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Optimal Purification of Arbitrary Quantum Mixed States

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Abstract

The quantum state purification is very important in quantum information processing. Our purpose is to purify arbitrary mixed state into some pure state. We present one simple method to purify arbitrary mixed state from its normal Schmidt decomposition. This scheme is also simplified by using only two special unitary transformations, and can be used to prove the typical entanglement thresholds for random mixed states.

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References

  1. Benenti, G., Casati, G., Strini, G.: Principles of Quantum Computation and Information, vol. I: Basic Concepts. World Scientific, Singapore (2004)

    Book  Google Scholar 

  2. Benenti, G., Casati, G., Strini, G.: Principles of Quantum Computation and Information, vol. II: Basic Tools and Special Topics. World Scientific, Singapore (2004)

    Google Scholar 

  3. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  4. Bouda, J., Buzek, V.: Phys. Rev. A 65, 034304 (2002)

    Article  ADS  Google Scholar 

  5. Constantinescu, T., Ramakrishna, V.: Quantum Inf. Process. 1, 409–424 (2003)

    Article  MathSciNet  Google Scholar 

  6. Kleinmann, M., Kampermann, H., Meyer, T., Bruß, D.: Phys. Rev. A 73, 062309 (2006)

    Article  ADS  Google Scholar 

  7. Chiribella, G., D’Ariano, G.M., Perinotti, P.: Phys. Rev. A 81, 062348 (2010)

    Article  ADS  Google Scholar 

  8. Benenti, G., Strini, G.: Phys. Rev. A 79, 052301 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  9. Bengtsson, I., Zyczkowski, K.: Geometry of Quantum States. Cambridge University Press, Cambridge (2006)

    Book  MATH  Google Scholar 

  10. Barnum, H., Nielsen, M.A., Schumacher, B.: Phys. Rev. A 57, 4153 (1998)

    Article  ADS  Google Scholar 

  11. Bowles, P., Guta, M., Adesso, G.: Phys. Rev. A 84, 022320 (2011)

    Article  ADS  Google Scholar 

  12. Zyczkowski, K., Horodecki, P., Sanpera, A., Lewenstein, M.: Phys. Rev. A 58, 833 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  13. Ralph, T.C., Langford, N.K., Bell, T.B., White, A.G.: Phys. Rev. A 65, 062324 (2002)

    Article  ADS  Google Scholar 

  14. Kok, P., Munro, W.J., Nemoto, K., Ralph, T.C., Dowling, J.P., Milburn, G.J.: Rev. Mod. Phys. 79, 135–174 (2007)

    Article  ADS  Google Scholar 

  15. Clark, A.S., Fulconis, J., Rarity, J.G., Wadsworth, W.J., O’Brien, J.L.: Phys. Rev. A 79, 030303 (2009)

    Article  ADS  Google Scholar 

  16. Kumar, P.: Quantum Inf. Process. 12, 1201–1223 (2013)

    Article  ADS  MATH  Google Scholar 

  17. Aubrun, G., Szarek, S.L.J., Ye, D.P.: Commun. Pure Appl. Math. (2013). doi:10.1002/cpa.21460

    Google Scholar 

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Acknowledgements

This work is supported by the Foundation of He’nan Educational Committee (No. 13A413750, 13A413747, 12A510022), the Natural Science Foundation of He’nan Province of China (No. 132300410393, 122102210543, 122102210544), and Xuchang Municipal Natural Science Foundation (No. 5018, 1101059), the National Natural Science Foundation of China (No. 11226336, 61170272), and the Fundamental Research Funds for the Central Universities (No. SWJTU11BR174).

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Authors and Affiliations

  1. Department of Computer Science and Technology, Xuchang University, Xuchang, 461000, China

    Yuan Ping, Huina Li & Zhili Zhang

  2. School of Information Engineering, Minzu University of China, Beijing, 100081, China

    Xiuqin Pan

  3. Information Security Center, Southwest Jiaotong University, Chengdu, 610031, China

    Mingxing Luo

  4. State Key Laboratory of Information Security, Graduate University of Chinese Academy of Sciences, Beijing, 100049, China

    Mingxing Luo

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  1. Yuan Ping
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  2. Huina Li
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  3. Xiuqin Pan
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  4. Mingxing Luo
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  5. Zhili Zhang
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Correspondence to Yuan Ping.

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Ping, Y., Li, H., Pan, X. et al. Optimal Purification of Arbitrary Quantum Mixed States. Int J Theor Phys 52, 4367–4373 (2013). https://doi.org/10.1007/s10773-013-1755-4

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  • DOI: https://doi.org/10.1007/s10773-013-1755-4

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