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arXiv:2610.19941

Joint-measurement advantage and finite-time transitions in accelerated detector registers

Zhiming Huang

quant-phSubmitted Oct 14, 2026• Announced Oct 15, 2026• 0 citations
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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.

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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>1r>1r>1, joint advantage exists precisely when the thermal excitation factor satisfies q<1/rq<1/rq<1/r. At finite positive temperature it ends at a unique finite time, while the remaining entanglement is nonzero. For r=2r=2r=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.
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.
We make a detailed comparison between entanglement harvesting for uniformly accelerated detectors in vacuum and static ones in a thermal bath at the Unruh temperature and find that, for a small energy gap relative to the Heisenberg energy of the detectors, static detectors in the thermal bath can harvest more entanglement and possess a comparatively larger harvesting-achievable range than the uniformly accelerated ones; however, as the energy gap grows sufficiently large, the uniformly accelerated detectors are instead likely to harvest more entanglement and possess a relatively larger harvesting-achievable range than inertial ones in the thermal bath. In comparison with static detectors in vacuum, there exist phenomena of acceleration-assisted entanglement harvesting but never that of thermal-noise-assisted one. A notably interesting feature is that, although both the amount of entanglement harvested and the harvesting-achievable interdetector separation for static detectors in a thermal bath are always a decreasing function of temperature, they are not always so for uniformly accelerated detectors as acceleration (Unruh temperature) varies, suggesting the existence of the anti-Unruh effect in the entanglement harvesting phenomena of the accelerated detectors.
We consider a variant of the entanglement of assistance, as independently introduced by D.P. DiVincenzo et al. (quant-ph/9803033) and O. Cohen (Phys. Rev. Lett. 80, 2493 (1998)). Instead of considering three-party states in which one of the parties, the assistant, performs a measurement such that the remaining two parties are left with on average as much entanglement as possible, we consider four-party states where two parties play the role of assistants. We answer several questions that arise naturally in this scenario, such as (i) how much more entanglement can be produced when the assistants are allowed to perform joint measurements, (ii) for what type of states are local measurements sufficient, (iii) is it necessary for the second assistant to know the measurement outcome of the first, and (iv) are projective measurements sufficient or are more general POVMs needed?
We consider a variant of the entanglement of assistance, as independently introduced by D.P. DiVincenzo et al. (quart-ph/9803033) and O. Cohen (Phys. Rev. Lett. 80, 2493 (1998)). Instead of considering three-party states in which one of the parties, the assistant, performs a measurement such that the remaining two parties are left with on average as much entanglement as possible, we consider four-party states where two parties play the role of assistants. We answer several questions that arise naturally in this scenario, such as (i) how much more entanglement can be produced when the assistants are allowed to perform joint measurements, (ii) for what type of states are local measurements sufficient, (iii) is it necessary for the second assistant to know the measurement outcome of the first, and (iv) are projective measurements sufficient or are more general POVMs needed?.
We analyze minimum-error discrimination of two qubit dynamical processes generated by phase-covariant amplitude-damping Lindbladians in a single-use scenario. The optimization involves both the input probe, possibly entangled with an isolated ancilla, and the interrogation time. For unassisted probes we obtain a closed expression for the optimal trace-norm distinguishability at fixed time, with distinct interior and boundary branches. For entanglement-assisted probes, the common phase covariance of the two channels reduces the diamond-norm optimization to a one-parameter Schmidt family. The resulting formula gives transparent sufficient conditions for fixed-time entanglement advantage and separates this local advantage from advantage after global optimization over time. We exhibit examples in which the best unassisted strategy is approached only asymptotically, whereas an entangled probe achieves a strictly smaller error probability at finite time.
Uniform acceleration induces a thermal response to the Minkowski vacuum and can thereby modify quantum correlations. For measurement-induced nonlocality (MIN), a form of nonclassical correlation distinct from entanglement, previous field-mode analyses of bosonic fields found that it decreases with increasing acceleration and vanishes in the infinite-acceleration limit. This raises the question of whether the disappearance of MIN is a generic consequence of the Unruh effect or depends on the physical description of the accelerated quantum system. To address this question, we study two uniformly accelerating Unruh-DeWitt detectors interacting with a massless scalar field. We find that the response of MIN to the Unruh temperature depends sensitively on the initial detector state: it can decrease monotonically, vanish at an intermediate temperature and subsequently recover, or increase monotonically. Moreover, for a broad class of initial states, MIN approaches a nonzero value in the high-temperature limit. These results show that the suppression of MIN under strong acceleration is not universal. Instead, Unruh-induced detector dynamics gives rise to a state-dependent response in which measurement-induced nonlocality can be suppressed, restored, or enhanced.