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Beam Propagation in Quantum Communication

Francesca Gerlin

Published Jan 31, 2014• 0 citations
OpenAlex

Abstract

The aim of my thesis is to demonstrate the feasibility of Quantum Communication in free space and space, pointing out how ESA Galileo constellation could be strengthens into an Optical Quantum Communication Network (OQCN), by the employment of a compact and low cost prototype (SaNe-QKD OPT). Considering table 2 according the guidelines of [70] (2012) for the European Quantum Information Processing and Quantum Communication, three crucial long term goals are fulfilled, (Satellite Quantum Communication, besides 1000 kilometers of spatial Quantum Cryptography, multi-node Quantum Network), with reference to Galileo constellation: the new devised OQCN will perform Quantum Communication between approaching satellites of the constellation in multi-node mode, and Quantum Key Distribution scheme will be employed over large distances, definitely above 1000 kilometers. My thesis summarizes three years of researches at the Luxor Laboratories in Padova. It is dedicated to two core topics, which are twofold aspects of the same issue: beam propagation in Quantum Communication over ground and over space, with the final realization of a Quantum Communication Network in which concretized the acquired knowledges in Quantum field. And Inter-island Canary links have been chosen as representing a worse case scenario for Quantum Communication experiments, an ideal test bed to investigate beam propagation in view of the space applications, where crucial aspects are the huge distances that Communication beams have to cover. The thesis is divided in two complementary parts: Ground beam propagation Beam propagation in free space along horizontal links in Canary Islands, performing long distances (143 kilometers) and aiming to exploit beam propagation through a turbulent medium. The results pointed out optical configurations and specifics in order to obtain an effective and stable communication link. These researches are within of the strategic project Quantum Future of the University of Padova, "the shift in the Quantum paradigm" Space beam propagation. The second part is dedicated to space beam propagation, regarding design and arrangement of the Quantum prototype SaNe-QKD to fuse with the Optical Communication prototype OPT (by Thales Alenia Space). The resulting system, SaNe-QKD OPT, will be positioned on board of Galileo satellites for performing Quantum Optical Inter-satellite links. Simulations about inter-satellite links, network topology features and key length evaluation, have allowed to obtain results and specifications about operative wavelengths and telescope apertures to use for inter-satellite communications. Then, the prototype SaNe-QKD have been arranged and is here shown in each part. This researches are part of the project "Application of Optical Quantum Communication Links for GNSS" by the European space Agency (ESA). My thesis is divided in four chapters, as follows Ground beam propagation Chapter 1 introduces an overview of main concepts of photonics, atmospheric models and turbulence parameters, optics and fiber-optics and telescopes, used throughout the treatment. The Newtonian telescope is investigated in order to analyze the optical path arriving at the prototype SaNe-QKD for space purpose and the Canary Telescope in order to realize an optical system implementing the centroid spot following system. Zemax simulations are presented for both to check aberrations and for collimation issues. For Newtonian off-axis field, coma and field curvature are revealed. For Canary Telescope chromatic aberration is revealed and the arrangement scheme of the experiment of beam propagation in free space in Canary Islands with co-propagating beams control is described. Kolmogorov atmospheric turbulence models with Hughnagel Valley model is then briefly reported too. It will be used in Canary experiments over 143 kilometers and in chapter 3 for up/downlink quantum communication simulations between a ground base transceiver and a satellite. Chapter 2. It is known that an unconfined optical mode propagating in a turbulent medium suffers of distortions. In Quantum Communication the information is encoded and transmitted as a train of single photons with mean average of about one photon for pulse; it follows that the link losses of a beam propagating in atmosphere increase with the distance; in contrast they cannot be reduced by increasing the signal power as in optical communication. Consequently, it is crucial to exploit beam propagation over long ranges, in order to analyze photon statistics, the transformations on the beam due to the ground in order to prevent the unleashing of the beam between transmitter and receiver. The turbulence introduces two contributes according the eddies size [51] [52]respect to the optical beam: • Beam wandering, which occurs when a laser beam is refracted by eddies with size larger than the beam diameter, causing a displacement of the beam center (centroid). • Beam spreading, which is due to the laser beam being refracted by eddies smaller than the beam diameter. The short-term beam spread is an additional spread with respect to the standard spread due to the free space laser beam propagation (without turbulence effects). These effects appears in relation to the exposition time: on short time scales the beam wandering is the dominant effect, while on long time scales the beam spread-ing is the dominant effect. Using turbulence as a resource, the research of beam propagation in free-space communication links opens to test a new equipment, the custom Canary telescope (Chapter1). The team performed two free-space propagation links with the telescope: the former, a ‘short’ local range (about 20 km) test link between Asiago and Monte Grappa (Italy) in order to examine the Canary Tele-scope and check the communication equipment at the transmitting part; the latter, a ‘long’ range (143 km long) link between La Palma and Tenerife (Canary Islands) for free-space propagation experiments with severe turbulence conditions. Developments and data analysis