94
6 Beyond Point-to-Point Quantum Key Distribution
point QKD scheme, i.e. when the PLOB bound is surpassed. We emphasize that this
theoretical prediction has been recently confirmed experimentally [18–22].
6.4 Twin-Field QKD with Finite Decoys and Asymmetric
Channels
In the paper that introduced the TF-QKD protocol without phase post-selection [13],
the key rate performance is mainly investigated in the unrealistic scenario where
Alice and Bob can use an infinite number of decoy intensity settings.
In order to investigate the real performance of the proposed TF scheme, in [24] we
derive analytical bounds on several yields appearing in the upper bound (6.22) on the
error rate E Z , when the parties have at their disposal either two, three, or four decoy
intensity settings each. These are the most relevant cases from an experimental point
of view. Since to every pair of decoy intensities corresponds a linear constraint on the
yields (see (6.23)), increasing the number of decoy intensities enables us to bound
a larger number of yields and more tightly. In the limit of infinitely many decoy
intensity settings, the parties can correctly estimate all the infinite yields appearing
in (6.22). Moreover, the larger the number of yields with an analytical bound, the
smaller the number of yields trivially bounded by one in (6.22). This has the obvious
effect of increasing the protocol’s key rate.
Furthermore, the yields bounds enable a closed analytical expression of the secret
key rate, which is particularly useful when optimizing the protocol’s performance
over a large set of parameters, e.g., in the finite-key regime.
Equipped with the derived bounds on the yields, we show that two decoy settings
are enough to beat the PLOB bound (6.1) and that four decoy settings are close to
optimal, i.e. the resulting key rate is almost indistinguishable from that where Alice
and Bob have infinite decoy settings.
In the performance analysis conducted in [13] it is also assumed that the losses
affecting the quantum channels of Alice and Bob are equal and so are the optimal
signal and decoy intensities. However, this does not reflect realistic scenarios where
two parties establishing a secret key, e.g., in the context of a quantum network, are
likely to be at different distances from the untrusted relay which processes their
signals according to the TF-QKD protocol in [13]. Moreover, potential intensity
fluctuations affecting the parties’ lasers are likely to be uncorrelated, causing the
parties to effectively employ different signal and decoy intensities.
In order to address these issues, in [25] we investigate the performance of the
TF-QKD protocol of [13] in asymmetric-loss scenarios and in the presence of independent laser intensity fluctuations. To this aim, we derive new analytical bounds
on the relevant yields appearing in (6.22), when the parties use two independent
sets of decoy intensities ({μ i } and {ν j }). In particular, based on the results of [24],
we consider the cases of two, three and four decoy intensity settings for each party.
6 Beyond Point-to-Point Quantum Key Distribution
point QKD scheme, i.e. when the PLOB bound is surpassed. We emphasize that this
theoretical prediction has been recently confirmed experimentally [18–22].
6.4 Twin-Field QKD with Finite Decoys and Asymmetric
Channels
In the paper that introduced the TF-QKD protocol without phase post-selection [13],
the key rate performance is mainly investigated in the unrealistic scenario where
Alice and Bob can use an infinite number of decoy intensity settings.
In order to investigate the real performance of the proposed TF scheme, in [24] we
derive analytical bounds on several yields appearing in the upper bound (6.22) on the
error rate E Z , when the parties have at their disposal either two, three, or four decoy
intensity settings each. These are the most relevant cases from an experimental point
of view. Since to every pair of decoy intensities corresponds a linear constraint on the
yields (see (6.23)), increasing the number of decoy intensities enables us to bound
a larger number of yields and more tightly. In the limit of infinitely many decoy
intensity settings, the parties can correctly estimate all the infinite yields appearing
in (6.22). Moreover, the larger the number of yields with an analytical bound, the
smaller the number of yields trivially bounded by one in (6.22). This has the obvious
effect of increasing the protocol’s key rate.
Furthermore, the yields bounds enable a closed analytical expression of the secret
key rate, which is particularly useful when optimizing the protocol’s performance
over a large set of parameters, e.g., in the finite-key regime.
Equipped with the derived bounds on the yields, we show that two decoy settings
are enough to beat the PLOB bound (6.1) and that four decoy settings are close to
optimal, i.e. the resulting key rate is almost indistinguishable from that where Alice
and Bob have infinite decoy settings.
In the performance analysis conducted in [13] it is also assumed that the losses
affecting the quantum channels of Alice and Bob are equal and so are the optimal
signal and decoy intensities. However, this does not reflect realistic scenarios where
two parties establishing a secret key, e.g., in the context of a quantum network, are
likely to be at different distances from the untrusted relay which processes their
signals according to the TF-QKD protocol in [13]. Moreover, potential intensity
fluctuations affecting the parties’ lasers are likely to be uncorrelated, causing the
parties to effectively employ different signal and decoy intensities.
In order to address these issues, in [25] we investigate the performance of the
TF-QKD protocol of [13] in asymmetric-loss scenarios and in the presence of independent laser intensity fluctuations. To this aim, we derive new analytical bounds
on the relevant yields appearing in (6.22), when the parties use two independent
sets of decoy intensities ({μ i } and {ν j }). In particular, based on the results of [24],
we consider the cases of two, three and four decoy intensity settings for each party.