Contributed Talk 1c

Abstract: High-dimensional (HD) entanglement promises both enhanced key rates and overcoming obstacles faced by modern-day quantum communication. However, modern convex optimization-based security arguments are limited by computational constraints; thus, accessible dimensions are far exceeded by progress in HD photonics, bringing forth a need for efficient methods to compute key rates for large encoding dimensions. In response to this problem, we present a flexible analytic framework facilitated by the dual of a semi-definite program and diagonalizing operators inspired by entanglement-witness theory, enabling the efficient computation of key rates in high-dimensional systems. To facilitate the latter, we show how matrix completion techniques can be incorporated to effectively yield improved, computable bounds on the key rate in paradigmatic high-dimensional systems of time- or frequency-bin entangled photons and beyond, revealing the potential for very high dimensions to surpass low dimensional protocols already with existing technology. In our accompanying work, we show how our findings can be used to establish finite-size security against coherent attacks for general HD-QKD protocols both in the fixed- and variable-length scenario and we examine the performance under realistic conditions. Detailed manuscripts for Refs. [1] and [2] can be found attached.

Abstract: Random numbers are used in a wide range of sciences. In many applications, generating unpredictable private random numbers is indispensable. Device-independent quantum random number generation is a framework that makes use of the intrinsic randomness of quantum processes to generate numbers that are fundamentally unpredictable according to our current understanding of physics. While device-independent quantum random number generation is an exceptional theoretical feat, the difficulty of controlling quantum systems makes it challenging to carry out in practice. It is therefore desirable to harness the full power of the quantum degrees of freedom (the dimension) that one can control. It is known that no more than 2log(d) bits of private device-independent randomness can be extracted from a quantum system of local dimension d. In this paper we demonstrate that this bound can be achieved for all dimensions d by providing a family of explicit protocols. In order to obtain our result, we develop new certification techniques that can be of wider interest in device-independent applications for scenarios in which complete certification ('self-testing') is impossible or impractical. With our C*-algebra representation tools, we are able to device-independently certify non-projective measurements for the purpose of randomness generation. Our protocols use a class of measurements we call "balanced informationally complete" (BIC) POVMs, which we anticipate to be useful in scenarios where normally symmetric informationally complete (SIC) POVMs are useful. Moreover, we explicitly construct BIC-POVMs in every dimension, circumventing the problem with SIC-POVMs which are only conjectured to exist in every dimension.

Abstract: The degree of experimentally attainable nonlocality, as gauged by the loophole-free or effective violation of Bell inequalities, remains severely limited due to inefficient detectors. We address an experimentally motivated question: Which quantum strategies attain the maximal loophole-free nonlocality in the presence of inefficient detectors? For any Bell inequality and any specification of detection efficiencies, the optimal strategies are those that maximally violate a tilted version of the Bell inequality in ideal conditions. In the simplest scenario, we demonstrate that the quantum strategies that maximally violate the doubly-tilted versions of Clauser-Horne-Shimony-Holt inequality are unique up to local isometries. We utilize Jordan's lemma and Grobner basis-based proof technique to analytically derive self-testing statements for the entire family of doubly-tilted CHSH inequalities and numerically demonstrate their robustness. These results enable us to reveal the insufficiency of even high levels of the Navascues-Pironio-Acin hierarchy to saturate the maximum quantum violation of these inequalities.

Abstract: Computational entropy notions play a central role in classical cryptography, with well-developed frameworks for analyzing unpredictability, leakage resilience, and pseudo-randomness. In the quantum setting, however, computational analogues of entropy remain largely unexplored. While quantum information theory provides powerful tools based on information-theoretic entropy, these do not capture the limitations of computationally bounded quantum adversaries. In this work, we initiate the study of quantum computational entropy by defining \emph{quantum computational unpredictability entropy}, a natural generalization of classical unpredictability entropy to the quantum setting. Our definition is based on the operational meaning of quantum min-entropy, but restricts the adversary to efficient quantum guessing strategies. We prove that this entropy satisfies several important properties, including a leakage chain rule that holds even in the presence of prior quantum side-information. We also show that unpredictability entropy supports pseudo-randomness extraction against quantum adversaries with bounded computational power. Together, these results lay a foundation for developing cryptographic tools that rely on min-entropy in the quantum computational setting.

Abstract: We develop a flexible and robust framework for finite-size security proofs of quantum key distribution (QKD) protocols under coherent attacks, applicable to both fixed- and variable-length protocols. Our methods achieve high finite-size key rates across a broad class of protocols while imposing minimal requirements. In particular, it eliminates the need for restrictive assumptions such as limited repetition rates or the implementation of virtual tomography procedures. To achieve this goal, we introduce new numerical techniques for the evaluation of conditional sandwiched Renyi entropies, enabling tight key rate bounds without compromising generality. In doing so, we find an alternative formulation of the ``QKD cone'' studied in previous work, which may be of independent interest. Moreover, we illustrate the versatility of our framework by applying it to several practically relevant protocols, including decoy-state protocols. Furthermore, we extend the analysis to accommodate realistic device imperfections, such as independent intensity and phase imperfections. Overall, our framework provides both greater scope of applicability and better key rates than existing techniques, especially for small block sizes, offering a scalable path toward secure quantum communication under realistic conditions.