Evolution of quantum state texture under Lorentz transformations: Invariance, competition, and sensitivity in single-particle and bipartite entangled systems
Phys. Rev. A 113, 062438 – Published 15 June, 2026
DOI: https://doi.org/10.1103/hts6-k7d3
Abstract
Quantum state texture (QST), an emerging resource quantifying the global structural complexity of quantum states within a computational basis, exhibits dynamical behavior under relativistic frameworks that remains largely unexplored. This paper systematically investigates the evolution of QST under Lorentz boosts for single-particle and bipartite entangled Gaussian wave-packet systems. Based on Lorentz group representation theory and the Wigner rotation mechanism, we derive analytical expressions for the texture measure for both the single-particle and the bipartite entangled systems. The study reveals the following: (1) For a single-particle system, under the approximation that the wave-packet width is much smaller than the mass and the specific configuration where the initial momentum is perpendicular to the boost direction, both quantum coherence (QC) and QST remain invariant, determined solely by the initial spin angle, and the physical origin lies in the symmetry of the probability transfer between spin states induced by relativistic effects; (2) under the same approximations, for a bipartite entangled system, QC is conserved under arbitrary Lorentz boosts, while QST and quantum entanglement (QE) exhibit a competitive relationship with the relativistic effect parameter—QST increases monotonically with the parameter, whereas QE monotonically decays, and when both particles are Lorentz boosted simultaneously relativistic effects enhance the texture while further degrading entanglement compared to the single-particle boost scenario; (3) the reduced single-particle state obtained from the bipartite system exhibits texture and coherence that are completely unaffected by relativistic effects, indicating that the system's texture and overall coherence are stored within nonlocal correlations. To test the range of the narrow-packet approximation, we also evaluate the unexpanded Wigner-rotation integral numerically for finite widths , finding that the same monotonic trends persist while the second-order analytical formula mildly overestimates the exact integral. The sensitivity of QST to the phase distribution reorganization caused by Wigner rotations establishes it as an effective complementary resource for probing the fine phase structure of relativistic quantum systems, offering significant insights for quantum information processing in high-speed or noninertial frames.
