Giuseppe Vallone

Quantum Random Number Generators (QRNGs) exploit intrinsic probabilistic quantum processes to generate true random numbers. This tutorial reviews the experimental methods and theoretical tools necessary for generating and certifying random numbers using quantum systems. We explore various QRNG implementations, discuss their advantages and limitations, and examine the protocols used to verify the randomness and security of the generated numbers.

A wide range of applications require, by hypothesis, to have access to a private and genuine random source. Quantum Random Number Generators (QRNGs) are currently the sole technology capable of producing true randomness. Nevertheless, other factors must be considered when addressing real-world use cases, and the bulkiness of current implementations significantly limits their adoption. In this work, we present a high-performance source-device independent QRNG leveraging a custom-made integrated silicon photonic chip. The proposed scheme exploits the properties of a heterodyne receiver to enhance security and integration to promote spatial footprint reduction while simplifying its implementation. Such characteristics could represent a significant advancement toward the development of generators better suited to meet the demands of portable and space applications. Indeed, the system can deliver secure random numbers at a rate greater than 20 Gbps with a reduced encumbrance.

We propose Qubit4Sync, a synchronization method for Quantum Key Distribution (QKD) setups, based on the same qubits exchanged during the protocol and without requiring additional hardware other than the one necessary to prepare and measure the quantum states, in a similar fashion to the clock recovery used in classical communications. Our approach introduces a new cross-correlation algorithm achieving the lowest computational complexity, to our knowledge, for high channel losses. We tested the robustness of our scheme in a real QKD implementation, and we believe it may find application in other quantum communication protocols

Random numbers are a fundamental ingredient in fields such as simulation, modeling, and cryptography. Good random numbers should be independent and uniformly distributed. Moreover, for cryptographic applications, they should also be unpredictable. A fundamental feature of quantum theory is that certain measurement outcomes are intrinsically random and unpredictable. These can be harnessed to provide unconditionally secure random numbers. We demonstrate a real-time self-testing source-independent quantum random-number generator (SI QRNG) that uses squeezed light as a source. We generate secure random numbers by measuring the quadratures of the electromagnetic field without making any assumptions about the source other than an energy bound; only the detection device is trusted. We use homodyne detection to measure alternately the Q and P conjugate quadratures of our source. P measurements allow us to estimate a bound on any classical or quantum side information that a malicious eavesdropper may obtain. This bound gives the minimum number of secure bits we can extract from the Q measurement. We discuss the performance of different estimators for this bound. We operate this QRNG with a squeezed-state source and compare its performance with a thermal-state source. This is a demonstration of a QRNG using a squeezed state, as well as an implementation of real-time quadrature switching for a SI QRNG.

Here we present a simple and robust polarization encoded QKD experiment where synchronization, polarization compensation and QKD are all performed with the same optical setup, without requiring any changes or any additional hardware, by exploiting only the transmission of quantum states. Furthermore, the developed polarization encoder exhibits high stability and the lowest intrinsic Quantum Bit Error Rate ever reported.

Space-based quantum key distribution would allow, in the near future, secure communications be- tween parties over continental distances, complementing short-range fiber-based quantum networks. However, further demonstrations of daylight operations over free-space channels and the full compatibility with the telecom-based fiber infrastructure are still necessary. Here we present the prototype for daylight QKD at 1550 nm we developed as a demonstrator for application of QKD both on ground and in Space. Our QKD source, exploiting integrated silicon photonics technology, allows to reach a QBER of 1% during the field-test performed over a 145 m link, and represents a promising resource to design quantum optical payloads to be implemented in future satellite missions.

We present a versatile hybrid encoder for quantum key distribution that supports both discrete variable (DV) and continuous variable (CV) protocols. The encoder, based on an iPOGNAC modulator, utilizes commercial off-the-shelf components and can be reconfigured for efficient polarization modulation in DV protocols or polarization-independent phase modulation in CV protocols. This innovative design enhances flexibility, enabling the selection of the most efficient protocol based on link parameters. We experimentally realized the proposed device and tested it with both DV and CV receivers to demonstrate its performance.

