**Lisbon-Düsseldorf Quantum Cryptography workshop **

**Date**: Wednesday, December 06, 2023

**Time**: 10:00 – 13:00

**Place**: seminar room 25.32.03.51

**This short**** workshop ****aims to present an**** overview of the research ****conducted**** in Düsseldorf and Lisbon ****in the area of quantum cryptography. Please contact **

**if you**

**would like to attend the workshop**

**or**

**if you are interested in a streaming option.**

**Schedule:**

10:00 – 10:25 Federico Grasselli (Düsseldorf/Paris)

10:25 – 10:50 Mariano Lemus (Lisbon)

10:50 – 11:15 Giacomo Carrara (Düsseldorf)

11:15 – 11:45 Coffee break

11:45 – 12:10 Chrysoula Vlachou (Lisbon)

12:10 – 12:35 Anton Trushechkin (Düsseldorf)

12:35 – 13:00 Nikola Paunkovic (Lisbon)

**Abstracts**

**Federico Grasselli**

**Title: Security proof for BB84-style QKD protocols without assumption of equal detection probabilities**

A crucial security parameter in BB84-style QKD protocols is the so-called phase error rate. Most security proofs and relative implementations can easily estimate the phase error rate by assuming that the detection probability in the two measuring bases of Bob is equal, for any input state. In this case, the phase error rate reduces to the bit error rate that Alice and Bob observe in the test basis (i.e., the complementary basis to the key generation basis). However, there are certain QKD setups where the assumption on the equal detection probability is not justified experimentally. Our work aims at deriving a fully-analytical security proof for BB84-style QKD protocols, where the main challenge is estimating the phase error rate without relying on the assumption of equal detection probabilities.

**Mariano Lemus**

**Title: Computationally Secure Oblivious Transfer in the Quantum Setting: Results from the QuantumPrime project.**

Motivated by the usefulness of secure multiparty computation as a privacy-protecting data analysis tool, and identifying its oblivious transfer as one of its main practical enablers, we propose a practical realization of quantum oblivious transfer, which uses cryptographic hash functions to implement commitments. The security of the resulting oblivious transfer is analyzed and compared to both quantum and classical alternatives. Furthermore, the protocol is implemented experimentally to measure its current real-world performance. The proposed version is shown to offer security advantages over existing classical solutions based on public key cryptography primitives in exchange for lower key generation rates. We will also explore potential of additional advantages that the protocol can provide that are subject to further exploring.

**Giacomo Carrara**

**Title: Multipartite randomness extraction with almost unentangled states**

Bell inequalities represent a fundamental tool for many quantum information tasks. In particular, past research has shown that the certification of the violation of a Bell inequalities allows the parties to extract perfectly random outcomes, which cannot be guessed by potential eavesdroppers. Moreover, the power of Bell inequalities has been shown in [Phys. Rev. Lett., 108, 100402 (2012)], where the authors show that the parties can extract perfect randomness even if the violation of the Bell inequality is achieved by a state which can be arbitrarily close to a separable state. In this work, we try to extend this result to the multipartite scenario. In particular, we analyze the amount of randomness that can be extracted from an multipartite Bell inequality, which is maximally violated by a state arbitrarily close to a fully separable multipartite state. In order to achieve this result, we aim to employ both standard numerical convex optimization and newly developed analytical methods, to obtain a better bound on the randomness extraction rate.

**Chrysoula Vlachou**

**Title: Quantum Universally Composable Oblivious Linear Evaluation**

Oblivious linear evaluation is a cryptographic primitive whereby two distrustful parties obliviously compute a linear function, f(x) = ax + b, i.e., each one provides their inputs that remain unknown to the other, in order to compute the output f(x) that only one of them receives. From both a structural and a security point of view, oblivious linear evaluation is fundamental for arithmetic-based secure multi-party computation protocols. In the classical case, oblivious linear evaluation protocols can be generated using oblivious transfer, and their quantum counterparts can, in principle, be constructed as straightforward extensions using quantum oblivious transfer. Here, we present the first, to the best of our knowledge, quantum protocol for oblivious linear evaluation that, furthermore, does not rely on quantum oblivious transfer. Our protocol uses high-dimensional quantum states to obliviously compute f(x) on Galois Fields of prime and prime-power dimension. Our construction utilizes the existence of a complete set of mutually unbiased bases in prime-power dimension Hilbert spaces and their linear behaviour upon the Heisenberg-Weyl operators. We prove the protocols to have static security in the framework of quantum universal composability.

**Anton Trushechkin**

**Title: Problem of symmetric postprocessing in quantum conference key agreement**

In the present-day quantum conference key agreement one party ('Alice') has a distinguished role: her bit string after finishing the quantum part and sifting is considered to be corrected, while discrepancies with the bit strings of are treated as errors on their sides. Alice announces information (e.g., error correction syndrome) for other parties in order to allow them to recover her string. Recently, F. Salek and A. Winter proposed to use the symmetric postprocessing, where each participant announces information that is enough for all other parties to recover his bit string. Then they merge their strings as a preliminary key and perform privacy amplification to it to obtain a final key. However, the question of which scheme (with the distinguished Alice or symmetric) is more efficient is open. This question will be discussed in the talk.

**Nikola Paunkovic**

**Title: Quantum information at SQIG-IT — cryptography, prime number generation and causality**

I will present part of the research in our group (SQIG-IT – Security and Quantum Information Group at Instituto de Telecomunicações) related to quantum information, in particular the results in cryptography developed within the QuantumPrime project. I will also present a measurement that distinguishes between definite and superposed causal orders and how to achieve quantum-mechanical closed timelike curves in the presence of the latter. Finally, I will briefly mention other interdisciplinary works on the gauge-protected gravity-matter entanglement, violation of the weak equivalence principle in the presence of superposed gravitational fields, operational emergence and verification of spacetime manifold, as well as applications of quantum information geometry to the study of phase transitions.