In polarization-encoding free-space Quantum Key Distribution (QKD), unwanted variations in the states of polarization may cause errors, leading to an increase in the quantum bit error rate (QBER), and a reduction of the Secure Key Rate (SKR). Optical elements that reflect or transmit the quantum signal at the transmitter and/or receiver are the main cause of polarization variations in the quantum states. Although most of these optical elements affect polarization in a constant manner, requiring relatively simple compensation techniques, mobile elements such as steering mirrors, cause time-varying polarization variations that are more complex to characterize and correct. In this work, we simulate the effect of steering mirrors’ typical values of angular rotation on the QBER. In particular, we show that, for most cases, an active correction of the polarization reference frame and a passive correction of the phase shift between the electric field components is sufficient to obtain QBER values due to the steering mirrors below 0.2%. This avoids the need of a fully active correction strategy, which increases the complexity, weight, and cost of the implementation. Furthermore, we present different design considerations to further reduce the steering mirrors’ contribution to the QBER (less than 0.05%).
In polarization-encoding free-space Quantum Key Distribution (QKD), unwanted variations in the states of polarization may cause errors, leading to an increase in the quantum bit error rate (QBER), and a reduction of the Secure Key Rate (SKR). Optical elements that reflect or transmit the quantum signal at the transmitter and/or receiver are the main cause of polarization variations in the quantum states. Although most of these optical elements affect polarization in a constant manner, requiring relatively simple compensation techniques, mobile elements such as steering mirrors, cause time-varying polarization variations that are more complex to characterize and correct. In this work, we simulate the effect of steering mirrors’ typical values of angular rotation on the QBER. In particular, we show that, for most cases, an active correction of the polarization reference frame and a passive correction of the phase shift between the electric field components is sufficient to obtain QBER values due to the steering mirrors below 0.2%. This avoids the need of a fully active correction strategy, which increases the complexity, weight, and cost of the implementation. Furthermore, we present different design considerations to further reduce the steering mirrors’ contribution to the QBER (less than 0.05%).
Prepare-and-measure quantum key distribution (QKD) schemes with polarization encoding require the minimization of polarization degradation, i.e., undesired variations in the state of polarization, in the transmitter and receiver designs. In particular, the polarization extinction ratio (PER) should be maintained as high as possible to reduce the quantum bit error rate (QBER). In this paper, we analyze the polarization degradation and its correction in the design of free-space QKD systems. The polarization of a wavefront can be degraded in two different ways: uniformly, or non-uniformly; the latter known as polarization aberrations. While uniform polarization degradation of the beam wavefront can be easily corrected with standard retardation plates, polarization aberrations are more complex and require a different correction approach. BB84 diagonal linearly-polarized states are especially affected by polarization degradation as they are reflected off certain optical elements, and its correction is essential to achieve a low QBER. We have experimentally characterized the polarization degradation in a QKD transmitter and its impact in the QBER and achieved an almost perfect correction of the diagonal linearly polarized states when choosing a specific optical design.
Due to the fast-paced advancements of the quantum computing field, current public key cryptographic protocols need to be rethought. One promising solution is Quantum Key Distribution (QKD), whose security is robust to any computational advancement. The security of QKD relies on the laws of quantum mechanics, ensuring that any eavesdropper attempting to access the data will be detected. In particular, polarization-encoding QKD systems allow to generate secret keys in two remote locations to encode/decode information, using the State of Polarization (SOP) of single photons. Although its security has been theoretically proven, its practical implementation poses some challenges, part of which are the main focus of this PhD thesis. One relevant process in QKD systems is the synchronization between the transmitter and receiver, namely, the frame synchronization. This way, in this thesis, a frame synchronization method is developed and implemented, showing its potential for the use in prepare-and-measure QKD systems. The developed method has been shown to be effective, even with a low number of photons reaching the receiver. Furthermore, its architecture allows it to be adjusted for different attenuation regimes of the QKD system. The ability to encode data on the physical properties of single photons, in this case, polarization, highly depends on the capacity to accurately generate the required polarization states on demand. This way, an automatic SOP generation method, comprising an optical polarization monitoring system and a dedicated algorithm was developed and implemented, capable of generating four SOPs. This method reached an average Quantum Bit Error Rate (QBER) of 0.75%, which is well below the security threshold. After the SOP generation, and their transmission through the quantum channel, polarization alignment algorithms are required to compensate for the random rotations induced by birefringence in the optical fiber. In this thesis, a non-iterative polarization compensation method was implemented. This method requires only three QBER estimations to re-align the polarization, reaching average QBERs of 1.8%. Additionally, multiple iterative methods were implemented for comparison purposes, with the results clearly showing a better efficiency of the deterministic method. Beyond fiber-based transmissions, free-space transmissions were analysed due to their ability to reach sites without installed fiber and due to its potential for satellite-based quantum communications. This thesis demonstrates the feasibility of polarization-encoding QKD over free-space channels, by subjecting quantum signals to atmospheric turbulence to study its impact. In that sense, polarization variations over a 1.8 km outdoor free-space channel were monitored, to understand the effect of atmospheric turbulence on polarization. These results have shown that SOP variations in free-space links are slow, allowing their compensation. Furthermore, it was identified that, under conditions tested, the Secret Key Rate (SKR) could reach values up to 8.7×10ˉ⁴ bits per second, allowing QKD over free space for distances up to 2.31 km.
