Final Activity Report Summary - QC CN (Quantum Cryptography and Communication Networks)
We have recently witnessed the birth of a new interdisciplinary science called quantum information. In this new field, quantum key distribution (QKD) is one of the most promising areas. QKD represents the most secure way to distribute secret keys between two honest parties. This is because the security of QKD relies upon the uncertainty principle which is unbreakable by any eavesdropper.
During my fellowship I showed that suitable iterations of the uncertainty principle could be used to non-trivially improve the security of standard QKD protocols. This iteration was possible using schemes based on multiple quantum communications. The most important case was the two-way protocol where one party, e.g. Alice, prepared a quantum system in a random state, sent this system to the other party, e.g. Bob, who then performed a secret transformation before sending it back. Once the system was received by Alice, a suitable measurement revealed Bobs transformation to Alice. During this process, the two parties were able to extract a secret-key as long as the noise in the communication line was below a certain threshold, otherwise a potential eavesdropper, e.g. Eve, could access all the information on the shared key.
I developed this protocol using quantum systems with continuous variables, like the radiation modes of the electromagnetic field. My most important achievement was the proof that security could be activated by the two-way quantum communication. In few words, whereas standard one-way protocols failed to be secure because of the high noise in a communication line, two-way protocols could still guarantee the distribution of a secret-key. Thanks to this result, quantum cryptography was more robust against noise and losses and, therefore, could be implemented in longer communication lines.
This security activation could also be induced by protocols with n greater than two rounds of quantum communication. Such an extension to arbitrary n had remarkable consequences, since n-way protocols could be suitably modified into network protocols involving n different parties. As a result, we could increase the robustness to noise of a QKD network, which was a necessary step for its scalability.
An important problem that was connected with these investigations was the study of the security properties of the Gaussian channels, representing the most important communication lines in continuous variable quantum information. Given a one-mode Gaussian channel, I characterised the most general attack which generated that channel. In other words, I gave the first full characterisation of the so-called collective Gaussian attacks, which represented the most important eavesdropping strategy in continuous-variable quantum cryptography. Thanks to this characterisation I was also able to estimate the optimal secret-key rates which were achievable by two parties connected through a Gaussian channel. In particular, I introduced the notion of reverse secret-key capacity, which gave the optimal secret-key rate under the assumption of a single feedback classical communication. This quantity was also connected with the reverse coherent information, which was a lower bound for the entanglement distribution capacity via feedback classical communications. In these works, my collaborators and I proved that a single feedback communication was able to outperform any forward strategy, i.e. based on forward classical communications, for the task of distributing entanglement and secret correlations.
During the fellowship I also proposed the first continuous variable schemes for quantum direct communication (QDC). In QDC quantum systems were used to transmit confidential messages directly, i.e. without the use of a pre-shared secret-key, and with an acceptable degree of privacy. This technique was very demanding and required that the parties were very close to each other. Message transmission was promptly stopped whenever real-time checks of the channel revealed the presence of an eavesdropper, in such a way that the number of stolen bits was always negligible. QDC was a very young topic with non-trivial applications in short-range communications.
During my fellowship I showed that suitable iterations of the uncertainty principle could be used to non-trivially improve the security of standard QKD protocols. This iteration was possible using schemes based on multiple quantum communications. The most important case was the two-way protocol where one party, e.g. Alice, prepared a quantum system in a random state, sent this system to the other party, e.g. Bob, who then performed a secret transformation before sending it back. Once the system was received by Alice, a suitable measurement revealed Bobs transformation to Alice. During this process, the two parties were able to extract a secret-key as long as the noise in the communication line was below a certain threshold, otherwise a potential eavesdropper, e.g. Eve, could access all the information on the shared key.
I developed this protocol using quantum systems with continuous variables, like the radiation modes of the electromagnetic field. My most important achievement was the proof that security could be activated by the two-way quantum communication. In few words, whereas standard one-way protocols failed to be secure because of the high noise in a communication line, two-way protocols could still guarantee the distribution of a secret-key. Thanks to this result, quantum cryptography was more robust against noise and losses and, therefore, could be implemented in longer communication lines.
This security activation could also be induced by protocols with n greater than two rounds of quantum communication. Such an extension to arbitrary n had remarkable consequences, since n-way protocols could be suitably modified into network protocols involving n different parties. As a result, we could increase the robustness to noise of a QKD network, which was a necessary step for its scalability.
An important problem that was connected with these investigations was the study of the security properties of the Gaussian channels, representing the most important communication lines in continuous variable quantum information. Given a one-mode Gaussian channel, I characterised the most general attack which generated that channel. In other words, I gave the first full characterisation of the so-called collective Gaussian attacks, which represented the most important eavesdropping strategy in continuous-variable quantum cryptography. Thanks to this characterisation I was also able to estimate the optimal secret-key rates which were achievable by two parties connected through a Gaussian channel. In particular, I introduced the notion of reverse secret-key capacity, which gave the optimal secret-key rate under the assumption of a single feedback classical communication. This quantity was also connected with the reverse coherent information, which was a lower bound for the entanglement distribution capacity via feedback classical communications. In these works, my collaborators and I proved that a single feedback communication was able to outperform any forward strategy, i.e. based on forward classical communications, for the task of distributing entanglement and secret correlations.
During the fellowship I also proposed the first continuous variable schemes for quantum direct communication (QDC). In QDC quantum systems were used to transmit confidential messages directly, i.e. without the use of a pre-shared secret-key, and with an acceptable degree of privacy. This technique was very demanding and required that the parties were very close to each other. Message transmission was promptly stopped whenever real-time checks of the channel revealed the presence of an eavesdropper, in such a way that the number of stolen bits was always negligible. QDC was a very young topic with non-trivial applications in short-range communications.