René Schwonnek

Many fundamental quantities in quantum information processing are instances of quantum divergences - functionals on quantum states that satisfy natural axioms grounded in information-theoretic principles. Recently, a new class of divergences - the f-divergences - has gained prominence in quantum information theory and received operational interpretations, while being long established in the classical setting. Furthermore, Frenkel showed that the Umegaki relative entropy is a special case of a quantum f-divergence for the function f(x) = x log x; building on this, Hirche et al. introduced a parameterized family of f-divergences that, in appropriate regimes, recovers the sandwiched and Petz relative entropies as regularizations. Taken together, these results reveal a tight link between the best-understood quantum divergences - the Umegaki, Petz, and sandwiched relative entropies - on a technical level and the general class of f-divergences, thereby strongly motivating a program that connects f-divergences to concrete quantum information tasks as already started by Cheng et al. In this contribution, we develop a variational formulation that approximates general quantum f-divergences to arbitrary precision. These approximations yield (i) efficient evaluation of the quantum relative entropy of channels and already used as the core numerical method in quantum many body physics and (ii) computation of asymptotic key rates in DIQKD in particular in the scenario of two switches in routed Bell scenarios.

The security of finite-length keys is essential for the implementation of device-independent quantum key distribution (DIQKD). Presently, there are several finite-size DIQKD security proofs, but they are mostly focused on standard DIQKD protocols and do not directly apply to the recent improved DIQKD protocols based on techniques such as noisy preprocessing and random key measurements. Here, we provide a general finite-size security proof that can simultaneously encompass these approaches, using tighter finite-size bounds than previous analyses. In doing so, we develop a method to compute tight lower bounds on the asymptotic keyrate for any such DIQKD protocol with binary inputs and outputs. With this, we show that positive asymptotic keyrates are achievable up to depolarizing noise values of 9.26%, exceeding all previously known noise thresholds. Furthermore, we also consider in greater detail a particular form of generalized CHSH inequality, and derive partial closed-form results for such cases. We discuss the potential advantage of this approach for realistic photonic implementations of DIQKD.

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.

We present a numerical framework for the reliable estimation of conditional von Neumann entropy in device-independent quantum cryptography and randomness extraction sceratios. By leveraging a hierarchy of semidefinite programs derived from the Navascués--Pironio--Acín (NPA) hierarchy, our method efficiently computes entropy bounds based solely on observed statistics, under the assumption that quantum mechanics holds true. Our approach is built on a recent integral representation presented by [Frenkel, Quantum 7, 1102 (2023)] and extends the landscape of methods for computing provable lower bounds on the conditional von Neumann entropy. Notably, it requires approximately half as many support variables compared to the Brown--Fawzi--Fawzi method, with the additional advantage that these variables can be chosen projectively. The method facilitates the derivation of provable bounds on extractable randomness even in noisy scenarios and aligns with modern entropy accumulation theorems. This makes our framework a versatile tool for practical quantum cryptographic protocols, broadening the possibilities for secure communication in untrusted environments.

Providing estimations and numerical approximations for expected rates of entanglement generation in quantum repeater protocols has been the focus of a lot of research to date. We contribute to this work by providing a set of analytical results for a large class of possible models, with respect to generalized anti-bunched photon emissions statistics of qubit sources. These allow us on the one hand to verify existing estimations and on the other hand to construct new lower bound estimations for the time-resolved execution of quantum repeater processes.

The QKD-setup under consideration is comprised of two initially independent squeezed continuous Gaussian states (squeezing 11 dB, anti-squeezing 16 dB) at 1550 nm which become entangled by a 50:50 beam splitter. F. Furrer et al presented a security analysis for the setting we explained above assuming collective and coherent attacks [PRL 109, 100502 (2012)]. We will especially discuss the subtleties of the key generation and propose a new error correction algorithm allowing for the generation of a coherent-attack-secure key in experiment.