Phase-controlled recoverable entanglement in accelerated detector registers

Abstract

We study recoverable entanglement in a four-qubit cluster-state register whose two detector qubits couple to a scalar field. A local preparation phase leaves the initial reference--register entanglement and detector marginal unchanged, but controls protection under collective noise. At the optimal phase, a fixed decoder recovers a Bell pair after any channel preserving the singlet and triplet sectors. For uniformly accelerated detectors at finite separation, an exact trace-norm formula shows that the same phase is optimal at every time within the secular weak-coupling dynamics. Small separation produces a slow decay, whose rate and phase-dependent amplitude we derive. Matching the local response to an inertial thermal bath gives an analytic optimum time for the entanglement contrast. A detector measurement and conditional phase correction recover a two-qubit teleportation resource. Spatial smearing and an ordered weak-coupling then small-separation limit specify the microscopic scope of the lifetime prediction.