Polarization encoding has been extensively used in quantum key distribution (QKD) implementations along free-space links. However, the calculation model to characterize channel transmittance and quantum bit error rate (QBER) for free-space QKD has not been systematically studied. As a result, it is often assumed that misalignment error is equal to a fixed value, which is not theoretically rigorous. In this paper, we investigate the depolarization and rotation of the signal beams resulting from spatially-dependent polarization effects of the use of curved optics in an off-axis configuration, where decoherence can be characterized by the Huygens-Fresnel principle and the cross-spectral density matrix (CSDM). The transmittance and misalignment error in a practical free-space QKD can thus be estimated using the method. Furthermore, the numerical simulations clearly show that the polarization effect caused by turbulence can be effectively mitigated when maintaining good beam coherence properties.
Polarization qubits offer a direct route to fiber-based quantum communication, yet the fiber that carries them also scrambles their reference frame through uncontrolled birefringence. Active compensation commonly relies on monitoring and feedback, raising a natural question: can the link itself suppress coherent polarization drift before it reaches the receiver? We show that it can within a regime of sufficiently correlated unitary drift. Our central idea is to embed a fixed cyclic sequence of Pauli rotations along the fiber, turning propagation distance into a spatial toggling frame. Rather than estimating and inverting the unknown transformation, the sequence repeatedly reverses its leading action. We establish exact refocusing for constant generators compatible with a two-segment echo, show that a four-frame Pauli cell cancels the leading contribution of any traceless quasi-static generator, and bound the residual error for smoothly varying birefringence. We then connect these guarantees to operational BB84 quantities, including measured QBERs, the resulting secret fraction, and insertion loss. In simulations of a 50 km fiber with spatially correlated birefringence, a representative design reduces the mean QBER from 6.11% to 0.224% at a device spacing of 1.25 km. With an assumed per-device transmission of t = 0.997, this raises the asymptotic key rate per launched pulse by a factor of approximately 2.5. For this parameter set, the best design in the tested scan is not the densest one: error suppression and optical loss create a finite operating window. These results provide a loss-aware design principle for passive polarization stabilization and suggest a low-overhead complement to active tracking in polarization-encoded QKD networks.
The field of quantum key distribution (QKD) has seen many advancements since its conception in 1984. Recently there have been developments towards establishing free space optical links between satellites and earth to enable global QKD networks. Polarization encoded photos are commonly utilized as qubits for these free space links, placing polarization distortion constrains on the optics used. \n \nTwo polarization distortion studies were conducted in this thesis. The first is a simulation of stress induced birefringence in the Window Observational Research Facility window on board the International Space Station (ISS). Atmospherics pressure inside the ISS elicits stress on window leading to optical birefringence, which in turn can distort the polarization of photons as they pass through the window. The model studies the birefringent effects for incoming optical beams over different polarizations, diameters and incoming angles. \n \nAs part of free space optical quantum links, it can be beneficial to utilize beam steering optics to manage the spatial positioning of various components in the system. Implementing beam steering optics can aid in achieving spatial and maneuverability requirements for ground stations and satellites as they track each other. However, these optics can have an adverse effect on incoming photon polarization states. Because of this, the effects of various different beam steering configurations were characterized experimentally, and compared to a corresponding simulated model. \n \nThe studies presented in this thesis have revealed that common optics such as windows and mirrors can distort polarization based quantum signals. The polarization distortion of the studied optics have shown high dependencies on the angular orientation of the incoming optical beam. However, the distortions measured can be noticeably reduced by implementing compensation optics. As a result, their distortions are not detrimental to a quantum link that utilizes them. The studies presented in this thesis are critical to the design of polarization based quantum receivers as they shed light on potential sources of link distortions. This work is part of a large collection of developments bringing the implementation of global quantum key distribution networks closer to reality.
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.