[17] R. Schwonnek, D. Reeb, and R. F. Werner.
Measurement uncertainty for finite quantum ob-
servables. Mathematics, 4(2):38, 2016. DOI:
10.3390/math4020038. arXiv:1604.00382.
[18] J. M. Renes, V. B. Scholz, and S. Huber. Un-
certainty relations: An operational approach
to the error-disturbance tradeoff. Quantum,
1(20), 2016. DOI: 10.22331/q-2017-07-25-20.
arXiv:1612.02051.
[19] A. A. Abbott and C. Branciard. Noise
and disturbance of qubit measurements: An
information-theoretic characterization. Phys.
Rev. A, 94:062110, 2016. DOI: 10.1103/Phys-
RevA.94.062110. arXiv:1607.00261.
[20] A. Barchielli, M. Gregoratti, and A. Toigo. Mea-
surement uncertainty relations for discrete ob-
servables: Relative entropy formulation. Comm.
Math. Phys., (357):1253–1304, 2016. DOI:
10.1007/s00220-017-3075-7. arXiv:1608.01986.
[21] H. Maassen and J. B. M. Uffink. Generalized
entropic uncertainty relations. Phys. Rev. Lett.,
60:1103–1106, 1988. DOI: 10.1103/Phys-
RevLett.60.1103.
[22] R. F. Werner. Quantum states with einstein-
podolsky-rosen correlations admitting a hidden-
variable model. Phy. Rev. A, 40(8):4277, 1989.
DOI: 10.1103/PhysRevA.40.4277.
[23] S. Friedland, V. Gheorghiu, and G. Gour.
Universal uncertainty relations. Phys. Rev.
Lett., 111(23):230401, 2013. DOI: 10.1103/Phys-
RevLett.111.230401. arXiv:1304.6351.
[24] A. Einstein, B. Podolsky, and N. Rosen. Can
quantum-mechanical description of physical re-
ality be considered complete? Phys. Rev., 47
(10):777, 1935. DOI: 10.1103/PhysRev.47.777.
[25] E. Schrödinger. Die gegenwärtige Situation in
der Quantenmechanik. Naturwiss., 23(48):807–
812, 1935. DOI: 10.1007/BF01491891.
[26] H.M. Wiseman, S. J. Jones, and A. C. Doherty.
Steering, entanglement, nonlocality, and the
Einstein-Podolsky-Rosen paradox. Phys. Rev.
Lett., 98(14):140402, 2007. DOI: 10.1103/Phys-
RevLett.98.140402. arXiv:quant-ph/ 0612147.
[27] G. Sharma, C. Mukhopadhyay, S. Sazim, and
A.K. Pati. Quantum uncertainty relation based
on the mean deviation. and arXiv:1801.00994.
[28] D. Deutsch. Uncertainty in quantum measure-
ments. Phys. Rev. Lett., 50:631–633, 1983. DOI:
10.1103/PhysRevLett.50.631.
[29] C. E. Shannon. A mathematical theory of com-
munication. The Bell System Technical Jour-
nal, 27(3):379–423, 1948. DOI: 10.1002/j.1538-
7305.1948.tb01338.x.
[30] A.N. Kolmogorov. On tables of random num-
bers. Theoretical Computer Science, 207(2):387–
395, 1998. DOI: 10.1016/S0304-3975(98)00075-9.
[31] Hmolpedia. The Neumann-Shannon anec-
dote. http://www.eoht.info/page/
Neumann-Shannon+anecdote.
[32] M. Tribus and E. C. Mc Irvine. Energy and in-
formation. Sc. Am., 224:178–184, 1971. DOI:
10.1038/scientificamerican0971-179.
[33] F. Rozpędek, J. Kaniewski, P. J. Coles, and
S. Wehner. Quantum preparation uncertainty
and lack of information. New Journal of
Physics, 19(2):023038, 2016. DOI: 10.1088/1367-
2630/aa5d64. arXiv:1606.05565.
[34] K. Abdelkhalek, R. Schwonnek, H. Maassen,
F. Furrer, J. Duhme, P. Raynal, B.G.
Englert, and R.F. Werner. Optimality
of entropic uncertainty relations. Int. J.
Quant. Inf., 13(06):1550045, 2015. DOI:
10.1142/S0219749915500458. arXiv:1509.00398.
[35] H. Hadwiger. Minkowskische Addition und Sub-
traktion beliebiger Punktmengen und die The-
oreme von Erhard Schmidt. Math.Z., 53(3):
210–218, 1950.
[36] H. F. Hofmann and S. Takeuchi. Violation of lo-
cal uncertainty relations as a signature of entan-
glement. Phys.Rev. A., 68:032103, 2003. DOI:
10.1103/PhysRevA.68.032103. arXiv:quant-
ph/0212090.
[37] O. Gühne. Detecting quantum entanglement: en-
tanglement witnesses and uncertainty relations.
PhD thesis, Universität Hannover, 2004. URL
http://d-nb.info/972550216.
[38] B. Lücke, J. Peise, G. Vitagliano, J. Arlt, L. San-
tos, G. Tóth, and C. Klempt. Detecting multi-
particle entanglement of Dicke states. Phys. Rev.
Lett., 112:155304, 2014. DOI: 10.1103/Phys-
RevLett.112.155304. arXiv:1403.4542.
[39] O. Gühne and G. Tóth. Entanglement detection.
Phys. Rep., 474(1–6):1 – 75, 2009. ISSN 0370-
1573. DOI: 10.1016/j.physrep.2009.02.004.
[40] O. Gühne and A. Costa. Private communication,
2017.
[41] I. Białynicki-Birula and J. Mycielski. Un-
certainty relations for information entropy in
wave mechanics. Communications in Mathe-
matical Physics, 44(2):129–132, 1975. DOI:
10.1007/BF01608825.
[42] W. Beckner. Inequalities in Fourier analysis. An-
nals of Mathematics, pages 159–182, 1975. DOI:
10.2307/1970980.
[43] I. I. Hirschman. A note on entropy. American
Journal of Mathematics, 79(1):152–156, 1957.
DOI: 10.2307/1970980.
[44] H. Maassen. The discrete entropic uncertainty
relation. Talk given in Leyden University. Slides
of a later version available from the author’s web-
site, 2007.
[45] H. Maassen. Discrete entropic uncertainty rela-
tion. Springer, 1990. DOI: 10.1007/BFb0085519.
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