In the fast evolving world of quantum information, several key ideas are reshaping how we understand and utilize quantum systems. One of the most fascinating is quantum non-locality, the concept that the predictions of quantum theory fundamentally challenge the classical notion of local realism. Roughly speaking, quantum non-locality reveals that the behavior of entangled particles cannot be explained by any theory that assumes objects are only influenced by their immediate surroundings (a more precise definition will be given in the thesis). Two main contributions that developed this idea are the EPR (Einstein–Podolsky–Rosen) paradox and the work of J.S. Bell, both of which forced us to rethink the very nature of reality and had profound implications for the development of quantum technologies. A fundamental framework for exploring quantum non-locality is the Bell's scenario. It involves a physical system, prepared in an entangled state, that is shared and measured by two spatially separated users, that have access to a set of quantum observables. Since the measurement process is intrinsically probabilistic, their outcomes can be used to generate random numbers. This task is crucial in many fields: for instance, in cryptography, the security of encryption keys and protocols relies on generating truly random values, ensuring that keys are unpredictable and resistant to attacks. Another example is in statistics, where Monte Carlo methods depend on the quality of the random number generator, as their accuracy is tied to the randomness of the samples. Furthermore, quantum mechanics is the only known way to generate true randomness: generators based on classical mechanics are deterministic and thus output pseudo-random numbers, which are, in principle, predictable. The challenging part of generating random number with Bell's scenarios is making sure that everything is working as expected, for example it has to be verified that the system is actually entangled and the functionality of the complex measurement apparatus. To address these problems, the concept of self-testing has become an invaluable tool: it allows the verification of quantum devices without requiring knowledge of their internal workings. By analyzing the outcomes of a Bell's scenario, self-testing can confirm that all devices are performing the expected quantum operations, even if their internal mechanisms are not known or trusted. Hence, outcomes are used both to generate random bits and to ensure the integrity of the system. A major limitation of the proposed scenario is the low extraction rate: since there are only two users, we can generate at most two numbers from each entangled state, but creating and preserving entanglement is particularly challenging. A natural solution is to sequentially increase the number of users, in the sense that each new pair will measure on the post-measurement state of the previous one. This works provided that each post-measurement state is still entangled, which is achieved by using generalized operators in place of projective ones. In this thesis we will explore those topics, explaining in more details what is non-locality, self-testing and how to generate secure random numbers from quantum mechanics. In particular we will propose an innovative approach to extend a large family of Bell protocols to the sequential case with three users. Those results will also be theoretically proved and validated by using recent numerical simulations techniques, such as the NPA hierarchy.

In the fast evolving world of quantum information, several key ideas are reshaping how we understand and utilize quantum systems. One of the most fascinating is quantum non-locality, the concept that the predictions of quantum theory fundamentally challenge the classical notion of local realism. Roughly speaking, quantum non-locality reveals that the behavior of entangled particles cannot be explained by any theory that assumes objects are only influenced by their immediate surroundings (a more precise definition will be given in the thesis). Two main contributions that developed this idea are the EPR (Einstein–Podolsky–Rosen) paradox and the work of J.S. Bell, both of which forced us to rethink the very nature of reality and had profound implications for the development of quantum technologies. A fundamental framework for exploring quantum non-locality is the Bell's scenario. It involves a physical system, prepared in an entangled state, that is shared and measured by two spatially separated users, that have access to a set of quantum observables. Since the measurement process is intrinsically probabilistic, their outcomes can be used to generate random numbers. This task is crucial in many fields: for instance, in cryptography, the security of encryption keys and protocols relies on generating truly random values, ensuring that keys are unpredictable and resistant to attacks. Another example is in statistics, where Monte Carlo methods depend on the quality of the random number generator, as their accuracy is tied to the randomness of the samples. Furthermore, quantum mechanics is the only known way to generate true randomness: generators based on classical mechanics are deterministic and thus output pseudo-random numbers, which are, in principle, predictable. The challenging part of generating random number with Bell's scenarios is making sure that everything is working as expected, for example it has to be verified that the system is actually entangled and the functionality of the complex measurement apparatus. To address these problems, the concept of self-testing has become an invaluable tool: it allows the verification of quantum devices without requiring knowledge of their internal workings. By analyzing the outcomes of a Bell's scenario, self-testing can confirm that all devices are performing the expected quantum operations, even if their internal mechanisms are not known or trusted. Hence, outcomes are used both to generate random bits and to ensure the integrity of the system. A major limitation of the proposed scenario is the low extraction rate: since there are only two users, we can generate at most two numbers from each entangled state, but creating and preserving entanglement is particularly challenging. A natural solution is to sequentially increase the number of users, in the sense that each new pair will measure on the post-measurement state of the previous one. This works provided that each post-measurement state is still entangled, which is achieved by using generalized operators in place of projective ones. In this thesis we will explore those topics, explaining in more details what is non-locality, self-testing and how to generate secure random numbers from quantum mechanics. In particular we will propose an innovative approach to extend a large family of Bell protocols to the sequential case with three users. Those results will also be theoretically proved and validated by using recent numerical simulations techniques, such as the NPA hierarchy.

