UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)
UvA-DARE (Digital Academic Repository)
Cryptography in a quantum world
Wehner, S.D.C.Publication date 2008
Link to publication
Citation for published version (APA):
Wehner, S. D. C. (2008). Cryptography in a quantum world.
General rights
It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons).
Disclaimer/Complaints regulations
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.
List of Figures
1.1 Encrypted pottery glaze formula, Mesopotamia 1500 BC . . . 4
1.2 QKD today . . . 4
1.3 Schematic run of a BC protocol when Alice and Bob are honest. . 9
1.4 Schematic run of a 1-2 OT protocol. . . 13
2.1 Bloch vector (rx, ry, rz) = (cos ψ sin θ, sin ψ sin θ, cos θ) . . . . 34
2.2 Latin Square (LS) . . . 40
2.3 Mutually Orthogonal LS . . . 40
3.1 Using post-measurement information. . . 44
4.1 2n = 2-cube . . . 85
4.2 2n = 4-cube . . . 85
5.1 A locking protocol for 2 bases. . . 95
5.2 Measurement for |1, 1. . . 101
6.1 Alice and Bob measure many copies of |Ψ . . . 107
6.2 Multiplayer non-local games. . . 111
6.3 Original problem . . . 117
6.4 Derived problem . . . 117
7.1 Optimal vectors for n = 4 obtained numerically using Matlab. . . 128
8.1 Tradeoff for p = 0.6. . . . 137
8.2 Tradeoff for 2 outcomes. . . 138
9.1 A one-round XOR proof system. . . 143
10.1 Moving from a set of string with g(x) = y to a set of strings with g(x) = (y mod 5) + 1. . . 157
248 List of Figures
11.1 Bob performs a partial measurementPi, followed by noiseN , and
out-puts a guess bit xg depending on his classical measurement outcome,
the remaining quantum state, and the additional basis information. . . 175
11.2 h((1− ar)/2)/4 + log(1+r2 ) log(4/3)/2, where we only show the re-gion below 0, i.e., where security can be attained. . . 184
C.1 Two vectors . . . 206
C.2 a∧ b . . . 207
C.3 b∧ a . . . 207
C.4 Projections onto a vector . . . 208
C.5 Reflection of a around m . . . 209
C.6 Reflection of a plane perpendicular to m . . . 210
C.7 Hadamard transform as reflection . . . 210
C.8 Rotating in the plane m∧ n. . . 211
