In 1-out-of-2 oblivious transfer (OT), Alice inputs numbers x0, x1, Bob inputs a bit b and outputs x b . 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 x b within R b , 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.
Spacetime-constrained oblivious transfer (SCOT) extends the fundamental primitive of oblivious transfer to Minkowski space. SCOT and location oblivious data transfer (LODT) are the only known cryptographic tasks with classical inputs and outputs for which unconditional security needs both quantum theory and relativity. We give an unconditionally secure SCOT protocol that, contrasting previous SCOT and LODT protocols, is practical to implement with current technology, where distant agents need only communicate classical information, while quantum communication occurs at a single location. We also show that our SCOT protocol can be used to implement unconditionally secure quantum relativistic bit commitment. √ 2 |0 + (−1) a |1 , for a ∈ {0, 1}.
III. A PRACTICAL AND UNCONDITIONALLY SECURE SCOT PROTOCOLWe present an unconditionally secure SCOT protocol, consisting of two main stages. Stage I includes quantum communication between the laboratories adjacent to location L and can be completed within any finite time in the past light cone of P . Stage II includes fast classical processing and communication between Alice's and Bob's agents at the locations L, L 0 and L 1 , as well as classical communication between Alice's (Bob's) agents at the locations L and L i , for i ∈ {0, 1}. Steps 1-6 take place in the past of P . Our protocol is illustrated in Fig. 1.A. Stage I
We consider the quantum and local hidden variable (LHV) correlations obtained by measuring a pair of qubits by projections defined by randomly chosen axes separated by an angle θ. LHVs predict binary colourings of the Bloch sphere with antipodal points oppositely coloured. We prove Bell inequalities separating the LHV predictions from the singlet quantum correlations for θ ∈ 0, π 3 . We raise and explore the hypothesis that, for a continuous range of θ > 0, the maximum LHV anticorrelation is obtained by assigning to each qubit a colouring with one hemisphere black and the other white.
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