Chapter 7
Device-Independent Quantum
Cryptography
Bell’s theorem, formulated in 1964, is one of the profound
scientific discoveries of the century. Alain Aspect
Abstract The Chapter is organized as follows. In Sect. 7.1 we introduce the concept of non-local correlations and show how they can be witnessed through a Bell
inequality violation. We formalize the definitions of different kinds of correlations in
Sect. 7.2. In Sect. 7.3 we link the observation of a Bell violation to the security proof
of device-independent (DI) protocols. In Sect. 7.4 we describe the bipartite DIQKD
protocol based on the Clauser-Horne-Shimony-Holt (CHSH) inequality and prove
its security in Sect. 7.5. In Sect. 7.6 we generalize the security proof technique to
a whole class of multiparty DI protocols. We conclude by discussing the suitability of full-correlator Bell inequalities for DICKA and present a multipartite Bell
inequality specifically built for the task of DICKA (Sect. 7.7). In the Appendix of
this Chapter (Sects. 7.8 and 7.9) we provide additional details on the security proof
of the CHSH-based DIQKD protocol.
We have already seen in Chaps. 5 and 6 how imperfections in the quantum devices
employed in a QKD protocol, when not accounted for in the security proof, can
be exploited by an eavesdropper to spoil the protocol’s security. In this context,
measurement-device-independent (MDI) QKD and twin-field (TF) QKD protocols
represent possible solutions as they do not require to trust the measurement devices,
which can be completely controlled by the eavesdropper, and yet allow to derive a
secret key. However, both MDI-QKD and TF-QKD still require to trust the sources
held by the parties.
In the previous Chapters we presented QKD protocols where at least some devices
in the experimental apparatus need to be trusted. Of course, we could place our trust
in such devices more lightheartedly upon deeply characterizing their functioning.
However, the characterization process is often challenging and we might not be
© 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_7
105
Device-Independent Quantum
Cryptography
Bell’s theorem, formulated in 1964, is one of the profound
scientific discoveries of the century. Alain Aspect
Abstract The Chapter is organized as follows. In Sect. 7.1 we introduce the concept of non-local correlations and show how they can be witnessed through a Bell
inequality violation. We formalize the definitions of different kinds of correlations in
Sect. 7.2. In Sect. 7.3 we link the observation of a Bell violation to the security proof
of device-independent (DI) protocols. In Sect. 7.4 we describe the bipartite DIQKD
protocol based on the Clauser-Horne-Shimony-Holt (CHSH) inequality and prove
its security in Sect. 7.5. In Sect. 7.6 we generalize the security proof technique to
a whole class of multiparty DI protocols. We conclude by discussing the suitability of full-correlator Bell inequalities for DICKA and present a multipartite Bell
inequality specifically built for the task of DICKA (Sect. 7.7). In the Appendix of
this Chapter (Sects. 7.8 and 7.9) we provide additional details on the security proof
of the CHSH-based DIQKD protocol.
We have already seen in Chaps. 5 and 6 how imperfections in the quantum devices
employed in a QKD protocol, when not accounted for in the security proof, can
be exploited by an eavesdropper to spoil the protocol’s security. In this context,
measurement-device-independent (MDI) QKD and twin-field (TF) QKD protocols
represent possible solutions as they do not require to trust the measurement devices,
which can be completely controlled by the eavesdropper, and yet allow to derive a
secret key. However, both MDI-QKD and TF-QKD still require to trust the sources
held by the parties.
In the previous Chapters we presented QKD protocols where at least some devices
in the experimental apparatus need to be trusted. Of course, we could place our trust
in such devices more lightheartedly upon deeply characterizing their functioning.
However, the characterization process is often challenging and we might not be
© 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_7
105