are presented, pointing out methodologies for turbulence characterization in Ground Quantum Optical Links. The results of the propagation of single, double beams along 143 kilometers have demonstrated that it is possible to optimize an optical system in order to reconstruct the beam long-term diameter and by techniques of beam co-propagating technique, the loss link could be reduced. This is promising as link losses are crucial aspect in Quantum Communication, when in a noisy channel the quantum signal (the in-formation encoded in single photons) cannot be improved by increasing the signal power. Besides we observed that the statistic of arrival of single photons over a free-space 143 km optical link confirms that there is a transformation from Poissonian to log-normal distribution: There is still the evidence of consecutive subintervals of low losses allowing us to envisage the exploitation of turbulence as an SNR improvement technique. Space beam propagation Chapter 3 according the requests of the ESA project, a feasibility study for Quantum Communication applications to Galileo constellation is shown. The chapter starts with an overview of the merits of Optical Communication (data rate exchanging, lightness, compactness, low power consumption..) Pointing out that the intrinsically secure is the added value that only the Quantum counterpart could supply. A brief part recalling orbital motion in space in order to check satellite orbital motion. Then we open to up/downlink simulations overview: recalling the simulations in literature of ground to space or space to ground beam propagation through the atmosphere, the feasibility study shows that unfortunately Galileo constellation can realize only inter-satellite communication links, as the atmosphere and the altitude of the satellite constellation prevents any effective and real single photon transmission with the current technologies. However, simulation results of inter-satellite beam propagation show us that the huge distances can be overwhelmed (derived requirements are telescope diameters >20 cm and operating wavelength <532nm), and time interval within perform Quantum Communication can be calculated: respect to a reference satellite of different orbital plane, the time interval in which the intra-satellite distances are within 15000 kilometers are • For satellite called three of about 176 minutes • For satellite called two of about 168 minutes Then exploiting the relative motion of satellites lying in different orbital planes, we show that it is possible to target communication between satellites that are closer in turns, and to achieve appreciable transmission rates: the distance intervals in which we calculated the raw key rate values are 6000, 10000 and 19000 kilometers, and the best values in raw key rates (18M bits/s at 6600 kilometers, related to lower attenuation values) are obtained for a telescope diameter of 50 cm and wavelength of 50nm, while the worse values in raw key rates (2.2 Kbits/s at 6600 kilometers, related to higher attenuation values) are for a telescope diameter of 20 cm and wavelength of 800nm. Finally, today information-based society security is of paramount importance: Galileo Optical Quantum Network will guarantee intrinsically secure key exchanging, free of PSN attack, within a satellite distance signed by decoy scheme approach. After a brief review of a model for a Quantum Communication System, simulations about key rate are shown in the final section, showing that for same wavelengths and within same beam propagation distances, larger apertures present higher values of key rate[bit/s]. At the same time we have observed that shorter operating wave- lengths presents higher values of key rate, assuring that in merit to Galileo OQCN decoy schemes could be applied in order to beat PNS attack over well defined communication links in relation to the link distance covered, the operative

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Quantum communication channels between earth and space and space to earth

Andrea Tomaello

The work presented in this thesis, on the topics of global quantum network, is the result of a set of research activities done at the CNR-IFN Luxor laboratory over these three years. The main goal that we would reach is the feasibility demonstration of quantum communication in free-space, without excluding from the definition "free space" any possible scenario. This is the way that in the future may lead to a global quantum network all over the world, that involves satellites and earth station. We may identify three major link families, that should help the reader to classify the research activities presented: • Satellite to Earth and Earth to satellite link - called in the thesis Vertical link • Point to point horizontal link - called in the thesis Horizontal link • Satellite to satellite link - called in the thesis Intersatellite link In a certain way we tried to deal with all of them trough analysis and simulation or experimental campaigns. The core topics of this works however are those related to the experimental campaigns, respectively: • Laser beam propagation in a free-space horizontal link: we established an optical link of 144km between Canary islands in order to improve the knowledge on horizontal laser propagation over atmosphere and to define the setup requirements and the most suitable condition to get an effective quantum link. This work is presented in Chapter 3. • Polarization maintenance over a space quantum link: we designed, realized and installed a polarimeter to reconstruct the polarization state of photons in a space optical link in the MLRO. Our quantum information, in fact, is codified in the polarization state of photons. To pave the way for future developments and implementations (i.e. quantum transmitter and receiver hosted in satellites) we must as first prove the maintenance or the retreadability of the polarization state. The yet existing laser ranging facilities are examples of optical links between Earth and space that can be exploited for polarization analysis and reconstruction providing them with a polarimeter. This work is presented in Chapter 6. The thesis is arranged as follows: