The uncertainty principle in the presence of quantum memory

Nature Physics

Volumn 6, Issue 9, 2010, Pages 659-662

  Berta, Mario ^a,b   Christandl, Matthias ^a,b   Colbeck, Roger ^a,c   Renes, Joseph M ^d   Renner, Renato ^a  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF MUNICH   (Germany)

^c PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

^d DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

QUANTUM ENTANGLEMENT; UNCERTAINTY ANALYSIS;

A-PARTICLES; ARBITRARY PRECISION; HEISENBERG; LOWER BOUNDS; QUANTUM MEMORY; UNCERTAINTY PRINCIPLES;

QUANTUM CRYPTOGRAPHY;

EID: 77956305813     PISSN: 17452473     EISSN: 17452481     Source Type: Journal    
DOI: 10.1038/nphys1734     Document Type: Article

References (30)

1. Heisenberg, W. Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z. Phys. 43, 172-198 (1927).
2. Julsgaard, B., Sherson, J., Cirac, J. I., Fiuráek, J. & Polzik, E. S. Experimental demonstration of quantum memory for light. Nature 432, 482-486 (2004).
3. Robertson, H. P. The uncertainty principle. Phys. Rev. 34, 163-164 (1929).
4. Białynicki-Birula, I. & Mycielski, J. Uncertainty relations for information entropy in wave mechanics. Commun. Math. Phys. 44, 129-132 (1975).
5. Deutsch, D. Uncertainty in quantum measurements. Phys. Rev. Lett. 50, 631-633 (1983).
6. Kraus, K. Complementary observables and uncertainty relations. Phys. Rev. D 35, 3070-3075 (1987).
7. Maassen, H. & Uffink, J. B. Generalized entropic uncertainty relations. Phys. Rev. Lett. 60, 1103-1106 (1988).
8. Devetak, I. & Winter, A. Distillation of secret key and entanglement from quantum states. Proc. R. Soc. A 461, 207-235 (2005).
9. Horodecki, M., Horodecki, P. & Horodecki, R. Separability of mixed states: Necessary and sufficient conditions. Phys. Lett. A 223, 1-8 (1996).
10. Terhal, B. M. Bell inequalities and the separability criterion. Phys. Lett. A 271, 319-326 (2000).
11. Lewenstein, M., Kraus, B., Cirac, J. I. & Horodecki, P. Optimization of entanglement witnesses. Phys. Rev. A 62, 1-16 (2000).
12. Gühne, O. & Tóth, G. Entanglement detection. Phys. Rep. 747, 1-75 (2009).
13. Wiesner, S. Conjugate coding. Sigact News 15, 78-88 (1983).
14. Bennett, C. H. & Brassard, G. in Proc. IEEE Int. Conf. on Computers, Systems and Signal Processing, Bangalore, India 175-179 (IEEE, 1984).
15. Deutsch, D. et al. Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys. Rev. Lett. 77, 2818-2821 (1996).
16. Lo, H-K. & Chau, H. F. Unconditional security of quantum key distribution over arbitrarily long distances. Science 283, 2050-2056 (1999).
17. Shor, P. W. & Preskill, J. Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 85, 441-444 (2000).
18. Christandl, M., Renner, R. & Ekert, A. A generic security proof for quantum key distribution. Preprint at http://arxiv.org/abs/quant-ph/0402131 (2004).
19. Renner, R. & König, R. Universally composable privacy amplification against quantum adversaries. Theory of Cryptography Conference, TCC 2005 407-425 1).
20. Renner, R. Security of quantum key distribution. Int. J. Quantum Inform. 6, 1-127 (2008).
21. Koashi, M. Unconditional security of quantum key distribution and the uncertainty principle. J. Phys. Conf. Ser. 36, 98-102 (2006).
22. Ekert, A. Quantum cryptography based on Bell's theorem. Phys. Rev. Lett. 67, 661-663 (1991).
23. Renes, J. M. & Boileau, J-C. Conjectured strong complementary information tradeoff. Phys. Rev. Lett. 103, 020402 (2009).
24. Christandl, M., König, R. & Renner, R. Postselection technique for quantum channels with applications to quantum cryptography. Phys. Rev. Lett. 102, 020504 (2009).
25. Renner, R. & Scarani, V. Quantum cryptography with finite resources: Unconditional security bound for discrete-variable protocols with one-way postprocessing. Phys. Rev. Lett. 100, 200501 (2008).
26. Chandran, N., Fehr, S., Gelles, R., Goyal, V. & Ostrovsky, R. Position-based quantum cryptography. Preprint at http://arxiv.org/abs/1005.1750 (2010).
27. DiVincenzo, D. P., Horodecki, M., Leung, D. W., Smolin, J. A. & Terhal, B. M. Locking classical correlations in quantum states. Phys. Rev. Lett. 92, 067902 (2004).
28. Christandl, M. & Winter, A. Uncertainty, monogamy and locking of quantum correlations. IEEE Trans. Inf. Theory 51, 3159-3165 (2005).
29. König, R., Renner, R. & Schaffner, C. The operational meaning of min-and max-entropy. IEEE Trans. Inf. Theory 55, 4337-4347 (2009).
30. Tomamichel, M., Colbeck, R. & Renner, R. A fully quantum asymptotic equipartition property. IEEE Trans. Inf. Theory 55, 5840-5847 (2009).