van der Lugt, Tein (2021) Relativistic limits on quantum operations. [Preprint]

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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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Item Type:	Preprint
Creators:	Creators Email ORCID van der Lugt, Tein teinvdlugt@gmail.com 0000-0003-3648-8055
Additional Information:	Submitted in May 2021 in partial fulfillment of the requirements for Part III of the Mathematical Tripos at the University of Cambridge.
Keywords:	Quantum mechanics; Relativity theory; Quantum operations; Relativistic causality; Algebraic quantum field theory; Hilbert space
Subjects:	Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory
Depositing User:	Mr Tein van der Lugt
Date Deposited:	12 Aug 2021 03:12
Last Modified:	12 Aug 2021 03:12
Item ID:	19427
Subjects:	Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory
Date:	6 May 2021
URI:	https://philsci-archive.pitt.edu/id/eprint/19427

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• Relativistic limits on quantum operations. (deposited 07 Aug 2021 23:52)
  • Relativistic limits on quantum operations. (deposited 12 Aug 2021 03:12) [Currently Displayed]

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