a first chapter introduce the atmospheric model and the most common quantities used in this field to describe the effects of turbulence. Follows an analysis and simulation chapter (Ch.2) on space to Earth and Earth to space quantum links. The treatment proceed with the experimental results of the Canary campaign (Ch.3) on horizontal quantum link. Chapters 4 and 5 are related on the polarimetry topic: starting from formalisms and definitions, are presented the simulations that have lead to the requirements for polarimeter design. In the second-last (Ch.6) is described the polarimeter in all its subsystems, calibration and first test results. Chapter 7, the last one, regards on intersatellite quantum link: the treatment is purely focused on model definition and feasibility analysis. A detailed abstract of the main chapters is reported below: • Chapter 2 - Vertical Link - (Analysis and numerical simulation chapter): As mentioned in the introduction: on a global space quantum network we have to deal with satellite to earth and earth to satellite links. To investigate the feasibility of quantum communication over these long distance in a space scale we have to understand the behaviour of a laser beam propagating into a turbulent media. As introduced in chapter [1], the atmospheric turbulence is a source of beam wandering and beam spreading respectively due to small or large eddies if compared with the beam size. These different effects are appreciable considering the exposure time: for short time, the beam appears spread but more over, wandering from the ideal centroid positions; instead for long time scale the wandering effects integrated over time, gives rise to a dominant beam broadening. The beam preserves its Gaussian profile, but more larger in size. A beam affected at the start of its path by the degradation induced by atmosphere will arrive at the receiver plane far away from the unperturbed expected position. On the same way, a beam affected at the end of its path will be barely modified. The results obtained show that the effect of beam wandering is strongly different for the uplink and downlink, up to about two orders of magnitude. A few ten thousand meters of beam radius are reached in a very long distance (like GEO satellite) in the uplink, while a beam radius on the order of few hundred meters is calculated in the case of downlink. From simulation of the beam displacement , appears that it is clearly negligible for downlink in which the main input affecting the beam is the broadening due to turbulence eddies, therefore related to short term beam effects. Instead for the uplink the beam displacement appears monotonically increasing with the distance, due to the atmosphere at the beginning of the path. For a downlink a greater portion of sky compared to uplink falls in the "good SNR cone", allowing a longer time-slot for quantum communication. The SNR is closed to 0.7dB at zenith for Galileo satellites; the situation is most promising for GPS satellites in which the SNR is around 2.2dB. In both cases the values, de facto prove the unfeasibility of quantum communication with the simulated setup, but gives good wishes related to further technological improvements. The actual feasibility of QKD is related to link distances in the range of LEO orbits, a good SNR can be achieved without stretching the telescope field-of-view to the technological limit. Small improvements on IFOV can shift the link distance feasibility limit toward higher orbits, allowing quantum communication even with GPS and Galileo satellites. • Chapter 3 - Free-space long distance horizontal optical link - (Canary experimental results): In the perspective of the extension of Quantum Communication (QC) in free-space to long distances, the analysis of the phenomena that occur to a visible or near-infrared beam in the propagation in atmosphere and their understanding is of crucial importance for devising the most convenient optical terminal. The investigation on the ground-ground case is used also to envisage the space QC, along with a vast area of research in satellite Classical Communications [58]. More in details, optical propagation in atmosphere in the case of links length of over 100km is affected by several transformations of the beam parameters, resulting in an increase of the link losses. Moreover, the long range optical communication at the single photon limit exploiting the quantum protocols, on the other side, differs from the classical protocols in that the signal to be transmitted cannot be intensified, being a train of very weak pulses with an average about one photon per pulse. The understanding of the effects induced by the propagation in both the irradiance at the receiver as well as in the temporal statistics is crucial to assess the quality of the communication and eventually the feasibility of the link. Moreover, for the very long links, fading and losses are induced by the decoupling of the beam with the receiver due to large wandering of the beam spot, as it was also investigated for the space channel [86]. 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The whole beam at the receiver was acquired and the scintillation analysis carried out and compared to models including the meteorological data from the Canary Observatories. The design of the optical setup for long range quantum communications is crucial, and we addressed this issue by developing an optimized telescope for the experiments. The literature on horizontal propagation is quite poor mainly because for decades of years the interest was focused on vertical propagation -for astronomical purposes-. As first we needed to understand the effects of atmospheric turbulence in beam propagation: like wandering, spreading and scintillation. This led us, as last step, to identify the best design parameters for transmitters and receiver and for communication protocol. 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Advanced techniques for quantum communications in free-space channels

Alberto Dall’Arche

