Sobre a segurança em canais quânticos bipartidos via taxa de chave

Abstract

The purpose of this work is to study a method of attesting the security of a quantum channel shared by two legitimate users (Alice and Bob), defined in terms of a bipartite state ρAB. A protocol in which users want to share a secret key to encrypt and decrypt messages was considered where the channel security is guaranteed by quantifying the value of the secret key rate (K). It is defined in terms of the user’s mutual information and the mutual information that a spy (Eve) shares with one of the users, in this case Alice, when invading the channel. Eve’s invasion is described by an operator B, which defines the measurement of an observable by intercepting the state that is sent to Bob. Thus, due to the non-local nature of quantum theory, Eve’s intervention promotes state collapse, and users receive in their labs a state defined by the action of a projective measurement map. Thus , we sought to find a general expression for the secret key rate in terms of entropies and then promote a case study using the density matrix for the Werner state using general spin operators as an observable quantity. With the study of the case, an equation was found in terms of the angles that determine the general measures of spin where a parameter r was defined, with r given by the dot product of the unit vector that defines the measures of spin for Alice with the unit vector for Eve spin measurements. From the results we found, it is concluded that the modulus of r can be interpreted as the degree of Eve interference in the channel, so that the higher the value of r, the lower the value of the graph that is found when plotting K in terms of μ. In this way, it is verified that the secret key rate can be a way of attesting the security of a channel, so that users can securely share a key.