Relativistic limits on quantum operations
- URL: http://arxiv.org/abs/2108.05904v1
- Date: Thu, 12 Aug 2021 18:04:20 GMT
- Title: Relativistic limits on quantum operations
- Authors: Tein van der Lugt
- Abstract summary: We review a recent proposal by Fewster and Verch for a generally covariant measurement scheme in AQFT.
We argue that the framework as set up in its original proposal can be greatly simplified without losing generality or physical motivation.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this essay, we explore the limits imposed by the impossibility of
superluminal signalling on the class of physically realisable quantum
operations, focusing on the difference in approaches one can take towards this
problem in Hilbert space quantum theory and algebraic quantum field theory
(AQFT). We review a recent proposal by Fewster and Verch for a generally
covariant measurement scheme in AQFT, which we call the FV scheme; along the
way, we argue that the framework as set up in its original proposal can be
greatly simplified without losing generality or physical motivation. We then
discuss the problem, introduced by Sorkin, that naive generalisations of the
notion of operation to the relativistic context can lead to signalling between
spacelike observers by introducing a third observer. We consider approaches to
tackle this problem in Hilbert space quantum theory and argue that these are
sometimes ambiguous, since the physical (im)possibility of operations depends
in part on the specific spacetime embodiment of the quantum system under
consideration, which lies outside the Hilbert space formalism. In the AQFT
context, we review and generalise a recent result showing that operations
induced by the FV measurement scheme do not enable superluminal signalling. We
connect this result to Hilbert space by introducing a concrete model of AQFT,
which we call the `hybrid model' as it provides a way to explicitly embed
Hilbert space quantum theory into spacetime using the formalism of AQFT.
Finally, we show that in this model, under suitable necessary and sufficient
conditions, the converse result also holds: every operation that does not
enable superluminal signalling can be implemented in the FV framework.
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