  Within the broad research scenario of quantum secure communication, Two-Way
Quantum Key Distribution (TWQKD) is a relatively new proposal for sharing
secret keys that is not fully explored yet. We analyse the security of TWQKD
schemes that use qubits prepared in non-orthogonal states to transmit the key.
Investigating protocols that employ an arbitrary number of bases for the
channel preparation, we show, in particular, that the security of the LM05
protocol can not be improved by the use of more than two preparation bases. We
also provide a new proof of unconditional security for a deterministic TWQKD
protocol recently proposed [Phys. Rev. A 88, 062302 (2013)]. In addition, we
introduce a novel deterministic protocol named TWQKD six-state and compute an
analytical lower bound (which can be tightened) for the maximum amount of
information that an eavesdropper could extract in this case. An interesting
advantage of our approach to the security analysis of TWQKD is the great
simplicity and transparency of the derivations.
