Does relativistic motion really freeze initially maximal entanglement?

TL;DR

This work investigates how relativistic motion influences multipartite entanglement in the tetrapartite cluster state $CL_{4}$ using a fully operational Unruh-DeWitt detector framework. By modeling A,B,C as inertial and D as uniformly accelerated, and tracing out the field, the authors compute the reduced density matrix $ ho^{ABCD}_t$ and evaluate the 1-3 tangles; they show that $N_{A(BCD)}=1$ for all accelerations, indicating complete freezing of the entanglement between an inertial qubit and the rest, while the other tangles $N_{C(ABD)}$ and $N_{D(ABC)}$ exhibit partition-dependent degradation. The results reveal an asymmetric robustness of entanglement under the Unruh effect and identify a new acceleration-invariant entanglement resource, with potential applications for relativistic quantum information processing in non-inertial or curved-spacetime settings. The study challenges the common view that acceleration universally diminishes maximal entanglement and points to the CL4 state's suitability for robust quantum protocols in extreme relativistic regimes.

Abstract

We investigate the relativistic dynamics of quantum entanglement in a four-qubit cluster ($CL_4$) state using a fully operational Unruh-DeWitt detector framework. Contrary to the widely held expectation that the Unruh effect inevitably degrades initially maximal entanglement, we demonstrate that the 1-3 bipartite entanglement of the $CL_4$ state remains strictly maximal for all accelerations, including the infinite-acceleration limit. This result uncovers a previously unexplored phenomenon, namely the ``complete freezing of initially maximal entanglement" under relativistic motion. To the best of our knowledge, this is the first identification and systematic characterization of such a phenomenon within a relativistic framework. These findings overturn the conventional view that acceleration universally diminishes maximal entanglement and establish the $CL_4$ state as a promising resource for quantum information processing in non-inertial or curved-spacetime settings.

Figures (4)

• Figure 1: Schematic illustration of the Unruh-DeWitt detector configuration. Four observers (Alice, Bob, Charlie, David) each carry an Unruh-DeWitt detector modeled as a two-level atom. The detectors of Alice, Bob and Charlie remain stationary, while David's detector undergoes uniform acceleration $a$ during a time interval $\Delta$.
• Figure 2: The $1-3$ tangle of $CL_{4}$ state as a function of the acceleration parameter $q$. The effective coupling parameter is fixed as $\nu^2=0.01$.
• Figure 3: The $1-3$ tangle of the $CL_{4}$ state as a function of the effective coupling parameter $\nu$ with a fixed acceleration parameter $q=0.99$.
• Figure 4: The $N_{C(ABD)}$ and $N_{D(ABC)}$ of the $CL_4$ state as functions of the interaction time duration $\vartriangle$ and the energy gap $\Omega$, with $\epsilon^{2}=8\pi^{2}\cdot10^{-6}$, $\kappa=0.02$, and $q=0.9999$.