902-1–037902-4 (2003)ADSGoogle Scholar - 19.Fedrizzi, A., Zuppardo, M., Gillett, G.G., Broome, M.A., Almeida, M.P., Paternostro, M., White, A.G., Paterek, T.: Experimental distribution of entanglement with separable carriers. Phys. Rev. Lett.
**111**, 230504-1–230504-5 (2013)ADSCrossRefGoogle Scholar - 20.Vollmer, C.E., Schulze, D., Eberle, T., Händchen, V., Fiurásek, J., Schnabel, R.: Experimental entanglement distribution by separable states. Phys. Rev. Lett.
**111**, 230505-1–230505-5 (2013)ADSCrossRefGoogle Scholar - 21.Peuntinger, C., Chille, V., Mista Jr., L., Korolkova, N., Förtsch, M., Korger, J., Marquardt, C., Leuchs, G.: Distributing entanglement with separable states. Phys. Rev. Lett.
**111**, 230506-1–230506-5 (2013)ADSCrossRefGoogle Scholar - 22.Mista Jr., L., Korolkova, N.: Distribution of continuous-variable entanglement by separable Gaussian states. Phy. Rev. A
**77**, 050302(R)-1–050302(R)-4 (2008)ADSMathSciNetCrossRefGoogle Scholar - 23.Mista Jr., L., Korolkova, N.: Improving continuous-variable entanglement distribution by separable states. Phy. Rev. A
**80**, 032310-1–032310-7 (2009)ADSCrossRefGoogle Scholar - 24.Karimipour, V., Memarzadeh, L., Bordbar, N.T.: Systematics of entanglement distribution by separable states. Phys. Rev. A
**92**, 032325-1–032325-5 (2015)ADSGoogle Scholar - 25.Streltsov, A., Kampermann, H., Bru, D.: Quantum cost for sending entanglement. Phys. Rev. Lett.
**108**, 250501-1–250501-5 (2012)ADSCrossRefGoogle Scholar - 26.Chuan, T.K., Maillard, J., Modi, K., Paterek, T., Paternostro, M., Piani, M.: Quantum discord bounds the amount of distributed entanglement. Phys. Rev. Lett.
**109**, 070501-1–070501-5 (2012)ADSCrossRefGoogle Scholar - 27.Streltsov, A., Augusiak, R., Demianowicz, M., Lewenstein, M.: Progress towards a unified approach to entanglement distribution Phys. Rev. A
**92**, 012335-1–012335-14 (2015)CrossRefGoogle Scholar - 28.Pal, R., Bandyopadhyay, S., Ghosh, S.: Entanglement sharing through noisy qubit channels: one-shot optimal singlet fraction. Phys. Rev. A
**90**, 052304-1–052304-8 (2014)ADSGoogle Scholar - 29.Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett.
**80**, 2245–2248 (1998)ADSCrossRefMATHGoogle Scholar - 30.King, C., Ruskai, M.B.: Minimal entropy of states emerging from noisy quantum channels. IEEE Trans. Inf. Theory
**47**, 192–209 (2001)MathSciNetCrossRefMATHGoogle Scholar - 31.Fujiwara, A., Algoet, P.: One-to-one parametrization of quantum channels. Phys. Rev. A
**59**, 3290–3294 (1999)ADSCrossRefGoogle Scholar - 32.Ruskai, M.B., Szarek, S., Werner, E.: An analysis of completely-positive trace-preserving maps on M2. Linear Algebra Appl.
**347**, 159–187 (2002)MathSciNetCrossRefMATHGoogle Scholar - 33.Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A
**65**, 032314-1–032314-11 (2002)ADSCrossRefGoogle Scholar - 34.Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett.
**77**, 1413–1415 (1996)ADSMathSciNetCrossRefMATHGoogle Scholar