The successful application of Quantum Key Distribution is dependent on the accurate generation and detection of quantum states, and a communication mechanism that can withstand disturbances caused in the channel. The selection of the optimal encoding strategy is complex and is influenced by external elements such as the characteristics of the quantum channel. Polarization encoding is acknowledged for its dependability and low error rate, rendering it ideal for free-space links, whereas time-bin encoding is robust to birefringence, thereby making it suitable for optical fiber networks. The strength of polarization-based protocols is based on the full characterization of the receiver, to reconstruct the information encoded in the shared qubits. This is typically achieved through tomographic analysis, which adds to the complexity of the final protocol. In this research, we introduce a unique cross-encoded method, where high precision quantum states are produced using a self-regulating, calibration-free polarization modulator and then conveyed through a polarization-to-time-bin converter. A hybrid receiver is used to carry out both time-of-arrival and polarization measurements for decoding the quantum states. Moreover, the suggested receiver is optimized to perform a self-characterization process, utilizing the same photons in which the information is encoded. The adaptability of our approach can lead to a significant advancement in the creation of hybrid networks that incorporate both optical fiber and free-space networks.

Intermodal quantum key distribution enables the integration of fiber networks and free-space channels, essential components for developing a global quantum network. We conducted a field trial of an intermodal quantum key distribution system, featuring two polarization-based transmitters and a single receiver. In this trial, the active channel was alternately switched between a 620-meter free-space link and a 17-kilometer deployed fiber in the metropolitan area of Padova. The free-space channel's performance was assessed in relation to atmospheric turbulence strength. The field trial, conducted over several hours in daylight, demonstrated the intermodal functionality between fiber and free-space channels. Our switching system offers a cost-effective solution for a trusted quantum key distribution network, minimizing the number of necessary devices across different network topologies.

Over the last decades, Quantum Key Distribution (QKD) has risen as a promising solution for secure communications, a pressing subject in the aftermath of the security threat posed by Quantum Computers and the Shor's Algorithm. Offering a theoretically secure way to share secret keys between parties, QKD state of the art has witnessed remarkable progress in the last years. Nonetheless, although theoretically secure, QKD is not implementation-secure and until now, the study of physical vulnerabilities in QKD setups has mainly focused on the optical channel. The concept of attacking a cryptographic system via its physical characteristics and associated leakages, known as side-channel analysis, was firstly introduced in classical cryptography, with the seminal work of Paul Kosher. Since then, power and electromagnetic side-channel analysis have become a staple in classical cryptanalysis. However, these concepts have hardly been applied to QKD. In this work, we propose and implement a new method for side-channel analysis on QKD systems, by exploiting the power consumption of the electronic driver controlling the electro-optical components of the QKD transmitter. For high-rate transmission, QKD modules typically require electronic drivers, such as Field Programmable Gate Arrays (FPGAs). Here, we will show that the FPGA's power consumption can leak information about the QKD operation, and consequently the transmitted key. The analysis was performed on the QKD transmitter at the University of Padua. Our results are consistent and show critical information leakage, having reached a maximum accuracy of 73.35% in the prediction of transmitted random keys at 100 MHz repetition frequency.

