Davide Rusca

We experimentally tested an alternative fiber-based setup for 4D-QKD, with time and phase encoding and one-decoy technique. We evaluated the secret key rate achievable in a finite-key scenario and we compared it with the binary-encoded BB84 protocol, which was tested with the same experimental setup. Our 4D-QKD system makes it possible to improve the secret key rate by more than a factor 2 in the saturation-regime of single-photon detectors, without requiring additional expensive resources to the 2D-QKD setup. In comparison to previous works, our scheme allows to measure the 4D states with a simplified and compact receiver, thus making it a cost-effective solution for practical and fiber-based QKD.

**merged with** Thomas Van Himbeeck and Stefano Pironio. Correlations and Randomness Generation based on an Energy Constraint In a previous paper, we introduced a semi-device-independent scheme consisting of an untrusted source sending quantum states to an untrusted measuring device, with the sole assumption that the average energy of the states emitted by the source is bounded. Given this energy constraint, we showed that certain correlations between the source and the measuring device can only occur if the outcomes of the measurement are non-deterministic, i.e., these correlations certify the presence of randomness. In the present paper, we go further and show how to quantify the randomness as a function of the correlations and prove the soundness of a QRNG protocol exploiting this relation. For this purpose, we introduce (1) a semidefinite characterization of the set of quantum correlations, (2) an algorithm to lower-bound the Shannon entropy as a function of the correlations and (3) a proof of soundness using finite trials compatible with our energy assumption.

In recent years, quantum key distribution (QKD) has transitioned from a purely academic field to a commercially available cryptographic solution, supported by mathematically formulated security proofs. However, due to the fragmented nature of the literature, obtaining a comprehensive understanding of these proofs and their limitations remains a considerable challenge. Our work addresses this by providing a rigorous finite-size security proof for the 1-decoy and 2-decoy BB84 protocols against coherent attacks, based on Renner's entropic uncertainty relation (EUR) framework. We resolve key technical issues in previous analyses, including the treatment of fixed-length protocols and acceptance testing. Special attention is given to the 1-decoy protocol, where statistics are computed after error correction, leading to important subtleties when applying the entropic uncertainty relation. By unifying and refining results from the literature, our work contributes to a more robust and accessible understanding of QKD security.

Bandwidth-limited devices in the transmitter of fast QKD implementations cause pulse correlations that leak information about previous setting choices. To take them into account in the existing security proofs, a measure of their strengths is needed. This is experimentally challenging, especially for long-range correlations, which are not experimentally accessible. In this work, we propose a new characterization method that exploits a linear model of the modulation devices. We show that this model predicts an upper bound for arbitrary order correlations that makes their characterization possible. We also present experimental results using the proposed method. In doing so, we can retrieve security even in the presence of arbitrary long correlations, with similar performance to classical security proofs.

Quantum key distribution (QKD) has raised as an attractive alternative to classical cryptography due to its security being provided by quantum mechanics rather than relying on algorithms that could potentially be broken in the future, rendering current communications insecure. However, many of the security proofs rely on assumptions that may not agree with reality, for instance, device imperfections can open loopholes that could potentially be exploited by a malicious party in order to extract part, if not all, of the secret key.

Quantum key distribution (QKD) protocols leverage quantum mechanics to achieve information theoretically secure communication, yet real-world implementations must address experimental limitations, particularly phase correlations in weak coherent laser pulses (WCPs). High-speed gain-switching lasers, commonly used in QKD, can exhibit residual photons causing phase correlations between consecutive pulses, challenging the perfect phase randomization assumption crucial for the decoy-state BB84 protocol. Theoretical work has proposed security proofs that require knowledge of how closely each phase's probability distribution approximates uniformity, which is complex to estimate experimentally. In this study we introduce an experimental method to characterise phase correlations of any length under realistic conditions by modelling the phase generation process within the laser cavity. Additionally, we experimentally benchmark this practical routine for measuring second-order correlations using a double Michelson interferometer with tunable amplitude attenuators, allowing comprehensive characterisation of the phase generation process and accurate measurement of the phase probability distribution, thus enhancing the security of QKD systems.

