Information-Disturbance Model For Quantum Cryptographical Protocols

Quantum Cryptograpy, one of the hot topics in computer science and physics, supplies uswith a perfect scheme for unconditional secure communication. Its security is based on the basicprincipal in quantum mechanics. However, the inevitable distortion in channel and the physicalimperfection of communicative device have nowadays become the potential menace to itsunconditional security. Since the first quantum cryptographical protocol BB84, the securityanalysis of these protocols has been started. The well-known attacks includes cloning, IRUD,mid-basis measurement, PNS, and joint attack. The first 3 can be considered as the special casesof individual attack which are more easily obtainable in physical laboratories.In the view of quantum fidelity, we here propose an "Information-Disturbance" model forIndividual attack. In comparison with classical information processing, there is not a quantummeasurement process that could gain some information on unknown quantum state withoutdisturbing it. As a general rule, the more information is extracted from a measurement process,the more its state has to be disturbed. Thus, the amount of the disturbance can be served as agood estimation of the information retrieved by Eve. To explore the tradeoff ofinformation-disturbance emphasized in this model is equivalently to explore the maximuminformation Eve may eavesdropped in whatever physically available strategies with some givendisturbance.In this thesis, we present another derivation of the tradeoff for the unkown bipartitemaximally entangled pure state with the help of Ref. Then we improve the quantum circuits forthe Non-Demolition Bell measurement and generalized it to a much genral case. Furthermore,we prove its optimality. In practice, the entanglement obtained in the lab is always equivalent toa kind of partial entangled state. We considered the bepartite partially entangled state for a givendegree of entanglement. For the special degree of b=(3/5)^1/2, we obtain an analytical solution tothe tradeoff and as well as the corresponding measurement. However, for a more general degree,we can only present the numerical solution. Furthermore, in order to put such a trdeoff into amore practical way, we construct a nearly optimal solution which conincides with the numericalones very well.Three-party entanglement is a kind of state that is widely used in the quantum secrectsharing protocols. To give a lower bound to these protocols, we continue to study the problem oftradeoff for GHZ state. For 2-dimensional systems, we obtain that the maximal estimationfidelity can attain a value of 13/54, and also the optimal tradeoff. Such a result gives us alowerbound for security secret sharing.