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For instance, any attempt by Eve to shift the wavelength of the signals into a region of a higher detection efficiency of Bob's detectors can be blocked by the use of a narrow frequency filter.
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For instance, any attempt by Eve to shift the wavelength of the signals into a region of a higher detection efficiency of Bob's detectors can be blocked by the use of a narrow frequency filter.
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In order to show that Eve can always phase lock her local oscillator to the coherent light source of Alice, note that she could employ, for instance, the following recursive method. First, she uses a beam splitter to extract a portion of light of several (say M) consecutive signal states emitted by Alice. Afterwards, she continues splitting N more times these M pulses that she has just extracted. As a result, she obtains N trains of M pulses each. These pulses maintain the same phase relationship as the original ones sent by Alice. Now, she measures out the first train of pulses by using the same detection apparatus as Bob. With some finite probability she can identify the relative phase of some pairs of consecutive pulses inside this train. Once this process ends, Eve discards, from the remaining N-1 trains of M signals, those pairs of pulses whose relative phase was not unambiguously determined on the first train. Finally, she combines the remaining pairs using a 50:50 beam splitter. This way, Eve can obtain N-1 new trains of pulses containing a smaller number of them. Most importantly, since Eve knows the relative phase of each pair of pulses that entered the beam splitter in the previous step, and as a result of this, she knows in which output port of it she has a pulse of coherent light. This means, in particular, that the amplitudes of these new coherent pulses contained in the new N-1 trains are also amplified. Eve repeats this procedure several times on these remaining N-1 trains of signals, i.e., she measures out the first of these trains by using again the same detection device as Bob, and then she follows the same steps described above. As a result, and assuming that M and N are large enough, Eve can obtain a very bright single pulse and she can measure its phase.
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This measurement strategy is very similar to the one considered in Ref.. Note, however, that it provides Eve with a higher success probability of unambiguously identifying a sequence of signal states. The reason for this is that in Ref. Eve first divides her data of measurement outcomes into different blocks of the same length and, afterwards, she analyzes each block of data independently, i.e., without considering the data included in adjacent blocks. Therefore, in this scenario it may happen that two consecutive blocks do not contain enough successful USD outcomes to consider their sequences of measurement results successful unless the data included in both blocks is jointly evaluated.
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This measurement strategy is very similar to the one considered in Ref.. Note, however, that it provides Eve with a higher success probability of unambiguously identifying a sequence of signal states. The reason for this is that in Ref. Eve first divides her data of measurement outcomes into different blocks of the same length and, afterwards, she analyzes each block of data independently, i.e., without considering the data included in adjacent blocks. Therefore, in this scenario it may happen that two consecutive blocks do not contain enough successful USD outcomes to consider their sequences of measurement results successful unless the data included in both blocks is jointly evaluated.
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Note that Bob can also obtain a click in temporal mode n=0 due to the time delay introduced by Bob's interferometer in one of its paths.
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Note that Bob can also obtain a click in temporal mode n=0 due to the time delay introduced by Bob's interferometer in one of its paths.
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Since in DPS QKD Bob does not monitor the coherence between states with different photon number, there is no difference for Eve whether she sends to Bob the signal states ρek given by Eq. 18, or she sends him the signal states | ψk = m=1 pm exp (i m) | ψkm , with | ψkm given by Eq. 19.
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Since in DPS QKD Bob does not monitor the coherence between states with different photon number, there is no difference for Eve whether she sends to Bob the signal states ρek given by Eq. 18, or she sends him the signal states | ψk = m=1 pm exp (i m) | ψkm, with | ψkm given by Eq. 19.
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In this section we shall use the parameter d defined as d = æ td fc æ instead of the parameter d employed in Sec. 4. The main motivation for this change of the notation is to try to avoid ambiguities when referring to the parameter d. In particular, since in the calibrated device scenario we impose d=0 for the blocks of signal states illustrated in Fig. 2.
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In this section we shall use the parameter d defined as d = æ td fc æ instead of the parameter d employed in Sec. 4. The main motivation for this change of the notation is to try to avoid ambiguities when referring to the parameter d. In particular, since in the calibrated device scenario we impose d=0 for the blocks of signal states illustrated in Fig. 2.
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In this extended version of the DPS QKD protocol Alice and Bob could as well employ the double click rate information that is measured in the experiment to try to discard those sequential attacks that highly decrease the value of the double click rate expected by the legitimate users. For instance, we have shown in Sec. 4 that the eavesdropping strategy employed by Eve for the case of uncalibrated devices produces a double click rate equal to 0. However, if we consider a real implementation of the protocol, then this last scenario is not so simple, since the double click rate expected by Alice and Bob due to the dark counts of the detectors is usually quite low.
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In this extended version of the DPS QKD protocol Alice and Bob could as well employ the double click rate information that is measured in the experiment to try to discard those sequential attacks that highly decrease the value of the double click rate expected by the legitimate users. For instance, we have shown in Sec. 4 that the eavesdropping strategy employed by Eve for the case of uncalibrated devices produces a double click rate equal to 0. However, if we consider a real implementation of the protocol, then this last scenario is not so simple, since the double click rate expected by Alice and Bob due to the dark counts of the detectors is usually quite low.
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In this section we consider that the parameter ηdet also includes the losses due to Bob's interferometer.
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In this section we consider that the parameter ηdet also includes the losses due to Bob's interferometer.
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Note that in this definition we treat double clicks as single click events.
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Note that in this definition we treat double clicks as single click events.
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