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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 $p_?$. 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 $p_?$. 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 $p_?$., Comment: 12 pages, 3 figures; v2: added Appendix C and other minor additions

Oblivious transfer (OT) is an important cryptographic primitive. Any multi-party computation can be realised with OT as building block. XOR oblivious transfer (XOT) is a variant where the sender Alice has two bits, and a receiver Bob obtains either the first bit, the second bit, or their XOR. Bob should not learn anything more than this, and Alice should not learn what Bob has learnt. Perfect quantum OT with information-theoretic security is known to be impossible. We determine the smallest possible cheating probabilities for unrestricted dishonest parties in non-interactive quantum XOT protocols using symmetric pure states, and present an optimal protocol, which outperforms classical protocols. We also "reverse" this protocol, so that Bob becomes sender of a quantum state and Alice the receiver who measures it, while still implementing oblivious transfer from Alice to Bob. Cheating probabilities for both parties stay the same as for the unreversed protocol. We optically implemented both the unreversed and the reversed protocols, and cheating strategies, noting that the reversed protocol is easier to implement., Comment: 23 pages, 6 figures; v2: added Subsection IV.A and other minor additions