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This is a theoretical quantum-information paper on how much entanglement a four-qubit cluster state retains when two assisting nodes undergo generalized amplitude damping, and when joint versus local measurements can recover it. Its exact results (the joint optimum equals bipartition negativity, with a finite-time transition at finite temperature) are analytic and limited to a specific independent weak-coupling model. Practitioners working on measurement-based or distributed quantum resources should note the conditions under which joint assistance is necessary, but the findings have not been tested experimentally.
Joint-measurement advantage and finite-time transitions in accelerated detector registers
arXiv:2610.19941v1 Announce Type: new Abstract: The Unruh response thermalizes accelerated detectors, but the entanglement remaining in a register does not by itself specify what distributed measurements can recover. We study this distinction for a four-qubit cluster state whose two assisting nodes independently undergo generalized amplitude damping, while the target nodes remain isolated and the environments are inaccessible. We derive the exact joint-assisted concurrence and the exact one-way value for arbitrary local measurements. The joint optimum equals the bipartition negativity, and computational-basis measurements attain the one-way optimum. A polar-decomposition argument, together with compactness, establishes a necessary and sufficient condition for separable measurements to attain the joint optimum and proves a strict gap whenever this condition fails. For assisting detectors at equal Unruh temperature with relaxation-rate ratio $r>1$, joint advantage exists precisely when the thermal excitation factor satisfies $q<1/r$. At finite positive temperature it ends at a unique finite time, while the remaining entanglement is nonzero. For $r=2$, both the transition time and remaining resource have closed expressions. These results identify when joint assistance is necessary within the independent weak-coupling thermalization model.
Abstract:The Unruh response thermalizes accelerated detectors, but the entanglement remaining in a register does not by itself specify what distributed measurements can recover. We study this distinction for a four-qubit cluster state whose two assisting nodes independently undergo generalized amplitude damping, while the target nodes remain isolated and the environments are inaccessible. We derive the exact joint-assisted concurrence and the exact one-way value for arbitrary local measurements. The joint optimum equals the bipartition negativity, and computational-basis measurements attain the one-way optimum. A polar-decomposition argument, together with compactness, establishes a necessary and sufficient condition for separable measurements to attain the joint optimum and proves a strict gap whenever this condition fails. For assisting detectors at equal Unruh temperature with relaxation-rate ratio $r>1$, joint advantage exists precisely when the thermal excitation factor satisfies $q<1/r$. At finite positive temperature it ends at a unique finite time, while the remaining entanglement is nonzero. For $r=2$, both the transition time and remaining resource have closed expressions. These results identify when joint assistance is necessary within the independent weak-coupling thermalization model.
arXiv:2610.19941 [quant-ph]
(or arXiv:2610.19941v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.19941 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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