This thesis is focused on the development of advanced techniques for quantum communications in free-space channels. At present there are several demonstrations of quantum communication protocols at long distances, many of these exploit optical fiber as transmission channel. The optical fiber is very advantageous in that it is scarcely influenced by external conditions and allows to connect remote localities that are not in direct line of sight. On the other hand, it presents strong limitations in transmission distance because of dispersion and attenuation. It is therefore necessary to explore new transmission channels in order to allow a global spread of quantum communication. The free-space channels are good candidates, both the vertical ones (between earth and space) and the horizontal ones. The study of these is of fundamental importance for the extension of quantum communication over a global scale. Since the eighties to present day have been defined several quantum communication protocols such as Bennet-Brassard 84 (BB84), Bennet 92 (B92), Ekert 91, Decoy State, Dense Coding, etc.. These protocols present different characteristic such as reliability, security and key rate. These three parameters are very important for the characterization of a communication protocol and are directly related to each other. The development of new quantum communication protocols that maximize these parameters is very important for future progress of quantum communications. This thesis is divided into three parts. In the first part we consider the characteristics and the behaviour of a free-space horizontal quantum channel. We study the impact of atmospheric turbulence in the case of single beam propagation and twin-beam propagation. We then measure the losses of the channel and analyse the effect of turbulence on photon statistics. Finally, we propose a method that exploits the turbulence to improve the signal to noise ratio (SNR) of the channel. In the second part we take into consideration the security and efficiency of Quantum Key Distribution (QKD) protocols . We propose the experimental demonstration of the B92 protocol with non-maximally entangled states . Using this kind of states allow us to improve the security and the key rate of this protocol. Finally, in the last part, we presented a possible way to improve the quantum channel capacity exploiting hyperentangled photon pairs. We designed and experimentally tested a system that can be used to transmit hyperentangled states at long distances.

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The aim of my thesis is to demonstrate the feasibility of Quantum Communication in free space and space, pointing out how ESA Galileo constellation could be strengthens into an Optical Quantum Communication Network (OQCN), by the employment of a compact and low cost prototype (SaNe-QKD OPT). Considering table 2 according the guidelines of [70] (2012) for the European Quantum Information Processing and Quantum Communication, three crucial long term goals are fulfilled, (Satellite Quantum Communication, besides 1000 kilometers of spatial Quantum Cryptography, multi-node Quantum Network), with reference to Galileo constellation: the new devised OQCN will perform Quantum Communication between approaching satellites of the constellation in multi-node mode, and Quantum Key Distribution scheme will be employed over large distances, definitely above 1000 kilometers. My thesis summarizes three years of researches at the Luxor Laboratories in Padova. It is dedicated to two core topics, which are twofold aspects of the same issue: beam propagation in Quantum Communication over ground and over space, with the final realization of a Quantum Communication Network in which concretized the acquired knowledges in Quantum field. And Inter-island Canary links have been chosen as representing a worse case scenario for Quantum Communication experiments, an ideal test bed to investigate beam propagation in view of the space applications, where crucial aspects are the huge distances that Communication beams have to cover. The thesis is divided in two complementary parts: Ground beam propagation Beam propagation in free space along horizontal links in Canary Islands, performing long distances (143 kilometers) and aiming to exploit beam propagation through a turbulent medium. The results pointed out optical configurations and specifics in order to obtain an effective and stable communication link. These researches are within of the strategic project Quantum Future of the University of Padova, "the shift in the Quantum paradigm" Space beam propagation. The second part is dedicated to space beam propagation, regarding design and arrangement of the Quantum prototype SaNe-QKD to fuse with the Optical Communication prototype OPT (by Thales Alenia Space). The resulting system, SaNe-QKD OPT, will be positioned on board of Galileo satellites for performing Quantum Optical Inter-satellite links. Simulations about inter-satellite links, network topology features and key length evaluation, have allowed to obtain results and specifications about operative wavelengths and telescope apertures to use for inter-satellite communications. Then, the prototype SaNe-QKD have been arranged and is here shown in each part. This researches are part of the project "Application of Optical Quantum Communication Links for GNSS" by the European space Agency (ESA). My thesis is divided in four chapters, as follows Ground beam propagation Chapter 1 introduces an overview of main concepts of photonics, atmospheric models and turbulence parameters, optics and fiber-optics and telescopes, used throughout the treatment. The Newtonian telescope is investigated in order to analyze the optical path arriving at the prototype SaNe-QKD for space purpose and the Canary Telescope in order to realize an optical system implementing the centroid spot following system. Zemax simulations are presented for both to check aberrations and for collimation issues. For Newtonian off-axis field, coma and field curvature are revealed. For Canary Telescope chromatic aberration is revealed and the arrangement scheme of the experiment of beam propagation in free space in Canary Islands with co-propagating beams control is described. Kolmogorov atmospheric turbulence models with Hughnagel Valley model is then briefly reported too. It