Spacetime-constrained oblivious transfer

In 1-out-of-2 oblivious transfer (OT), Alice inputs numbers x0,x1, Bob inputs a bit b and outputs xb. Secure OT requires that Alice and Bob learn nothing about b and xb, respectively. We define spacetime-constrained oblivious transfer (SCOT) as OT in Minkowski spacetime in which Bob must output xb within Rb, where R0 and R1 are fixed spacelike separated spacetime regions. We show that unconditionally secure SCOT is impossible with classical protocols in Minkowski (or Galilean) spacetime, or with quantum protocols in Galilean spacetime. We describe a quantum SCOT protocol in Minkowski spacetime, and we show it unconditionally secure.