Oblivious transfer and quantum channels as communication resources

We show that from a communication-complexity perspective, the primitive called oblivious transfer—which was introduced in a cryptographic context—can be seen as the classical analogue to a quantum channel in the same sense as non-local boxes are of maximally entangled qubits. More explicitly, one realization of non-cryptographic oblivious transfer allows for the perfect simulation of sending one qubit and measuring it in an orthogonal basis. On the other hand, a qubit channel allows for realizing non-cryptographic oblivious transfer with probability roughly 85 %, whereas 75 % is the classical limit