Chapter 5
Quantum Key Distribution with
Imperfect Devices
Abstract In this Chapter we outline some of the experimental flaws that allow a
potential eavesdropper to successfully breach the security of a QKD protocol. We
then focus on the solutions to such problems, which are given by a combination of
theoretical advances and clever experimental design. In particular, in Sects. 5.1 and
5.2 we discuss how security can be proven when the BB84 protocol is implemented
with weak coherent pulses instead of single-photon sources, with a particular mention to the decoy-state method. We then introduce measurement-device-independent
(MDI) QKD in Sect. 5.3 and consider a practical implementation of it in Sect. 5.4.
The information-theoretic security, which is in principle promised by QKD, is undermined by the difficulty of ensuring that the assumptions on its implementation (quantum sources and/or measurement devices) are met in practice.
5.1 BB84 with Weak Coherent Pulses
The majority of the sources used in QKD experiments are highly attenuated lasers
producing weak coherent pulses (WCPs). WCPs are well represented by coherent
states:
|α = e
−|α| 2
2
∞
n=0
α
n
√
n!
|n,
(5.1)
where |n is called a Fock state and represents n identical photons, while |α|
2 is the
intensity of the pulse and represents the average number of photons in the pulse.
Indeed, the probability of finding n photons in the coherent state (5.1) follows a
Poisson distribution and is given by:
Pr(n) = |n|α|
2
= e
−|α|
2 |α|
2n
n!
.
(5.2)
© 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_5
71
Quantum Key Distribution with
Imperfect Devices
Abstract In this Chapter we outline some of the experimental flaws that allow a
potential eavesdropper to successfully breach the security of a QKD protocol. We
then focus on the solutions to such problems, which are given by a combination of
theoretical advances and clever experimental design. In particular, in Sects. 5.1 and
5.2 we discuss how security can be proven when the BB84 protocol is implemented
with weak coherent pulses instead of single-photon sources, with a particular mention to the decoy-state method. We then introduce measurement-device-independent
(MDI) QKD in Sect. 5.3 and consider a practical implementation of it in Sect. 5.4.
The information-theoretic security, which is in principle promised by QKD, is undermined by the difficulty of ensuring that the assumptions on its implementation (quantum sources and/or measurement devices) are met in practice.
5.1 BB84 with Weak Coherent Pulses
The majority of the sources used in QKD experiments are highly attenuated lasers
producing weak coherent pulses (WCPs). WCPs are well represented by coherent
states:
|α = e
−|α| 2
2
∞
n=0
α
n
√
n!
|n,
(5.1)
where |n is called a Fock state and represents n identical photons, while |α|
2 is the
intensity of the pulse and represents the average number of photons in the pulse.
Indeed, the probability of finding n photons in the coherent state (5.1) follows a
Poisson distribution and is given by:
Pr(n) = |n|α|
2
= e
−|α|
2 |α|
2n
n!
.
(5.2)
© 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_5
71