Basis-independent coherence in noninertial frames

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 $$A$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> </mml:math> and $$B_{I}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>I</mml:mi> </mml:msub> </mml:math> decreases with increasing acceleration but remains finite even in the limit of infinite acceleration; (ii) at zero acceleration, the coherence between modes $$A$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> </mml:math> and $$B_{II}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mrow> <mml:mi>II</mml:mi> </mml:mrow> </mml:msub> </mml:math> is nonzero-contrasting with the behavior of basis-dependent coherence, which typically vanishes in this case; and (iii) the basis-independent coherence between modes $$B_I$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>I</mml:mi> </mml:msub> </mml:math> and $$B_{II}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mrow> <mml:mi>II</mml:mi> </mml:mrow> </mml:msub> </mml:math> remains constant regardless of acceleration, exhibiting a freezing phenomenon. These results demonstrate the intrinsic robustness of basis-independent coherence under Unruh effects.