Consistent circuits for indefinite causal order

Fuente: arXiv
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Main Authors: Vanrietvelde, Augustin, Ormrod, Nick, Kristjánsson, Hlér, Barrett, Jonathan
Format: Preprint
Published: 2022
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author Vanrietvelde, Augustin
Ormrod, Nick
Kristjánsson, Hlér
Barrett, Jonathan
author_facet Vanrietvelde, Augustin
Ormrod, Nick
Kristjánsson, Hlér
Barrett, Jonathan
contents Over the past decade, a number of quantum processes have been proposed which are logically consistent, yet feature a cyclic causal structure. However, there is no general formal method to construct a process with an exotic causal structure in a way that ensures, and makes clear why, it is consistent. Here we provide such a method, given by an extended circuit formalism. This only requires directed graphs endowed with Boolean matrices, which encode basic constraints on operations. Our framework (a) defines a set of elementary rules for checking the validity of any such graph, (b) provides a way of constructing consistent processes as a circuit from valid graphs, and (c) yields an intuitive interpretation of the causal relations within a process and an explanation of why they do not lead to inconsistencies. We display how several standard examples of exotic processes, including ones that violate causal inequalities, are among the class of processes that can be generated in this way; we conjecture that this class in fact includes all unitarily extendible processes.
format Preprint
id arxiv_https___arxiv_org_abs_2206_10042
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Consistent circuits for indefinite causal order
Vanrietvelde, Augustin
Ormrod, Nick
Kristjánsson, Hlér
Barrett, Jonathan
Quantum Physics
Over the past decade, a number of quantum processes have been proposed which are logically consistent, yet feature a cyclic causal structure. However, there is no general formal method to construct a process with an exotic causal structure in a way that ensures, and makes clear why, it is consistent. Here we provide such a method, given by an extended circuit formalism. This only requires directed graphs endowed with Boolean matrices, which encode basic constraints on operations. Our framework (a) defines a set of elementary rules for checking the validity of any such graph, (b) provides a way of constructing consistent processes as a circuit from valid graphs, and (c) yields an intuitive interpretation of the causal relations within a process and an explanation of why they do not lead to inconsistencies. We display how several standard examples of exotic processes, including ones that violate causal inequalities, are among the class of processes that can be generated in this way; we conjecture that this class in fact includes all unitarily extendible processes.
title Consistent circuits for indefinite causal order
topic Quantum Physics
url https://arxiv.org/abs/2206.10042