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85015756627
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note
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2 pairs of single-qunit observables that Alice and Bob are using.
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15
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85015733084
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note
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Wootters and Fields [16] showed that sets of pairwise complementary observables [17] are ideal for tomographic purposes and, extending earlier work by Ivanović [18], they constructed such sets for the case that n is a prime or a power of a prime. These distinguished sets of tomographically complete observables are central to the generalizations [19-21] of the 1987 spin-retrodiction puzzle of Vaidman, Aharonov, and Albert [22], of which a quantum-optical version was realized recently [23].
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17
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85015720469
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note
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Any single pair of complementary observables is algebraically complete, and for any quantum degree of freedom one can find such pairs, with characteristic properties. See Ref. [24] for a textbook discussion of these insights of Weyl [25] and Schwinger [26].
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23
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25
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Gruppentheorie und Quantenmechanik Hirzel, Leipzig
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English translation Dutton, New York
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J. Schwinger, Proc. Natl. Acad. Sci. U.S.A. 46, 570 (1960); in Exact Sciences and Their Philosophical Foundations, edited by W. Deppert, K. Hübner, A. Oberschelp, and V. Weidemann (Verlag Peter Lang, Frankfurt am Main, 1985).
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28
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85015736692
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note
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0 = n/ (n - 1), but this ratio is outside range (4) of physical interest.
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29
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85015729673
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note
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More generally, one could consider coherent attacks in which Eve prepares entangled multiqunit-pair states rather than the single-qunit-pair state of Eq. (3). Alice and Bob would then notice correlations between different qunit pairs. We take for granted that they protect themselves by also looking for such correlations at the time when they exchange information for the primary purpose of state tomography.
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31
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85015736636
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e-print quant-ph/0110089
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Wang Xiang-bin, e-print quant-ph/0110089.
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Wang, X.-B.1
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36
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85015720439
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note
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2 states of kind (28) for each value of m.
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39
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85015795639
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note
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tot(A & E), and has no effect on their difference.
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40
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6144265213
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Entanglement distillation was originally proposed for qubits under the name of quantum privacy amplification
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Entanglement distillation was originally proposed for qubits under the name of quantum privacy amplification by D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, Phys. Rev. Lett. 77, 2818 (1996).
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Deutsch, D.1
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43
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85015803351
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e-print quant-ph/0303184
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D. Bruß, M. Christandl, A. Ekert, B.-G. Englert, D. Kaszlikowski, and C. Macchiavello, e-print quant-ph/0303184.
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Bruß, D.1
Christandl, M.2
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Englert, B.-G.4
Kaszlikowski, D.5
Macchiavello, C.6
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44
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85015736354
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e-print quant-ph/0206058
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P.W. Shor, e-print quant-ph/0206058.
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Shor, P.W.1
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45
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85015743506
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note
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d(D) to convert our notational conventions to those of Ref. [9].
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