Basis-independent Coherence in Noninertial Frames

TL;DR

Problem addressed: how basis-independent quantum coherence behaves for a Dirac field when one observer undergoes uniform acceleration, i.e., under the Unruh effect. Approach: compute the basis-independent coherence measure $C( ho)=\sqrt{ S\left( \frac{\rho+\rho_M}{2} \right) - \frac{S(\rho) + \log_2 d}{2} }$ for the bipartitions $(A,B_I)$, $(A,B_{II})$, and $(B_I,B_{II})$ after tracing over the inaccessible region, using a single-mode approximation for the Unruh transformation. Findings: $C(\rho_{AB_I})$ decreases with acceleration but remains finite; $C(\rho_{AB_{II}})$ is nonzero at zero acceleration and grows with acceleration; $C(\rho_{B_IB_{II}})$ is independent of acceleration (a freezing phenomenon with a constant value about 0.558). Significance: demonstrates intrinsic robustness of basis-independent coherence under relativistic noise and motivates extensions to curved spacetime and multipartite relativistic quantum information tasks.

Abstract

We investigate the behavior of basis-independent quantum coherence between two modes of a free Dirac field as observed by relatively accelerated observers. Our findings reveal three key results: (i) the basis-independent coherence between modes A and BI decreases with increasing acceleration but remains finite even in the limit of infinite acceleration; (ii) at zero acceleration, the coherence between modes $A$ and $B_II$ is nonzero contrasting with the behavior of basis-dependent coherence, which typically vanishes in this case; and (iii) the basis-independent coherence between modes BI and BII remains constant regardless of acceleration, exhibiting a freezing phenomenon. These results demonstrate the intrinsic robustness of basis-independent coherence under Unruh effects.

Figures (1)

• Figure 1: Basis-independent coherence as a function of $r$.