Chapter 6
Beyond Point-to-Point Quantum Key
Distribution
Abstract In this chapter we present the recently-derived theoretical limits on
the secret key rate that can be extracted by any point-to-point QKD protocol
(Sect. 6.1). Subsequently, we present in detail the (arguably) simplest solution found
by researchers to overcome such limitations, which is twin-field (TF) QKD. TF-QKD
overcomes the point-to-point private capacity by exploiting single-photon interference in an intermediate untrusted station (Sects. 6.2 and 6.3). This is followed by a
detailed investigation of the performance of TF-QKD in realistic conditions, namely
finite number of decoy intensity settings and asymmetric channels (Sect. 6.4). Finally,
in Sect. 6.5 we generalize the founding idea of TF-QKD to a multiparty scenario by
describing a quantum conference key agreement (CKA) based on single-photon
interference events.
By definition, point-to-point QKD protocols are implemented with a single quantum channel which directly connects the two parties establishing the key, e.g., the
BB84 protocol introduced in Chap. 3.
6.1 Fundamental Limits of Point-to-Point QKD
The secret key rate of any QKD protocol is limited by the losses that inevitably occur
in the quantum channel(s) linking the end users. In most QKD implementations, the
information is encoded in one of the degrees of freedom of photons. The photons are
then transmitted over lossy quantum channels, whose transmittance η represents the
probability that a photon is successfully transmitted.
For instance, the optical attenuation in standard telecom fibres is about γ = 0.2
dB km
−1 , which leads to an overall loss of γ L over L kilometres of fibre. The
transmittance of an L-kilometre telecom fibre is thus given by: η = 10
−γ L/10 . This
shows that the probability of a photon being transmitted decreases exponentially with
the length of the channel, thus severely affecting the key rate.
The exact relation between the key rate and the channel transmittance depends on
the protocol. Nevertheless, researchers have recently derived fundamental bounds
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
F. Grasselli, Quantum Cryptography, Quantum Science and Technology,
https://doi.org/10.1007/978-3-030-64360-7_6
83
Beyond Point-to-Point Quantum Key
Distribution
Abstract In this chapter we present the recently-derived theoretical limits on
the secret key rate that can be extracted by any point-to-point QKD protocol
(Sect. 6.1). Subsequently, we present in detail the (arguably) simplest solution found
by researchers to overcome such limitations, which is twin-field (TF) QKD. TF-QKD
overcomes the point-to-point private capacity by exploiting single-photon interference in an intermediate untrusted station (Sects. 6.2 and 6.3). This is followed by a
detailed investigation of the performance of TF-QKD in realistic conditions, namely
finite number of decoy intensity settings and asymmetric channels (Sect. 6.4). Finally,
in Sect. 6.5 we generalize the founding idea of TF-QKD to a multiparty scenario by
describing a quantum conference key agreement (CKA) based on single-photon
interference events.
By definition, point-to-point QKD protocols are implemented with a single quantum channel which directly connects the two parties establishing the key, e.g., the
BB84 protocol introduced in Chap. 3.
6.1 Fundamental Limits of Point-to-Point QKD
The secret key rate of any QKD protocol is limited by the losses that inevitably occur
in the quantum channel(s) linking the end users. In most QKD implementations, the
information is encoded in one of the degrees of freedom of photons. The photons are
then transmitted over lossy quantum channels, whose transmittance η represents the
probability that a photon is successfully transmitted.
For instance, the optical attenuation in standard telecom fibres is about γ = 0.2
dB km
−1 , which leads to an overall loss of γ L over L kilometres of fibre. The
transmittance of an L-kilometre telecom fibre is thus given by: η = 10
−γ L/10 . This
shows that the probability of a photon being transmitted decreases exponentially with
the length of the channel, thus severely affecting the key rate.
The exact relation between the key rate and the channel transmittance depends on
the protocol. Nevertheless, researchers have recently derived fundamental bounds
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
F. Grasselli, Quantum Cryptography, Quantum Science and Technology,
https://doi.org/10.1007/978-3-030-64360-7_6
83