With the maturity of Quantum Technologies, namely Quantum Key Distribution (QKD) and Quantum Random Number Generation (QRNG), there has been mounting interest in scalable and inexpensive solutions for both academia and industry. To address the practicality and security requirements for QRNGs, we are developing a self-testing QRNG system based on homodyne detection with a fully integrated optical set-up. We use an Indium Phosphide (InP) photonic integrated circuit (PIC) with a high-speed 2.5GHz phase modulation that was designed and developed in collaboration with HHI Fraunhofer. All optical components are integrated in a 12×10 mm2 chip. It is then glued to a PCB designed in-house with electrical connections to the chip for full control and read-out of the results of the homodyne measurements. Another PCB, also designed in-house, is used to interface between the PIC and a field-programmable gate array (FPGA), which determines the quantum states to be prepared and reads out the homodyne detection. A graphics processing unit (GPU) connected to the FPGA then performs the statistical analysis of the data. The system operates at 1.25GHz and extraction rates above 18% are expected.

Quantum random number generators (QRNGs) have obtained notable attention and undergone substantial development, driven by their utility across diverse fields including simulations, gambling, and cryptography. This surge in interest stems from their unique capacity to deliver inherent randomness, which can only be derived from the probabilistic nature of quantum mechanics. The key challenge lies in validating the quantum origin of the randomness produced, which usually requires either a thorough characterization of the elements in the setup or very experimentally challenging loophole-free bell tests. In this work, we present a simple, self-testing and cost-effective quantum random number generator (QRNG) designed to operate with an untrusted measurement device and a partially characterized source, yielding a high rate of random bits. We consider a prepare-and-measure scenario where the preparation device takes a binary input x and a binary output b is received from the measurement device. Depending on the input, the preparation device sends either a weak coherent state (x=1) or a vacuum state (x=0). The measurement device employs homodyne detection to distinguish between these states, and the output value is chosen when the detector current is below (b=0) or above (b=1) a certain threshold. In order to certify the quantum origin of the randomness generated by output b, we need to track the correlations between input and output and the average energy per pulse must respect an upper bound. By using a continuous wave laser to seed the pulsed laser that generates the states, we avoid the need for expensive electro-optical modulators as used in https://arxiv.org/abs/2004.08307. With this scheme we achieve an extraction rate of certified quantum randomness of around 625kHz.

In this work we are designing and building an entangled photon pair source based on spontaneous parametric down-conversion. The source is highly non-degenerate to accommodate transmission in both fiber and free space. This source is intended for use in QKD applications. To achieve this, we explain and characterize the dependence on the temperature, poling period, phase matching, temporal walk-off, beam waist and the expected performance of this source.

Typical security proofs of quantum key distribution (QKD) require that the emitted signals are independent and identically distributed. In practice, however, this assumption is not met because intrinsic device flaws inevitably introduce correlations between the emitted signals. Although analyses addressing this issue have been recently proposed, they only consider a restrictive scenario in which the correlations have a finite and known maximum length that is much smaller than the total number of emitted signals. While it is expected that the magnitude of the correlations decreases as the pulse separation increases, the assumption that this magnitude is exactly zero after a certain point does not seem to have any physical justification. Concerningly, this means that existing analyses cannot guarantee the security of current QKD implementations. Here, we solve this pressing problem by developing a general framework that can handle pulse correlations of unbounded length. Our framework allows us to directly use existing proofs addressing this imperfection without the need to construct them from scratch, thus reestablishing the security of QKD in a simple and versatile manner.

Quantum key distribution (QKD) is at the verge of becoming a commercially viable security solution, backed by mathematically formulated security proofs. In the last two decades, much effort has been devoted to closing the gap between the models and practical implementations in order to account for device imperfections and counter the resulting side-channel attacks. As a result, the topic of evaluating and certifying QKD systems against these attacks is increasingly coming to the forefront. This last step however presents its own challenges, currently hindering the widespread adoption of QKD. In this work, we lay at the intersection between theory and practice, focusing on the process of preparing an in-house QKD system for evaluation. We first present a consolidated and accessible security proof for the one-decoy and two-decoy state BB84 protocols, which serves as a baseline for our QKD system. Building on this security proof, we identify the critical side-channels by evaluating the risk of most of today's known attacks. We then tackle the most critical attacks by discussing existing countermeasures that can be implemented both in the QKD system and within the security proof, where applicable. In this process, we develop new methods to characterize and evaluate QKD systems, which can later be used in evaluation laboratories. Evaluating the security of QKD systems additionally involves performing attacks to potentially identify new loopholes. Thus, we also aim to perform the first real-time Trojan horse attack on a decoy state BB84 system, further highlighting the need for robust countermeasures. By providing a critical evaluation of our QKD system and incorporating robust countermeasures against side-channel attacks, our research contributes to advancing the practical implementation and evaluation of QKD as a trusted security solution.