will be used in Canary experiments over 143 kilometers and in chapter 3 for up/downlink quantum communication simulations between a ground base transceiver and a satellite. Chapter 2. It is known that an unconfined optical mode propagating in a turbulent medium suffers of distortions. In Quantum Communication the information is encoded and transmitted as a train of single photons with mean average of about one photon for pulse; it follows that the link losses of a beam propagating in atmosphere increase with the distance; in contrast they cannot be reduced by increasing the signal power as in optical communication. Consequently, it is crucial to exploit beam propagation over long ranges, in order to analyze photon statistics, the transformations on the beam due to the ground in order to prevent the unleashing of the beam between transmitter and receiver. The turbulence introduces two contributes according the eddies size [51] [52]respect to the optical beam: • Beam wandering, which occurs when a laser beam is refracted by eddies with size larger than the beam diameter, causing a displacement of the beam center (centroid). • Beam spreading, which is due to the laser beam being refracted by eddies smaller than the beam diameter. The short-term beam spread is an additional spread with respect to the standard spread due to the free space laser beam propagation (without turbulence effects). These effects appears in relation to the exposition time: on short time scales the beam wandering is the dominant effect, while on long time scales the beam spread-ing is the dominant effect. Using turbulence as a resource, the research of beam propagation in free-space communication links opens to test a new equipment, the custom Canary telescope (Chapter1). The team performed two free-space propagation links with the telescope: the former, a ‘short’ local range (about 20 km) test link between Asiago and Monte Grappa (Italy) in order to examine the Canary Tele-scope and check the communication equipment at the transmitting part; the latter, a ‘long’ range (143 km long) link between La Palma and Tenerife (Canary Islands) for free-space propagation experiments with severe turbulence conditions. Developments and data analysis are presented, pointing out methodologies for turbulence characterization in Ground Quantum Optical Links. The results of the propagation of single, double beams along 143 kilometers have demonstrated that it is possible to optimize an optical system in order to reconstruct the beam long-term diameter and by techniques of beam co-propagating technique, the loss link could be reduced. This is promising as link losses are crucial aspect in Quantum Communication, when in a noisy channel the quantum signal (the in-formation encoded in single photons) cannot be improved by increasing the signal power. Besides we observed that the statistic of arrival of single photons over a free-space 143 km optical link confirms that there is a transformation from Poissonian to log-normal distribution: There is still the evidence of consecutive subintervals of low losses allowing us to envisage the exploitation of turbulence as an SNR improvement technique. Space beam propagation Chapter 3 according the requests of the ESA project, a feasibility study for Quantum Communication applications to Galileo constellation is shown. The chapter starts with an overview of the merits of Optical Communication (data rate exchanging, lightness, compactness, low power consumption..) Pointing out that the intrinsically secure is the added value that only the Quantum counterpart could supply. A brief part recalling orbital motion in space in order to check satellite orbital motion. Then we open to up/downlink simulations overview: recalling the simulations in literature of ground to space or space to ground beam propagation through the atmosphere, the feasibility study shows that unfortunately Galileo constellation can realize only inter-satellite communication links, as the atmosphere and the altitude of the satellite constellation prevents any effective and real single photon transmission with the current technologies. However, simulation results of inter-satellite beam propagation show us that the huge distances can be overwhelmed (derived requirements are telescope diameters >20 cm and operating wavelength <532nm), and time interval within perform Quantum Communication can be calculated: respect to a reference satellite of different orbital plane, the time interval in which the intra-satellite distances are within 15000 kilometers are • For satellite called three of about 176 minutes • For satellite called two of about 168 minutes Then exploiting the relative motion of satellites lying in different orbital planes, we show that it is possible to target communication between satellites that are closer in turns, and to achieve appreciable transmission rates: the distance intervals in which we calculated the raw key rate values are 6000, 10000 and 19000 kilometers, and the best values in raw key rates (18M bits/s at 6600 kilometers, related to lower attenuation values) are obtained for a telescope diameter of 50 cm and wavelength of 50nm, while the worse values in raw key rates (2.2 Kbits/s at 6600 kilometers, related to higher attenuation values) are for a telescope diameter of 20 cm and wavelength of 800nm. Finally, today information-based society security is of paramount importance: Galileo Optical Quantum Network will guarantee intrinsically secure key exchanging, free of PSN attack, within a satellite distance signed by decoy scheme approach. After a brief review of a model for a Quantum Communication System, simulations about key rate are shown in the final section, showing that for same wavelengths and within same beam propagation distances, larger apertures present higher values of key rate[bit/s]. At the same time we have observed that shorter operating wave- lengths presents higher values of key rate, assuring that in merit to Galileo OQCN decoy schemes could be applied in order to beat PNS attack over well defined communication links in relation to the link distance covered, the operative
