Quantum Rabin oblivious transfer using two pure states

Oblivious transfer between two untrusting parties is an important primitive in cryptography. There are different variants of oblivious transfer. In Rabin oblivious transfer, the sender Alice holds a bit, and the receiver Bob either obtains the bit, or obtains no information with probability <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>p</a:mi><a:mo>?</a:mo></a:msub></a:math>. Alice should not know whether or not Bob obtained the bit. We examine a quantum Rabin oblivious transfer (OT) protocol that uses two pure states. Investigating different cheating scenarios for the sender and for the receiver, we determine optimal cheating probabilities in each case. Comparing the quantum Rabin oblivious transfer protocol to classical Rabin oblivious transfer protocols, we show that the quantum protocol outperforms classical protocols, which do not use a third party, for some values of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>p</b:mi><b:mo>?</b:mo></b:msub></b:math>. We find that quantum Rabin OT protocols that use mixed states can outperform quantum Rabin OT protocols that use pure states for some values of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>p</c:mi><c:mo>?</c:mo></c:msub></c:math>.