Decoy-state quantum key distribution (QKD) represents nowadays the best countermeasure to attacks exploiting multi-photon emissions in realistic sources. A fundamental requirement is the uniform and independent distribution of phases of the transmitted pulses. However, this can not be true for lasers working under high-speed gain-switching conditions, as residual photons in the cavity can induce phase correlations across consecutive pulses. A security proof robust against such imperfections has been recently proposed, which requires knowledge of a parameter that quantifies how close the conditional distribution of each phase is to a uniform distribution. In this work we propose an experimental method to characterise this parameter in realistic setup conditions and we extend the application to the case of arbitrary length of correlations, aiming to enable experimental verification of the implementation security.

This research introduces a simplified variation of the time-based BB84 protocol, employing time-bin encoding and one decoy state. The proposed approach significantly simplifies the security analysis, enabling the identification of potential vulnerabilities by avoiding interference in the transmission of specific state combinations. This simplification reduces the reliance on finite key analysis and allows us to better characterize the source imperfections without much compromise on the secret key rate (SKR).

The ideal Quantum random number generator (QRNG) is a black box which allows the users to test the quantum nature of the generated numbers. Producing a device which is close to this ideal is very demanding and will yield a low rate of random bits. Here we propose a simple setup which is self-testing on the detection part, meaning that only the source has to be characterized. We expect the implementation of this device to yield a random bit rate of around 10 Mpbs.

We investigate a class of partially device-independent quantum key distribution protocols based on a prepare-and-measure setup which simplifies their implementation. The security of the protocols is based on the assumption that Alice’s prepared states have limited overlaps, but no explicit bound on the Hilbert space dimension is required. The protocols are therefore immune to attacks on Bob’s device, such as blinding attacks. The users can establish a secret key while continuously monitoring the correct functioning of their devices through observed statistics. We report a proof- of-principle demonstration, involving mostly off-the-shelf equipment, as well as a high-efficiency superconducting nanowire detector. A positive key rate is demonstrated over a 4.8km low-loss optical fiber with finite-key analysis. The prospects of implementing these protocols over longer distances is discussed.

We study information theoretical security for space links between a satellite and a ground-station. Quantum key distribution (QKD) is a well established method for information theoretical secure communication, giving the eavesdropper unlimited access to the channel and technological resources only limited by the laws of quantum physics. But QKD for space links is extremely challenging, the achieved key rates are extremely low, and day-time operating impossible. However, eavesdropping on a channel in free-space without being noticed seems complicated, given the constraints imposed by orbital mechanics. If we also exclude eavesdropper's presence in a given area around the emitter and receiver, we can guarantee that he has only access to a fraction of the optical signal. In this setting, quantum keyless private (direct) communication based on the wiretap channel model is a valid alternative to provide information theoretical security. Like for QKD, we assume the legitimate users to be limited by state-of-the-art technology, while the potential eavesdropper is only limited by physical laws: either by specifying her detection strategy (Helstrom detector) or by bounding her knowledge, assuming the most powerful strategy through the Holevo information. Nevertheless, we demonstrate information theoretical secure communication rates (positive keyless private capacity) over a classical-quantum wiretap channel using on-o -keying of coherent states. We present numerical results for a setting equivalent to the recent experiments with the Micius satellite and compare them to the fundamental limit for the secret key rate of QKD. We obtain much higher rates compared with QKD with exclusion area of less than 13 meters for Low Earth Orbit (LEO) satellites. Moreover, we show that the wiretap channel quantum keyless privacy is much less sensitive to noise and signal dynamics and daytime operation is possible.

We implement 5 GHz clocked polarization-based simplified BB84 protocol. Secret keys can be distributed over 151.5 km of standard telecom fiber at a rate of 54.5 kbps. The high clock frequency might give rise to correlations between the pulses. We characterize the correlations in decoy intensity, polarization and in the phase between the pulses and discuss their impact on the security of the protocol.