The work presented in this thesis, on the topics of global quantum network, is the result of a set of research activities done at the CNR-IFN Luxor laboratory over these three years. The main goal that we would reach is the feasibility demonstration of quantum communication in free-space, without excluding from the definition "free space" any possible scenario. This is the way that in the future may lead to a global quantum network all over the world, that involves satellites and earth station. We may identify three major link families, that should help the reader to classify the research activities presented: • Satellite to Earth and Earth to satellite link - called in the thesis Vertical link • Point to point horizontal link - called in the thesis Horizontal link • Satellite to satellite link - called in the thesis Intersatellite link In a certain way we tried to deal with all of them trough analysis and simulation or experimental campaigns. The core topics of this works however are those related to the experimental campaigns, respectively: • Laser beam propagation in a free-space horizontal link: we established an optical link of 144km between Canary islands in order to improve the knowledge on horizontal laser propagation over atmosphere and to define the setup requirements and the most suitable condition to get an effective quantum link. This work is presented in Chapter 3. • Polarization maintenance over a space quantum link: we designed, realized and installed a polarimeter to reconstruct the polarization state of photons in a space optical link in the MLRO. Our quantum information, in fact, is codified in the polarization state of photons. To pave the way for future developments and implementations (i.e. quantum transmitter and receiver hosted in satellites) we must as first prove the maintenance or the retreadability of the polarization state. The yet existing laser ranging facilities are examples of optical links between Earth and space that can be exploited for polarization analysis and reconstruction providing them with a polarimeter. This work is presented in Chapter 6. The thesis is arranged as follows: a first chapter introduce the atmospheric model and the most common quantities used in this field to describe the effects of turbulence. Follows an analysis and simulation chapter (Ch.2) on space to Earth and Earth to space quantum links. The treatment proceed with the experimental results of the Canary campaign (Ch.3) on horizontal quantum link. Chapters 4 and 5 are related on the polarimetry topic: starting from formalisms and definitions, are presented the simulations that have lead to the requirements for polarimeter design. In the second-last (Ch.6) is described the polarimeter in all its subsystems, calibration and first test results. Chapter 7, the last one, regards on intersatellite quantum link: the treatment is purely focused on model definition and feasibility analysis. A detailed abstract of the main chapters is reported below: • Chapter 2 - Vertical Link - (Analysis and numerical simulation chapter): As mentioned in the introduction: on a global space quantum network we have to deal with satellite to earth and earth to satellite links. To investigate the feasibility of quantum communication over these long distance in a space scale we have to understand the behaviour of a laser beam propagating into a turbulent media. As introduced in chapter [1], the atmospheric turbulence is a source of beam wandering and beam spreading respectively due to small or large eddies if compared with the beam size. These different effects are appreciable considering the exposure time: for short time, the beam appears spread but more over, wandering from the ideal centroid positions; instead for long time scale the wandering effects integrated over time, gives rise to a dominant beam broadening. The beam preserves its Gaussian profile, but more larger in size. A beam affected at the start of its path by the degradation induced by atmosphere will arrive at the receiver plane far away from the unperturbed expected position. On the same way, a beam affected at the end of its path will be barely modified. The results obtained show that the effect of beam wandering is strongly different for the uplink and downlink, up to about two orders of magnitude. A few ten thousand meters of beam radius are reached in a very long distance (like GEO satellite) in the uplink, while a beam radius on the order of few hundred meters is calculated in the case of downlink. From simulation of the beam displacement , appears that it is clearly negligible for downlink in which the main input affecting the beam is the broadening due to turbulence eddies, therefore related to short term beam effects. Instead for the uplink the beam displacement appears monotonically increasing with the distance, due to the atmosphere at the beginning of the path. For a downlink a greater portion of sky compared to uplink falls in the "good SNR cone", allowing a longer time-slot for quantum communication. The SNR is closed to 0.7dB at zenith for Galileo satellites; the situation is most promising for GPS satellites in which the SNR is around 2.2dB. In both cases the values, de facto prove the unfeasibility of quantum communication with the simulated setup, but gives good wishes related to further technological improvements. The actual feasibility of QKD is related to link distances in the range of LEO orbits, a good SNR can be achieved without stretching the telescope field-of-view to the technological limit. Small improvements on IFOV can shift the link distance feasibility limit toward higher orbits, allowing quantum communication even with GPS and Galileo satellites. • Chapter 3 - Free-space long distance horizontal optical link - (Canary experimental results): In the perspective of the extension of Quantum Communication (QC) in free-space to long distances, the analysis of the phenomena that occur to a visible or near-infrared beam in the propagation in atmosphere and their understanding is of crucial importance for devising the most convenient optical terminal. The investigation on the ground-ground case is used also to envisage the space QC, along with a vast area of research in satellite Classical