Universal bound on quantum coherence from information causality

We derive a universal upper bound on the temperature of macroscopic quantum coherence, based on information causality and quantum speed limits. The bound, \( T_c \leq \frac{\hbar}{2k_B} \cdot \frac{v_{\text{LR}}}{\xi_0} \), arises from the interplay between the Lieb-Robinson information speed and the energy-time uncertainty principle. Without any fitting parameters, it accurately predicts the superfluid transition temperature of $^4$He (2.185 K vs. experimental 2.172 K) when geometric effects are included. The bound applies across diverse systems—from superconductors to black holes—suggesting a fundamental connection between quantum coherence, causality, and information propagation. This work highlights information causality as a foundational constraint on macroscopic quantum phenomena.