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Remark on the additivity conjecture for a quantum depolarizing channel

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Abstract

We consider bistochastic quantum channels generated by unitary representations of a discrete group. We give a proof of the additivity conjecture for a quantum depolarizing channel Φ based on the decreasing property of the relative entropy. We show that the additivity conjecture holds for a channel Ξ = Ψ o Φ, where Ψ is a phase damping channel.

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References

  1. Holevo, A.S., Quantum Coding Theorems, Uspekhi Mat. Nauk, 1998, vol. 53, no. 6, pp. 193–230 [Russian Math. Surveys (Engl. Transl.), 1998, vol. 53, no. 6, pp. 1295–1331]; LANL e-print quant-ph/9808023.

    MATH  MathSciNet  Google Scholar 

  2. Amosov, G.G., Holevo, A.S., and Werner, R.F., On the Additivity Conjecture in Quantum Information Theory, Probl. Peredachi Inf., 2000, vol. 36, no. 4, pp. 25–34 [Probl. Inf. Trans. (Engl. Transl.), 2000, vol. 36, no. 4, pp. 305–313]; LANL e-print quant-ph/0003002.

    MATH  Google Scholar 

  3. Cortese, J., The Holevo-Schumacher-Westmoreland Channel Capacity for a Class of Qudit Unital Channels, LANL e-print quant-ph/0211093.

  4. Holevo, A.S., Remarks on the Classical Capacity of Quantum Covariant Channels, LANL e-print quant-ph/0212025.

  5. Shor, P.W., Equivalence of Additivity Questions in Quantum Information Theory, Comm. Math. Phys., 2004, vol. 246, no. 3, pp. 453–472; LANL e-print quant-ph/0305035.

    Article  MATH  MathSciNet  Google Scholar 

  6. Amosov, G.G. and Holevo, A.S., On the Multiplicativity Conjecture for Quantum Channels, Teor. Veroyatn. Primen., 2002, vol. 47, no. 1, pp. 143–146 [Theory Probab. Appl. (Engl. Transl.), 2003, vol. 47, no. 1, pp. 123–126]; LANL e-print quant-ph/0103015.

    MATH  Google Scholar 

  7. King, C., Additivity for Unital Qubit Channels, J. Math. Phys., 2002, vol. 43, no. 10, pp. 4641–4653; LANL e-print quant-ph/0103156.

    Article  MATH  MathSciNet  Google Scholar 

  8. King, C., The Capacity of the Quantum Depolarizing Channel, IEEE Trans. Inform. Theory, 2003, vol. 49, no. 1, pp. 221–229; LANL e-print quant-ph/0204172.

    Article  MATH  MathSciNet  Google Scholar 

  9. Shor, P.W., Additivity of the Classical Capacity of Entanglement-Breaking Quantum Channels, J. Math. Phys., 2002, vol. 43, no. 9, pp. 4334–4340; LANL e-print quant-ph/0201149.

    Article  MATH  MathSciNet  Google Scholar 

  10. Fannes, M., Haegeman, B., Mosconyi, M., and Vanpeteghem, D., Additivity of Minimal Entropy Output for a Class of Covariant Channels, LANL e-print quant-ph/0410195.

  11. Datta, N., Holevo, A.S., and Suhov, Yu., Additivity for Transpose Depolarizing Channels, LANL e-print quant-ph/0412034.

  12. Holevo, A.S. and Shirokov, M.E., On Shor’s Channel Extension and Constrained Channels, Comm. Math. Phys., 2004, vol. 249, no. 2, pp. 417–430; LANL e-print quant-ph/0306196.

    Article  MATH  MathSciNet  Google Scholar 

  13. Werner, R.F. and Holevo, A.S., Counterexample to an Additivity Conjecture for Output Purity of Quantum Channels, J. Math. Phys., 2002, vol. 43, no. 9, pp. 4353–4357; LANL e-print quant-ph/0203003.

    Article  MATH  MathSciNet  Google Scholar 

  14. Ohya, M. and Petz, D., Quantum Entropy and Its Use, Berlin: Springer, 1993.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, State University, Russia

    G. G. Amosov

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  1. G. G. Amosov
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Original Russian Text © G.G. Amosov, 2006, published in Problemy Peredachi Informatsii, 2006, Vol. 42, No. 2, pp. 3–11.

Supported in part by the INTAS, grant no. 00-738.

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Amosov, G.G. Remark on the additivity conjecture for a quantum depolarizing channel. Probl Inf Transm 42, 69–76 (2006). https://doi.org/10.1134/S0032946006020013

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  • DOI: https://doi.org/10.1134/S0032946006020013

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