Communications [58]. More in details, optical propagation in atmosphere in the case of links length of over 100km is affected by several transformations of the beam parameters, resulting in an increase of the link losses. Moreover, the long range optical communication at the single photon limit exploiting the quantum protocols, on the other side, differs from the classical protocols in that the signal to be transmitted cannot be intensified, being a train of very weak pulses with an average about one photon per pulse. The understanding of the effects induced by the propagation in both the irradiance at the receiver as well as in the temporal statistics is crucial to assess the quality of the communication and eventually the feasibility of the link. Moreover, for the very long links, fading and losses are induced by the decoupling of the beam with the receiver due to large wandering of the beam spot, as it was also investigated for the space channel [86]. In this perspective of free-space long range single-photon quantum link, we planned a set of experimental campaigns to study the propagation of a single or twin optical beams in scale length of several tens to a few hundreds kilometres. We address in this work the study of the phenomena induced in very long propagation by using of laser beams to investigate links whose length is of several tens to a few hundreds kilometers. In the experiments, the observation of the whole beam combined to the measure of the local irradiance at the receiver side are performed and then projected to the case of single photons links. In addition, with the aim to stabilize the centroid position at the receiver, the propagation of two beams forming a small mutual angle is studied in the framework of the isoplanatic angle spread for low and high orders of the beam spatial modes. The experimental models were realized in Alpine links as well as between the Tenerife and La Palma link in the Canary archipelagos. The whole beam at the receiver was acquired and the scintillation analysis carried out and compared to models including the meteorological data from the Canary Observatories. The design of the optical setup for long range quantum communications is crucial, and we addressed this issue by developing an optimized telescope for the experiments. The literature on horizontal propagation is quite poor mainly because for decades of years the interest was focused on vertical propagation -for astronomical purposes-. As first we needed to understand the effects of atmospheric turbulence in beam propagation: like wandering, spreading and scintillation. This led us, as last step, to identify the best design parameters for transmitters and receiver and for communication protocol. With the gained data we want to define a model or a set of criteria to be considered in designing an optical quantum link and to predict the link losses for a realistic receiver and, possibly to envisage the exploitation of the time-varying losses for the selection of the portion with the highest signal-to-noise ratio [77]. The observation of the propagation of a single or a pair of beams along very long paths of over 100km have shown that the beam is subjected to splitting into multiple spots but that its long-term diameter may be confined to a spot that is only a factor 3 to 5 the diffraction limit. This results have been obtained by using a suitable large aperture aplanatic refractive transmitter. In this way a significant reduction of the link losses for quantum communication channels in this extreme conditions are possible by the implementation of such scheme. This setup was used in both the OGS (Tenerife)-to-JKT (La Palma) propagation and the
This thesis is focused on the development of advanced techniques for quantum communications in free-space channels. At present there are several demonstrations of quantum communication protocols at long distances, many of these exploit optical fiber as transmission channel. The optical fiber is very advantageous in that it is scarcely influenced by external conditions and allows to connect remote localities that are not in direct line of sight. On the other hand, it presents strong limitations in transmission distance because of dispersion and attenuation. It is therefore necessary to explore new transmission channels in order to allow a global spread of quantum communication. The free-space channels are good candidates, both the vertical ones (between earth and space) and the horizontal ones. The study of these is of fundamental importance for the extension of quantum communication over a global scale. Since the eighties to present day have been defined several quantum communication protocols such as Bennet-Brassard 84 (BB84), Bennet 92 (B92), Ekert 91, Decoy State, Dense Coding, etc.. These protocols present different characteristic such as reliability, security and key rate. These three parameters are very important for the characterization of a communication protocol and are directly related to each other. The development of new quantum communication protocols that maximize these parameters is very important for future progress of quantum communications. This thesis is divided into three parts. In the first part we consider the characteristics and the behaviour of a free-space horizontal quantum channel. We study the impact of atmospheric turbulence in the case of single beam propagation and twin-beam propagation. We then measure the losses of the channel and analyse the effect of turbulence on photon statistics. Finally, we propose a method that exploits the turbulence to improve the signal to noise ratio (SNR) of the channel. In the second part we take into consideration the security and efficiency of Quantum Key Distribution (QKD) protocols . We propose the experimental demonstration of the B92 protocol with non-maximally entangled states . Using this kind of states allow us to improve the security and the key rate of this protocol. Finally, in the last part, we presented a possible way to improve the quantum channel capacity exploiting hyperentangled photon pairs. We designed and experimentally tested a system that can be used to transmit hyperentangled states at long distances.
