Einstein causality of quantum measurements in the Tomonaga-Schwinger picture

• URL: http://arxiv.org/abs/2506.14693v3
• Date: Wed, 25 Jun 2025 08:37:13 GMT
• Title: Einstein causality of quantum measurements in the Tomonaga-Schwinger picture
• Authors: Samuel Fedida,
• Abstract summary: We show that selective quantum measurements satisfy a state-independent anyonic commutation relation over spacelike-separated regions.<n>In the simplistic scenario where the measurements are assumed to be instantaneous, this implies quantum no-signalling for non-selective measurements.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: When quantum measurements are conducted over spacelike-separated regions of spacetime, a natural and commonly assumed physical postulate, called Einstein causality, asserts that they should commute. In this paper, we provide a generalisation to L\"uders' rule \`a la Aharonov-Albert in those globally hyperbolic spacetimes which allow unitarily equivalent Hilbert spaces to be defined along Cauchy hypersurfaces, thus relying on the existence of an interaction picture \`a la Tomonaga-Schwinger. We show that under this rule, selective quantum measurements satisfy a state-independent anyonic commutation relation over spacelike-separated (pre)compact regions. We highlight that this propagates to positive operator-valued measures (POVMs), where the commutation is necessarily bosonic. In the simplistic scenario where the measurements are assumed to be instantaneous, this implies quantum no-signalling for non-selective measurements. We then examine Sorkin's impossible measurements and show that immediate contradictions can be averted as long as collapse-inducing measurements are irreversible. We finish by discussing the possibility of extending such results beyond the interaction picture.

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