Vacuum-Induced Quantum Gate

We demonstrate that the quantum vacuum, as perceived by a uniformly accelerating observer, can be harnessed to perform a quantum Z-gate. A two-level Unruh-DeWitt detector, prepared in a superposition of its ground and excited states, undergoes a second-order interaction with the vacuum, resulting in a two-photon emission. We derive the exact analytical form of the final entangled detector-field state and show that this emission is conditional on a phase flip of the detector's initial state-the defining feature of the gate's operation. This process harvests entanglement from the Minkowski vacuum, producing photon pairs entangled across causally disconnected Rindler wedges. This work reframes acceleration-induced radiation not as thermal noise but as a coherent computational resource, offering new pathways for relativistic quantum information.