Security of differential phase shift QKD from relativistic principles
1Institute for Theoretical Physics, ETH Zürich, Wolfgang-Pauli-Str. 27, 8093 Zürich, Switzerland
2Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam, Germany
3Université Grenoble Alpes, Inria, 38000 Grenoble, France
4Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany
| Published: | 2025-01-27, volume 9, page 1611 |
| Editor: | Máté Farkas |
| Eprint: | arXiv:2301.11340v3 |
| Doi: | https://doi.org/10.22331/q-2025-01-27-1611 |
| Citation: | Quantum 9, 1611 (2025). |
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Abstract
The design of quantum protocols for secure key generation poses many challenges: On the one hand, they need to be practical concerning experimental realisations. On the other hand, their theoretical description must be simple enough to allow for a security proof against all possible attacks. Often, these two requirements are in conflict with each other, and the differential phase shift (DPS) QKD protocol exemplifies these difficulties: It is designed to be implementable with current optical telecommunication technology, which, for this protocol, comes at the cost that many standard security proof techniques do not apply to it. After about 20 years since its invention, this work presents the first full security proof of DPS QKD against general attacks, including finite-size effects. The proof combines techniques from quantum information theory, quantum optics, and relativity. We first give a security proof of a QKD protocol whose security stems from relativistic constraints. We then show that security of DPS QKD can be reduced to security of the relativistic protocol. In addition, we show that coherent attacks on the DPS protocol are, in fact, stronger than collective attacks. Our results have broad implications for the development of secure and reliable quantum communication technologies, as they shed light on the range of applicability of state-of-the-art security proof techniques.
Featured image: Overview of the differential phase shift QKD protocol. A phase modulator (PM) is used to apply a random phase $\phi \in \{0, \pi\}$ (represented by the shading in the diagram) to each pulse in a train of coherent states. Alice's key bit is determined by the relative phase $\Delta \phi$ between subsequent pulses. Bob obtains his key by measuring the relative phase using a Mach-Zehnder interferometer.
Popular summary
for sending secret messages, by guaranteeing unconditional security based only on the
laws of quantum physics. However, real-world devices often differ from their theoretical
descriptions, making practical QKD implementations vulnerable to attacks. Differential
phase shift (DPS) QKD is a widely studied protocol that is implementable with existing
technologies, but this comes at the cost of a more complicated theoretical description
which poses significant challenges to fully proving the security of DPS using standard
proof techniques. After more than two decades since its invention, our work achieves the
first full security proof of DPS QKD against general attacks, taking into account finite-size
statistics.
We achieve this by introducing an inter-disciplinary proof technique that integrates
methods from quantum information theory, quantum optics, quantum causality and
relativity. In particular, we overcome the obstacle posed by the infinite-dimensional
photonic Fock space involved in the description of the DPS protocol, by simplifying the
security analysis to a qubit space through quantum optics techniques. Relativistic causality
principles such as the impossibility of faster-than-light signaling play a crucial role in our
proof. Finally, we show that general attacks on the DPS protocol are stronger than attacks
that act independently and identically on each round. This highlights why proving security
for DPS is a challenging task.
Our work informs progress on bridging the gaps between theoretical and practical QKD,
paving the way for achieving full security proofs of a larger class of practically relevant
QKD protocols through the novel techniques introduced here.
► BibTeX data
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