Nuno A. Silva

Random prime number generation is crucial for the implementation of several encryption and signature protocols in cryptographic applications. Recently, Quantum Random Number Generators (QRNGs) have emerged as a solution to obtain information-theoretically secure randomness, setting them apart from algorithmic generators. Nonetheless, their output is still prone to deterioration under a flawed implementation and thus requires continuous statistical validation. This process is uniquely challenging for prime number generators since they cannot be submitted to the traditional testing suites, which are primarily designed to test uniform pseudorandom sources. Here, we enable direct statistical testing of prime Random Number Generators (RNGs) by extending a validation framework based on an equiprobable binning of the prime distribution with a predictive machine learning model, which can independently learn correlations in the prime output. The validity of this framework is then verified through extensive cryptanalysis of a prime QRNG based on quadrature measurements of the vacuum state. The developed model successfully identifies flawed configurations of the prime QRNG for output lengths up to 128 bits. This assessment was additionally extended to a purely classical scheme derived from electronic noise measurements. Although no increase in the model’s predictive capacity is seen, our testing framework can nonetheless demonstrate that this classical source produces a conclusively biased prime distribution. In turn, the implemented QRNG remains resilient against this type of cryptanalysis.

The ability to efficiently align the transmitter and receiver of a polarization-based Quantum Key Distribution (QKD) system at initialization and during the exchange of qubits is critical for its correct operation, otherwise resulting in a reduction of the secret key rate. We address this issue by implementing a deterministic polarization compensation method based on the reversal operator of polarization variations. The working principle of this reversal operator is based on Quantum Bit Error Rate (QBER) measurements and their mapping on the Poincaré sphere, enabling fast tracking and compensation of polarization misalignments. Our experimental implementation demonstrates that this method allows for an accurate alignment of the polarization coding and measurement basis using only three QBER measurements. The results confirm that the reversal operator method is exceptionally time-efficient when compared to the widely used compensation methods, such as gradient-based algorithms, requiring at least 5× fewer QBER measurements.

Secure data transmission is essential in today's world, and quantum key distribution (QKD) is widely recognized as the technology of choice to enable information-theoretical secure symmetric key generation. While optical fibers are typically used as a transmission channel, wireless transmission offers the flexibility to reach every part of the Earth; moreover, for Earth-Satellite QKD, wireless communication naturally becomes a necessity. In this study, we deployed a fiber-wireless optical system that transmitted a 64-QAM 400 Gbps classical signal for high-rate data exchange and a 1 MHz quantum signal for QKD. The impact of turbulence in the quantum system is evaluated by transmitting single-polarization quantum states through a turbulent free-space channel and by calculating the respective intrinsic quantum bit error rate (QBER). From this, we estimate the system's secret key rate (SKR) and its dependence on turbulence. The effects of atmospheric turbulence on the optical wireless signal were emulated and investigated by using a custom-made atmospheric chamber to induce different turbulent scenarios. The atmospheric chamber allowed us to vary the turbulence in a Rytov variance range from 0.06 to 2.52. The classical signal showed an overall average reliability of 82% for the mentioned turbulence regimes. The results of the quantum signal showed that for Rytov variances up to 1.3, and under the conditions tested, secret key generation is possible, reaching a maximum SKR of 8.7$\mathbf {\times 10^{-4}}$ bits per pulse during the produced turbulence regimes.

We demonstrate a polarization diversity conjugate homodyne detection scheme for DV-QKD, that does not require complex high computational demanding post-processing or single-photon detection. Unlike CV-QKD based on coherent detection, this work presents the advantage for saving computational resources highly-demanded by sophisticated carrier phase and frequency recovery schemes. A complete physical model of the DV-QKD system is assessed under a finite-key size analysis of the BB84 with 1 decoy state protocol and phase randomization between consecutive pulses. We show that, for practical post-processing block sizes of 108 bits, the system is able for key generation up to a secrete key fraction of 4% obtained after a post-selection stage to obtain discrete outcomes. Also, we demonstrate experimentally the decoding of quantum polarization states can be achieved with a inherent QBER lower than 1%.

Continuous variable quantum key distribution (CV-QKD) allows the distribution of symmetric keys in a secure manner. CV-QKD systems can extract keys at its maximum rate when using Gaussian modulation (GM). Nonetheless, GM demands high-capacity random number sources and tends to be very hard to approach in practice. To circumvent these disadvantages, higher-order probabilistic -shaped discrete modulation (DM) can be used. State-of-the-art works compute the key rates of DM-CV-QKD systems considering a fixed value for the reconciliation efficiency and do not take into account the frame error rate (FER) of the system, thus over or under estimating the key rates. In this work, we study the security bounds of CV-QKD systems considering probabilistic shaped DM formats with 256-symbols in the finite-size regime. This accounting for the true value of the reconciliation efficiency, and the FER of the information reconciliation step. Both conventional and hexagonal 256-quadrature amplitude modulation (QAM) constellations yield higher key rates than 256-amplitude and phase shift keying (APSK) constellations, with 256-QAM constellations being indistinguishable in performance with GM for high transmission distances. Minimum signal-to-noise ratio (SNR) values were fixed from a FER analysis through a CV-QKD simulation allowing for key extraction considering different FER levels. Lower FER values are associated with higher SNRs in the system and thus lower achievable transmission distances. Nonetheless, the FER maximizing the extraction key rate is not null. Our results show that the extraction key rate is maximized by SNR adjustment which should have in account both the reconciliation efficiency and the FER.

In this Letter we present a discrete modulated, continuous variables quantum key distribution implementation using two probabilistically shaped, 128-symbol, amplitude and phase shift keying constellations. At Bob’s detection side, a polarization diverse, true heterodyne receiver architecture is implemented for symbol recovery. We demonstrate experimentally that our system is capable of achieving security against collective attacks, while using accessible, telecom-grade material, and of functioning for an indefinitely long period of time at distances in excess of 185 km, in the asymptotic regime.