Ramona Wolf

Throughout history, cryptography has been caught in a vicious circle: Cryptographers keep inventing new methods to hide information, which in turn are broken by cryptanalysts, prompting cryptographers to devise even more sophisticated encryption methods, and so on. Quantum key distribution offers a way to break this circle by enabling information-theoretic secure encryption based (almost) solely on the laws of physics. Nonetheless, caution is still advised: Even these protocols can only break the vicious circle if they come with a complete security proof against all possible attacks. In this tutorial, I will introduce the principles underlying modern security proofs for QKD, including the assumptions on which they rely, discuss key techniques such as finite-key analysis, and survey recent advances to highlight both progress and remaining challenges.

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.

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.

Device-independent quantum key distribution (DIQKD) is the art of using untrusted devices to distribute secret keys in an unsecure network. It thus represents the ultimate form of cryptography, offering not only information-theoretic security against channel attacks, but also against attacks exploiting implementation loopholes~\cite{lydersen2010hacking}. At its heart, DIQKD utilises nonlocal correlations---detected and certified by a Bell inequality---to establish secret correlations between the users. In recent years, much progress has been made towards realising the first DIQKD experiments, but current proposals are just out of reach of today’s loophole-free Bell experiments. Here, in this work, we close the gap between the theory and practice of DIQKD with a simple variant of the original protocol based on the celebrated Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. In using two randomly chosen key generating bases instead of one, we show that the noise tolerance of DIQKD can be significantly improved. In particular, the extended feasibility region now covers some of the most recent loophole-free CHSH experiments, hence indicating that the first realisation of DIQKD already lies within the range of these experiments.

In this QCRYPT submission, we present a numerical toolbox that is capable of producing non-trivial lower bounds on the asymptotic secret key rate of any device-independent quantum key distribution (DIQKD) protocol. The main mechanism of our toolbox is a new method for estimating the entropy production of a quantum channel, giving rise to bounds that can be computed using the family of semidefinite programs (SDPs) known as the Navascues-Pironio-Acin (NPA) hierarchy.

Standard quantum information theory (QIT) quantifies correlations and independence using joint quantum states of physical systems. However, this formalism becomes insufficient when modelling randomness, since this requires talking about correlations between spacetime regions, which generally do not admit a well-defined quantum state description. Here, we show why modelling randomness therefore requires going beyond the standard QIT framework. We introduce a formalism that explicitly incorporates spacetime structure by representing global information in a "panorama" Hilbert space and associating spacetime regions with representations obtained through extraction maps. This allows correlations and independence to be defined even when the corresponding spacetime regions cannot be jointly described by a quantum state. Our approach provides a conceptual and mathematical basis for analysing randomness generation and other cryptographic tasks whose security fundamentally depends on spacetime structure.

One of the main challenges in device-independent quantum key distribution (DIQKD) is achieving the required Bell violation over long distances, as the channel losses result in low overall detection efficiencies. Recent works have explored the concept of certifying nonlocal correlations over extended distances through the use of a local Bell test. Here, an additional quantum device is placed in close proximity to one party, using short-distance correlations to verify nonlocal behavior at long distances. However, existing works have either not resolved the question of DIQKD security against active attackers in this setup, or used methods that do not yield tight bounds on the keyrates. In this work, we introduce a general formulation of the key rate computation task in this setup that can be combined with recently developed methods for analyzing standard DIQKD. Using this method, we show that if the short-distance devices exhibit sufficiently high detection efficiencies, positive key rates can be achieved in the long-distance branch with lower detection efficiencies as compared to standard DIQKD setups. This highlights the potential for improved performance of DIQKD over extended distances in scenarios where short-distance correlations are leveraged to validate quantum correlations.