Quantum correlations between measurements of two or more separated observers play a fundamental role in many applications, such as randomness generation or key distribution. Although security can be certified from correlations with minimal assumptions in the device-independent scenario, the performance of such protocols is currently limited. This limitation motivates the exploration of sequential measurements, that is, defined with precise temporal ordering, as a means of improving performance through the reuse of the quantum states. To date, the study of sequential quantum protocols has been modest, lacking a comprehensive mathematical framework to explore the properties of the obtainable correlations. In this study, we adopt a geometric perspective to investigate sequential quantum correlations, providing a general mathematical framework. Here, we analytically prove a Tsirelson-like boundary for sequential quantum correlations, expressed as a trade-off between the amount of nonlocality shared by each sequential user. This boundary is particularly beneficial for the generation of secure quantum randomness. Indeed, observing a correlation on it can certify the maximum attainable bits per state in the case of one remote party and two sequential parties. In contrast to all previous schemes, this can happen even if one of the sequential users does not share any nonlocality. We demonstrate that this quantum boundary can be reached with a simple qubit protocol and investigate numerically the robustness of randomness generation under realistic noise conditions, finding that it greatly improved compared to previous proposals. Our proof-of-concept photonic implementation of the protocol confirms experimentally that our approach certifies more bits per state compared to the standard Clauser-Horne-Shimony-Holt scenario for the same noise, affirming both feasibility and robustness. This study marks a significant advance in understanding sequential quantum correlations, offering valuable insights and new mathematical tools for further fundamental studies and practical applications of efficient device-independent protocols.

Entanglement is a unique and invaluable resource for quantum information processing because it highlights the non-locality property, which allows for device-independent (DI) quantum communication protocols, such as Quantum Key Distribution and Quantum Random Number Generation. However, the distribution of entanglement over long distances is challenging due to propagation losses and instability. Time-bin entanglement is a promising solution since it is robust in long-distance distribution over fiber optics and immune to the polarization distortion such a channel can introduce. Time-bin has also been demonstrated to be compatible with NV center-based quantum technologies, representing a crucial interface between the different devices in quantum networks. Nevertheless, its most common implementation suffers from a post-selection loophole (PSL), which invalidates Bell non-locality tests and renders it vulnerable to quantum hacking attacks, thus preventing its use for device-independent protocols. We present a scheme using optical switches to obtain only detection events displaying non-local interference, thereby closing the PSL. Our scheme works with 1550nm biphotons for entanglement distribution over existing fiber-based telecom networks. The switches show a high extinction ratio of up to 30dB and stability over extended periods. We also measure interferometric visibilities of over 94%, which corresponds to a CHSH S parameter of 2.65

For quantum communication applications, time-to-digital converters (TDCs) are a crucial tool whose performance can severely affect the quality of the entire application. Nowadays, FPGA-based TDCs present a viable alternative to ASIC ones, once the nonlinear behaviour due to the intrinsic nature of the device is properly mitigated. To compensate said nonlinearities, a calibration procedure is required. Maintaining this calibration consistent during long measurements requires either interpolation methods or stopping data acquisition for a fixed time to perform the calibration process. Here we present a design and demonstration of an FPGA-based TDC showing a residual jitter of 27 ps, that is scalable for multichannel operation. We present a unique calibration method that exploits single-photon detection, which does not require stopping the data acquisition or using any interpolation methods, while keeping the device calibrated to the best of its ability. This allows Bob to receive time-tags with the best possible accuracy while also removing data-loss phases. This calibration method was tested in a relevant environment, investigating the device behaviour between 5 °C and 80 °C, where the residual jitter of the TDC was shown to be kept under control.

We propose the MacZac, a time-bin encoder with ultra-low intrinsic QBER (<2e-5) and high stability. The device is based on nested Sagnac and Mach–Zehnder interferometers and uses a single phase modulator for both decoy and state preparation, greatly simplifying the optical setup. The encoder does not require any active compensation or feedback system and it can be scaled for the generation of states with arbitrary dimension. We realized and tested the device performances as a stand alone component and in a complete QKD experiment.

Semi-device independent (Semi-DI) quantum random number generators (QRNG) gained attention for security applications, offering an excellent trade-off between security and generation rate. This paper presents a proof-of-principle time-bin encoding semi-DI QRNG experiments based on a prepare-and-measure scheme. The protocol requires two simple assumptions and a measurable condition: an upper-bound on the prepared pulses' energy. We lower-bound the conditional min-entropy from the energy-bound and the input-output correlation, determining the amount of genuine randomness that can be certified. Moreover, we present a generalized optimization problem for bounding the min-entropy in the case of multiple input and outcomes, in the form of a semidefinite program (SDP). The protocol is tested with a simple experimental setup, capable of realizing two configurations for the ternary time-bin encoding scheme. The experimental setup is easy-to-implement and comprises commercially available off-the-shelf (COTS) components at the telecom wavelength, granting a secure and certifiable entropy source. The combination of ease-of-implementation, scalability, high security level and output-entropy, make our system a promising candidate for commercial QRNGs.

