Realizing quantum advantage without entanglement in single-photon states

We propose an optical circuit for attaining quantum measurement advantage in a system that has no quantum entanglement. Our device produces symmetric two-qubit X-states with controllable anti-diagonal elements, and does not require entangled states as input. We discuss the use of this device in a two-qubit quantum game. When entanglement is absent, the maximum quantum advantage in this game is 1/3 bit. A slightly diminished quantum advantage, 0.311 bit, can be realized with a simplified transaction protocol. (paper)