Security Of Quantum Key Distribution

Information theory,the foundation of moden communication industry,is a great discovery in middle 20^th century.Quantum mechanism is the most important discovery in 20^th century,which induces great innovation of dynamics and epistemology.Quantum mechanism also leads to an innovation to information theory and thus generates a new subject,quantum information theory.There are lots of properties quantum information theory has but classical information theory does not have,e.g.quantum key distribution and quantum computation.Quantum computation is a disaster to classical security,while quantum key distribution is an angle that can provide unconditional security which cannot be break even with a quantum computer.Quantum key distribution is formally proposed in 1984,and developed in recent years.Currrently the security of Qbit protocol is almost fully known.Its feasibility is already demonstrated by many experiments.The most important duty for experimentalist is to push it to engineering.However,we know few about non-Qbit protocols.My major works are on security and network structure,while my published work is to solve the most important remained problems.After over 20 year's development,the most important remained problems on security are security of continuous variable quantum key distribution,differential phase shift quantum key distribution and infinite dimensional system.I have done many works on these three major problems.The continuous variable quantum key distribution has been considered to have the potential to provide high secret key rate.However,in present experimental demonstrations,the secret key can be distilled only under very small loss rates.By calculating explicitly the computational complexity with the channel transmission,we showed that under high loss rate it is hard to distill the secret key in present continuous variable scheme and one of its advantages,the potential of providing high secret key rate,may therefore be limited.We gave an achievable secret key rate of a binary modulated continuous variable quantum key distribution schemes in the collective attack scenario considering quantum channels that impose arbitrary noise on the exchanged signals.Bob performs homodyne measurements on the received states and the two honest parties employ a reverse reconciliation procedure in the classical post-processing step of the protocol. Differential phase shift quantum key distribution systems have a high potential for achieving high speed key generation.However,its unconditional security proof is still missing,even though it has been proposed for many years.We proved its unconditional security attacks with a weak coherent light source in the noiseless case (i.e.no bit error).The only assumptions are that quantum theory is correct,the devices are perfect and trusted and the key size is infinite.Our proof works on threshold detectors.We computed the lower bound of the secret key generation rate using the information-theoretical security proof method.Our final result shows that the lower bound of the secret key generation rate per pulse is linearly proportional to the channel transmission probability if Bob's detection counts obey the binomial distribution.In the realistic quantum key distribution(QKD),Alice and Bob respectively get a quantum state from an unknown channel,whose dimension may be unknown. However,while discussing the security,sometime we need to know exact dimension, since current exponential de Finetti theorem,crucial to the information-theoretical security proof,is deeply related with the dimension and can only be applied to finite dimensional case.We addressed this problem in detail.We showed that if POVM elements corresponding to Alice and Bob's measured results can be well described in a finite dimensional subspace with sufficiently small error,then dimensions of Alice and Bob's states can be almost regarded as finite.Since the security is well defined by the smooth entropy,which is continuous with the density matrix,the small error of state actually means small change of security.Then the security of unknown-dimensional system can be solved.Finally we proved that for heterodyne detection continuous variable QKD and differential phase shift QKD,the collective attack is optimal under the infinite key size case.