Secure randomness from sequential quantum measurements

REZZI, ALESSANDRO
2023/2024

Abstract

In the fast evolving world of quantum information, several key ideas are reshaping how we understand and utilize quantum systems. One of the most fascinating is quantum non-locality, the concept that the predictions of quantum theory fundamentally challenge the classical notion of local realism. Roughly speaking, quantum non-locality reveals that the behavior of entangled particles cannot be explained by any theory that assumes objects are only influenced by their immediate surroundings (a more precise definition will be given in the thesis). Two main contributions that developed this idea are the EPR (Einstein–Podolsky–Rosen) paradox and the work of J.S. Bell, both of which forced us to rethink the very nature of reality and had profound implications for the development of quantum technologies. A fundamental framework for exploring quantum non-locality is the Bell's scenario. It involves a physical system, prepared in an entangled state, that is shared and measured by two spatially separated users, that have access to a set of quantum observables. Since the measurement process is intrinsically probabilistic, their outcomes can be used to generate random numbers. This task is crucial in many fields: for instance, in cryptography, the security of encryption keys and protocols relies on generating truly random values, ensuring that keys are unpredictable and resistant to attacks. Another example is in statistics, where Monte Carlo methods depend on the quality of the random number generator, as their accuracy is tied to the randomness of the samples. Furthermore, quantum mechanics is the only known way to generate true randomness: generators based on classical mechanics are deterministic and thus output pseudo-random numbers, which are, in principle, predictable. The challenging part of generating random number with Bell's scenarios is making sure that everything is working as expected, for example it has to be verified that the system is actually entangled and the functionality of the complex measurement apparatus. To address these problems, the concept of self-testing has become an invaluable tool: it allows the verification of quantum devices without requiring knowledge of their internal workings. By analyzing the outcomes of a Bell's scenario, self-testing can confirm that all devices are performing the expected quantum operations, even if their internal mechanisms are not known or trusted. Hence, outcomes are used both to generate random bits and to ensure the integrity of the system. A major limitation of the proposed scenario is the low extraction rate: since there are only two users, we can generate at most two numbers from each entangled state, but creating and preserving entanglement is particularly challenging. A natural solution is to sequentially increase the number of users, in the sense that each new pair will measure on the post-measurement state of the previous one. This works provided that each post-measurement state is still entangled, which is achieved by using generalized operators in place of projective ones. In this thesis we will explore those topics, explaining in more details what is non-locality, self-testing and how to generate secure random numbers from quantum mechanics. In particular we will propose an innovative approach to extend a large family of Bell protocols to the sequential case with three users. Those results will also be theoretically proved and validated by using recent numerical simulations techniques, such as the NPA hierarchy.
2023
Secure randomness from sequential quantum measurements
In the fast evolving world of quantum information, several key ideas are reshaping how we understand and utilize quantum systems. One of the most fascinating is quantum non-locality, the concept that the predictions of quantum theory fundamentally challenge the classical notion of local realism. Roughly speaking, quantum non-locality reveals that the behavior of entangled particles cannot be explained by any theory that assumes objects are only influenced by their immediate surroundings (a more precise definition will be given in the thesis). Two main contributions that developed this idea are the EPR (Einstein–Podolsky–Rosen) paradox and the work of J.S. Bell, both of which forced us to rethink the very nature of reality and had profound implications for the development of quantum technologies. A fundamental framework for exploring quantum non-locality is the Bell's scenario. It involves a physical system, prepared in an entangled state, that is shared and measured by two spatially separated users, that have access to a set of quantum observables. Since the measurement process is intrinsically probabilistic, their outcomes can be used to generate random numbers. This task is crucial in many fields: for instance, in cryptography, the security of encryption keys and protocols relies on generating truly random values, ensuring that keys are unpredictable and resistant to attacks. Another example is in statistics, where Monte Carlo methods depend on the quality of the random number generator, as their accuracy is tied to the randomness of the samples. Furthermore, quantum mechanics is the only known way to generate true randomness: generators based on classical mechanics are deterministic and thus output pseudo-random numbers, which are, in principle, predictable. The challenging part of generating random number with Bell's scenarios is making sure that everything is working as expected, for example it has to be verified that the system is actually entangled and the functionality of the complex measurement apparatus. To address these problems, the concept of self-testing has become an invaluable tool: it allows the verification of quantum devices without requiring knowledge of their internal workings. By analyzing the outcomes of a Bell's scenario, self-testing can confirm that all devices are performing the expected quantum operations, even if their internal mechanisms are not known or trusted. Hence, outcomes are used both to generate random bits and to ensure the integrity of the system. A major limitation of the proposed scenario is the low extraction rate: since there are only two users, we can generate at most two numbers from each entangled state, but creating and preserving entanglement is particularly challenging. A natural solution is to sequentially increase the number of users, in the sense that each new pair will measure on the post-measurement state of the previous one. This works provided that each post-measurement state is still entangled, which is achieved by using generalized operators in place of projective ones. In this thesis we will explore those topics, explaining in more details what is non-locality, self-testing and how to generate secure random numbers from quantum mechanics. In particular we will propose an innovative approach to extend a large family of Bell protocols to the sequential case with three users. Those results will also be theoretically proved and validated by using recent numerical simulations techniques, such as the NPA hierarchy.
device-independent
QKD
SDPA
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12608/70117