Coherent-pulse implementations of quantum cryptography protocols resistant to photon-number-splitting attacks

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 69, Issue 1, 2004, Pages 16-

  Acín, Antonio ^a   Gisin, Nicolas ^a   Scarani, Valerio ^a  

^a UNIVERSITY OF GENEVA   (Switzerland)

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EID: 84894238003     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.69.012309     Document Type: Article

References (38)

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22. We take (Formula presented) for all the figures in this paper.
23. We believe that Eve must necessarily have access to Bob’s lab in order to modify his detectors. In contrary to this, one might think that Eve is able to shift the signals she wants to be detected into a wavelength region of higher detector efficiency. But this can be simply avoided by putting a narrow filter before the detector. Or, she can send pulses with large mean photon number whenever she wants the pulse to be detected, but this produces a significant increase of the double counts when Bob chooses the wrong measurement.
24. In all of the article, we take as the computational basis, |0〉 and |1〉, the eigenvectors of (Formula presented) with eigenvalues ±1.
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36. After completition of this work, the optimal (Formula presented) phase covariant cloning machine was found in G. M. D’Ariano and C. Macchiavello, quant-ph/0301175. There, the optimal fidelity is shown to be equal to (Formula presented) slightly larger than the one given in Appendix D of the present paper, (Formula presented)
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38. There may be other generalizations of the initial four-state protocol. For instance, for (Formula presented) one can consider a bit encoding different from the one in Fig. 88. The bit (Formula presented) can be associated to the states |0〉, |π/4〉, |π〉, |5π/4〉, where (Formula presented) and (Formula presented) to the other four states. In the sifting process, Alice always announces two states having an overlap of (Formula presented) as in the initial four-state protocol. In this way, (i) the discrimination on Bob’s side is more robust against imperfect measurement apparatus and (ii) the probability of accepting a bit is greater, (Formula presented) and then (Formula presented) only increases linearly with (Formula presented) Since the mean photon number does not need to be very large for having the same key rate generation, the number of multiphoton pulses at a given distance is smaller, and the protocol is more secure against PNS attacks using unambiguous discrimination. However, when one considers storing attacks, the protocol is not efficient. Indeed, Eve can always keep some photons (Formula presented) without being detected and wait for Alice’s announcement. Then, she has to distinguish between (Formula presented) copies of two states with overlap (Formula presented) While (Formula presented) increases with the number of bases, the overlap is independent of (Formula presented) Therefore, to increase (Formula presented) does not provide any advantage to the honest parties when they use this alternative encoding.