Quantum diffeomorphisms cannot make indefinite causal order definite
- URL: http://arxiv.org/abs/2211.15685v1
- Date: Mon, 28 Nov 2022 19:00:01 GMT
- Title: Quantum diffeomorphisms cannot make indefinite causal order definite
- Authors: Anne-Catherine de la Hamette, Viktoria Kabel, Marios Christodoulou,
and \v{C}aslav Brukner
- Abstract summary: We provide an unambiguous definition of causal order between two events in terms of worldline coincidences and the proper time of a third particle.
We show that superpositions of causal order defined as such cannot be rendered definite even through the most general class of coordinate transformations.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The study of indefinite causal order has seen rapid development, both
theoretically and experimentally, in recent years. While classically the causal
order of two timelike separated events A and B is fixed - either A before B or
B before A - this is no longer true in quantum theory. There, it is possible to
encounter superpositions of causal orders. In light of recent work on quantum
reference frames, which reveals that the superposition of locations, momenta,
and other properties can depend on the choice of reference frame or coordinate
system, the question arises whether this also holds true for superpositions of
causal orders. Here, we provide a negative answer to this question for quantum
diffeomorphisms. First, we provide an unambiguous definition of causal order
between two events in terms of worldline coincidences and the proper time of a
third particle. Then, we show that superpositions of causal order defined as
such cannot be rendered definite even through the most general class of
coordinate transformations - quantum-controlled, independent diffeomorphisms in
each branch. Finally, based on our results, we connect the information
theoretic and gravitational perspectives on indefinite causal order.
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