Optical quantum communication utilizing satellite platforms has the potential to extend the reach of quantum key distribution (QKD) from terrestrial limits of ∼200 km to global scales. We have developed a thorough numerical simulation using realistic simulated orbits and incorporating the effects of pointing error, diffraction, atmosphere and telescope design, to obtain estimates of the loss and background noise which a satellite-based system would experience. Combining with quantum optics simulations of sources and detection, we determine the length of secure key for QKD, as well as entanglement visibility and achievable distances for fundamental experiments. We analyse the performance of a low Earth orbit satellite for downlink and uplink scenarios of the quantum optical signals. We argue that the advantages of locating the quantum source on the ground justify a greater scientific interest in an uplink as compared to a downlink. An uplink with a ground transmitter of at least 25 cm diameter and a 30 cm receiver telescope on the satellite could be used to successfully perform QKD multiple times per week with either an entangled photon source or with a weak coherent pulse source, as well as perform long-distance Bell tests and quantum teleportation. Our model helps to resolve important design considerations such as operating wavelength, type and specifications of sources and detectors, telescope designs, specific orbits and ground station locations, in view of anticipated overall system performance.
This thesis focuses on the two main applications where free-space optical communication (FSOC) can bring the most significant impact: interplanetary communications and quantum communications. Consequently, the dissertation is structured in two sections. In the first one, a novel proposal is suggested regarding to using Cherenkov telescopes as ground-station receivers. A feasibility study addresses the posibility of using the technology developed for the gamma-ray telescopes that will make up the Cherenkov Telescope Array (CTA) in the implementation of a new kind of ground station. Among the main advantages that these telescopes provide are the much larger apertures needed to overcome the power limitation that ground-based gamma-ray astronomy and deep-space optical communication both have. Also, the large number of big telescopes that will be built for CTA will make it possible to reduce unitary costs by economy-scale production. The second section of the thesis is framed in the field of free-space Quantum Key Distribution (QKD), which has become a new paradigm in the discipline of information security. This technique offers a theoretically-secure way to communicate over an insecure channel since the presence of an eventual eavesdropper can be detected. The main challenge of Free-space QKD is the need to operate both under strong atmospheric turbulence and daylight background noise. To mitigate these effects, a trade-off is usually required when designing the receiver's optics, since a narrow field-of-view improves background noise rejection, but increases turbulence-related losses and a wide field-of-view produces the opposite effect. A correction system for atmospheric turbulence is proposed to overcome both limitations at the same time, and different strategies are analyzed and experimented to carry out the implementation and integration within the QKD system.
Quantum Key Distribution (QKD) is a cryptography technique that allows two parties to share a secret common key that can be used for a secure exchange of information. To meet the requirements and interests of different final users, the technological development of this technique has rapidly led toward commercial systems for a global quantum infrastructure, namely a quantum network. Communication among parties requires an optical channel, which for short distances is typically provided by optical fiber. However, the limitation of optical losses on longer fiber links, or the unavailability of an exploitable deployed fiber, requires the use of a different QKD medium, i.e. free-space. At the University of Padova we are investigating, both theoretically and experimentally, how Adaptive Optics (AO) can be used to improve the performance of free-space quantum communication, with a particular focus on QKD. Following our theoretical studies on the optimal design for an intermodal free-space/ fiber link, we were able to realize different QKD field trials along a 600m-long free-space link exploiting polarization encoding. Besides the metropolitan area of Padova, we are now working on the development of an extra-urban free-space link, which is more prone to atmospheric turbulence effects. For this link, we equipped a radar tower located on a hill in Teolo with a remotised optical transmitter, and we are now developing the AO system for the receiving telescope, located at the Department of Information Engineering in Padova, with which we plan to realize QKD during day and night time.
The shift in the Communication paradigm from the bit to the qubit is increasingly exploited in terrestrial long range links and networks, with strong potentials in secure communications, quantum computing and metrology. The space-to-ground quantum key distribution was also considered as feasible. A new different scenario for the quantum communications is that of the intersatellite link. In this study we focus on the extension of intersatellite communications into the quantum domain. The long distances involved and the fast relative motion are severe constraints, partially compensated by the absence of beam degradation due to the propagation in the atmosphere as well as the relatively low background noise level. We address the conception of the optical terminal and the predicted performances in the case of constellations of LEO and MEO satellite including the quantum communications and quantum teleportation.