Cryptography Reference
In-Depth Information
[7] in 1992 and which uses only two nonorthogonal states prepared by Alice.
The receiver Bob cannot discriminate between these deterministically but he
can apply a generalized measurement using an ancillary system. This kind
of measurement, known as positive operator valued measurement (POVM
or POM), provides Bob with either a correct answer or with no answer, i.e.,
with an inconclusive result. Bob will get a bit string of 0's, 1's and ?'s, his 0's
and 1's being deterministic results perfectly correlated with those of Alice.
Discarding the events corresponding to his ?'s time slots via a public classical
channel, Alice and Bob can generate the shared key.
However, in this form the B92 protocol is not secure: eavesdropper Eve
could go for an intercept-resend strategy and perform on the intercepted bits
the same kind of measurements as Bob. She would then suppress the bits for
which she gets inconclusive results and resend only the ones she knows with
certainty. This loophole can be closed by sending a strong reference pulse
along with a faint signal pulse down the quantum channel. At the receiving
side, a weak part of the strong signal is split off and gives in interference
with the other weak signal the measurement results. In this scenario, Eve
can no longer remain unnoticed; in contrast to a weak signal with 0.1-0.4
photons per pulse, the strong reference part will give a macroscopic signal
on Bob's side and cannot be suppressed without being noticed. Whenever
the strong signal is present, at least the weak part that is split off from it
will enter Bob's remaining measurement device and leads there to a photo
detection event with some probability. This means that Eve cannot suppress
these events with certainty any more. Hence Eve is forced always to send
some signal with the strong pulse and will inevitably introduce errors.
As mentioned in the introduction, in 1995 Huttner et al. extended the
BB84 and B92 to the so-called 4
2 state protocol [8]. Basically it works with
the prepare and measure strategy of the BB84 protocol, but all four states are
nonorthogonal. In the QKD run, one of these four nonorthogonal coherent
states is polarization encoded using weak coherent pulses. The strong ref-
erence needed to support the security of the transmission is sent with the
same pulse using two orthogonally polarized modes, one for the signal and
the other for the reference. This setting is reminiscent of the Stokes operators
of Section 5.3: compare the picture “weak signal and strong reference pulse”
with the detection scheme of the Stokes operators (Figure 5.2). By a certain
change of the basis, one can represent any polarization state as a dark mode
containing information about the quantum polarization state and the mode
with a high photon number serving as a phase reference. To illustrate differ-
ences and similarities, it is worthwhile to visualize different protocols that use
polarization encoding on the Poincare sphere [2,8,25,30]. Notably, the signal
states of the 4
+
2 state, together with the respective reference pulses, form
on the Poincare sphere of Figure 5.3 exactly the same pattern as described
in the previous section if four slight modulations
+
(
+
δ
+
δ
)
(
+
δ
−
δ
)
S
2
,
S
3
,
S
2
,
S
3
,
(
−
δ
+
δ
)
(
−
δ
−
δ
)
are applied. Thus our protocol described be-
low can be easily reformulated in the established language of weak signal
and strong reference pulse, which is a useful tool in security considerations.
S
2
,
S
3
, and
S
2
,
S
3
