2008

The operational meaning of min- and max-entropy

Koenig, Robert, Renner, Renato, Schaffner, Christian

Understand

We show that the conditional min-entropy Hmin(A|B) of a bipartite state rho_AB is directly related to the maximum achievable overlap with a maximally entangled state if only local actions on the B-part of rho_AB are allowed.

In the special case where A is classical, this overlap corresponds to the probability of guessing A given B.
In a similar vein, we connect the conditional max-entropy Hmax(A|B) to the maximum fidelity of rho_AB with a product state that is completely mixed on A.
In the case where A is classical, this corresponds to the security of A when used as a secret key in the presence of an adversary holding B.

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Similar

R. Renner and S. Wolf, “Smooth Rényi entropy and applications,” in Proc. International Symposium on Information Theory . IEEE, 2004, p. 233
2004
Cited alongside, same era.
R. Renner, “Security of quantum key distribution,” Ph.D. dissertation, ETH Zurich, 2005, arXiv.org:quant-ph/0512258
2005
Cited alongside, same era.
M. Horodecki, J. Oppenheim, and A. Winter, “Quantum state merging and negative information,” 2005, arXiv.org:quant-ph/0512247
2005
Cited alongside, same era.
R. Renner, S. Wolf, and J. Wullschleger, “The single-serving channel capacity,” in Proceedings of 2006 IEEE International Symposium on Information Theory , 2006, pp. 1424–1427
2006
Cited alongside, same era.
M. Christandl and R. Renner, “Guessing and min-entropy,” 2006, unpublished notes
2006
Cited alongside, same era.
H. Buhrman, M. Christandl, P. Hayden, H.-K. Lo, and S. Wehner, “Security of quantum bit string commitment depends on the information measure,” Phys. Rev. Lett. , vol. 97, no. 25, p. 250501, 2006
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Cited alongside, same era.
I. Devetak and J. Yard, “The operational meaning of quantum conditional information,” 2006, arXiv:quant-ph/0612050
2006
Cited alongside, same era.
R. König and R. Renner, “Sampling of min-entropy relative to quantum knowledge,” 2007, arXiv.org:0712.4291
2007
Cited alongside, same era.

Then

A. Winter and R. Renner, “Single-shot state merging,” 2007, unpublished note
2007
Later among the works it cites.
I. B. Damgård, S. Fehr, R. Renner, L. Salvail, and C. Schaffner, “A tight high-order entropic quantum uncertainty relation with applications,” in Advances in Cryptology—CRYPTO ’07 , ser. Lecture Notes in Computer Science, vol. 4622. Springer-Verlag, 2007, pp. 360–378
2007
Later among the works it cites.
N. Datta and R. Renner, “Smooth renyi entropies and the quantum information spectrum,” 2008, arXiv:0801.0282
Original
2008
Closest in time.
M. Tomamichel, R. Colbeck, and R. Renner, “A fully quantum asymptotic equipartition property,” 2008, arXiv:0811.1221
Original
2008
Closest in time.
M. Berta, “Single-shot quantum state merging,” Master’s thesis, ETH Zurich, 2008
2008
Closest in time.
M. Horodecki, S. Lloyd, and A. Winter, “Quantum coding theorem from privacy and distinguishability,” Open Systems and Information Dynamics , vol. 15, p. 47, 2008, arXiv.org:quant-ph/0702006
2008
Closest in time.
S. Wehner, C. Schaffner, and B. M. Terhal, “Cryptography from noisy storage,” Phys. Rev. Lett. , vol. 100, no. 22, p. 220502, 2008
2008
Closest in time.
C. Schaffner, B. Terhal, and S. Wehner, “Robust cryptography in the noisy-quantum-storage model,” 2008, arxiv.org:0807.1333
2008
Closest in time.

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