Some Theoretical Study On Quantum Communication

With the development of quantum mechanics, a new interdiscipline of quantum theory and classical information theory, quantum information science, came into the world in the 1980s. The superposition principle and the uncertainty principle are the basic postulates of quantum mechanics, as well as the important resource and security basis of quantum information science. Quantum information mainly includes quantum computation and quantum communication. Exploiting the superposition principle of quantum states, quantum computation enables the computing ability growing exponen-tially, which becomes a research hotspots recently. The uncertainty principle guarantees that the quantum states are avoided from the adversaries’disturbance when performing quantum communication tasks so that the unconditional security of the communica-tion is ensured in a quantum way. One integral resource of quantum computation and quantum communication is the quantum entanglement of the superposition of multi-particle quantum states. Albert Einstein’s original conception of quantum entanglement is "spooky action at a distance". The Bell inequality based on entanglement is one of the most important fundamental theories to test whether quantum mechanics is com-plete. Different quantum correlations developed from quantum entanglement, such as quantum steering, quantum discord, are fundamental physical theories and properties of quantum mechanics. They all play a key role in different quantum tasks. In 1964, Bell proposed the first inequality that turned the debate of the completeness of quantum mechanics from abstract theory interpretation to real experimental tests. Since then, va-rieties of Bell inequalities arouse, including discrete-variable type, continuous-variable type, and entropy type, etc.Since the first experiment of Bell inequality was done by Alain Aspect in 1982, more than one hundred experiments of kinds of inequalities are tested. However, no experiment could definitely affirm the completeness of quantum mechanics until 2015 because of the difficulties in closing the efficiency loophole, locality loophole and ran-dom loophole simultaneously.In the post-quantum age, classical communication tasks based on computational complexity including encryption and decryption (key distribution), digital signature, se-cret sharing, cryptographic conferencing, bit commitment, are faced with fatal security challenges. Varieties of quantum communication tasks based on quantum physics laws emerged as the time requires. However, so far, only the quantum version of encryption and decryption, i.e. quantum key distribution, comes to the stage of application. Oth-er communication tasks are still limited to theoretical proposals and proof-of-principle experimental demonstrations. The main problem lies in that quantum key distribution is a communication task with two participants, which is simpler, while quantum dig-ital signatures, quantum secret sharing, and quantum cryptographic conferencing are multi-party quantum communication tasks involving multi participants. In the field of classical cryptography, encryption and decryption, digital signature, and secret shar-ing are the three most fundamental and widely applied tasks. Therefore, to develop highly-applicable quantum versions of them, i.e. quantum digital signatures and quan-tum secret sharing to the application level of quantum key distribution become the hot topic and difficulty in the field of quantum communication.During the PhD period, the author of this doctoral thesis focuses on theoretical tests of the fundamental concepts of loophole-free quantum mechanical theory, theoretical studies on quantum secret sharing, quantum cryptographic conferencing, and quantum digital signatures with practical prospects. In the aspect of testing fundamental concepts of quantum mechanics, we propose an entropic Bell inequality, using the continuous-variable system with two-mode squeezed vacuum state as the entanglement source as well as combining the quadrature measurements to test local realism. The continuous-variable entanglement source is advantageous for experimental tests, especially for a possible loophole-free test of nonlocality, as the quadrature measurements can be im-plemented with homodyne detections of nearly 100% detection efficiency under current technology.In the aspects of practical quantum secret sharing and quantum cryptographic con-ferencing, we propose a protocol with postselected GHZ entangled state and decoy-state method, we employ simple quantum state preparation and projection coincidence measurement to realize quantum secret sharing and quantum cryptographic conferenc-ing over a distance of more than 100 km. We overcome the harsh terms of preparing multiparty GHZ entangled states with high intensity and distributing high-fidelity GHZ entangled states through a long distance in previous protocols. We prove the uncondi-tional security of the protocol using entanglement purification and quantum error cor-rection techniques and obtain the practical secure key rates of the secret sharing and cryptographic conferencing changing with distances. In our protocol, we exploit entan-glement swapping to prevent all attacks from the detector side and guarantees a high security in reality.In the study of practical quantum digital signatures theory, we provide a quantum digital signature scheme with non-orthogonal four-state and six-state to realize digi-tal signatures without secure quantum channels. With the decoy-state theory, laser sources with the Poisson distribution could be used as quantum states to implement secure quantum digital signatures. We employ the entanglement swapping of copies of non-orthogonal encoded quantum states and quantum error correction code technique to prove that our protocol could prevent the forgery attack of insecure quantum channels. Random sampling technique combined with statistical fluctuation analysis method is used to prove the security against repudiation attack.