We consider a subclass of quantum Turing machines (QTM), named stationary rotational quantum Turing machine (SR-QTM), which halts deterministically and has deterministic tape head position. A quantum state transition diagram (QSTD) is proposed to describe SR-QTM. With QSTD, we construct a SR-QTM which is universal for all near-trivial transformations. This indicates there exists a QTM which is universal for the above subclass. Finally we show that SR-QTM is computational equivalent with ordinary QTM in the bounded error setting. It can be seen that SR-QTMs have deterministic tape head position and halt deterministically, and thus the halting scheme problem will not exist for this class of QTMs.
Public-key cryptosystems for quantum messages are considered from two aspects:public-key encryption and public-key authentication.Firstly,we propose a general construction of quantum public-key encryption scheme,and then construct an informationtheoretic secure instance.Then,we propose a quantum public-key authentication scheme,which can protect the integrity of quantum messages.This scheme can both encrypt and authenticate quantum messages.It is information-theoretic secure with regard to encryption,and the success probability of tampering decreases exponentially with the security parameter with regard to authentication.Compared with classical public-key cryptosystems,one private-key in our schemes corresponds to an exponential number of public-keys,and every quantum public-key used by the sender is an unknown quantum state to the sender.
An unconditionally secure authority-certified anonymous quantum key distribution scheme using conjugate coding is presented, based on which we construct a quantum election scheme without the help of an entanglement state. We show that this election scheme ensures the completeness, soundness, privacy, eligibility, unreusability, fairness, and verifiability of a large-scale election in which the administrator and counter are semi-honest. This election scheme can work even if there exist loss and errors in quantum channels. In addition, any irregularity in this scheme is sensible.