We describe a QKD field trial running on urban fibers deployed in Padua, Italy. This is the first validation outside of the laboratory environment of a new low-error and calibration-free polarization encoder, called iPOGNAC, which we also present here. Our system is resource- and cost-effective, and can be installed quickly in an existing fiber network.

The 18-month project called PROtocols for Space sEcure Quantum cOmmunication (PROSEQO), funded by the European Space Agency, was coordinated by the University of Padova with Sitael and Qascom as industrial partners. The scope of the project was to assess the protocols feasible for Satellite QKD and then realize an analytical model to describe all the elements that contribute to the Secret Key Rate (SKR). The analytical model was integrated in a dedicated software able to get several input parameters and orbit descriptions and calculate the final SKR. The software was tested in 10 different case studies. Therefore, this can be a useful tool for future Satellite QKD missions as a preliminary step to evaluate mission feasibility. It could also be the starting point for a numerical overview on the practicability of a satellite QKD infrastructure.

Randomness is a fundamental feature of quantum mechanics, which is an invaluable resource for both classical and quantum technologies. Practical quantum random number generators (QRNG) usually need to trust their devices, but their security can be jeopardized in case of imperfections or malicious external actions. In this work, we present a robust implementation of a Semi-Device-Independent QRNG that guarantees both security and fast generation rates. The system works in a prepare and measure scenario where measurement and source are untrusted, but a bound on the energy of the prepared states is assumed. Our implementation exploits heterodyne detection, which offers increased generation rate and improved long-term stability compared to alternative measurement strategies. In particular, due to the tomographic properties of heterodyne measurement, we can compensate for fast phase fluctuations via post-processing, avoiding complex active phase stabilization systems. As a result, our scheme combines high security and speed with a simple setup featuring only commercial-off-the-shelf components, making it an attractive solution in many practical scenarios.

We present two different QRNG devices which allow to maximize the entropy extraction of a system and so the generation rate. The two devices use single-photon avalanche diode along (SPAD) with FPGA device. The first device, Randy, uses only one SPAD and with a post-processing based on the Peres algorithm [Y. Peres, Ann. Statist. 20, 590 (1992)], has a generation rate of 1.8 Mbit/s. The second device, LinoSPAD, which is a CMOS SPAD array based device and integrate also a time-to-digital converter (TDC) on its FPGA, has a final generation rate of 310 Mbit/s thanks to a improved post-processing procedure which also includes the Zhou-Bruck algorithm [H. Zhou and J. Bruck, arXiv:1209.0726 (2012)].

In practical Quantum Key Distribution, there exist scenarios where the number of exchanged qubits is limited by physical constraints. A notable case is that of satellite QKD, where channel losses and visibility play a major role in limiting the efficiency and the availability of the quantum link. With this perspective in mind, the need for evaluating finite-key effects on the secret key rate is urgent. In this work, we experimentally evaluate, in a realistic setup and with different channel conditions, the robustness of a recent finite-key tight theoretical bound that ensures secrecy against the most general quantum attacks. We compare the experimental results obtained by this bound with the ones achieved with a new finite-key bound tailored for ensuring secrecy against individual attacks. We then show, the minimum number of raw bits to be exchanged in order to obtain a given secret key length, for different values of the QBER. This provides a valuable tool for practical QKD, as it allows to know in advance, depending on the channel noise, how may bits have to be exchanged for obtaining the desired secret key length. The results indicate that viable conditions for effective symmetric, and even one-time-pad, cryptography are achievable.