Existence of processes violating causal inequalities on time-delocalised subsystems

Wechs, Julian; Branciard, Cyril; Oreshkov, Ognyan

doi:10.48550/arxiv.2201.11832

Cited by 4 publications

(5 citation statements)

References 36 publications

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“…That is, given a state structure, is it possible to realize each of its elements in a lab experiment? Is there a systematic way to relate these abstract mathematical objects to a circuit realization, as is the case for quantum combs [3] and for time-delocalized subsystems [27,28]? One may expect that the canonical decomposition of general state structures into the union of several one-way signaling structures could prove useful for answering this question.…”

Section: Discussionmentioning

confidence: 99%

Projective characterization of higher-order quantum transformations

Timothée¹,

Oreshkov²

2022

Preprint

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Transformations of transformations, also called higher-order transformations, is a natural concept in information processing, which has recently attracted significant interest in the study of quantum causal relations. In this work, a framework for characterizing higher-order quantum transformations which relies on the use of superoperator projectors is presented. More precisely, working with projectors in the Choi-Jamio lkowski picture is shown to provide a handy way of defining the characterization constraints on any class of higher-order transformations. The algebraic properties of these projectors are furthermore identified as a model of multiplicative additive linear logic (MALL). The main novelty of this work is the introduction in the algebra of the 'prec' connector. It is used for the characterization of maps that are no signaling from input to output or the other way around. This allows to assess the possible signaling structure of any maps characterized within the projective framework. The properties of the prec are moreover shown to yield a canonical form for projective expressions. This provides an unambiguous way to compare different higher-order theories.

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Section: Discussionmentioning

confidence: 99%

Projective characterization of higher-order quantum transformations

Timothée¹,

Oreshkov²

2022

Preprint

Self Cite

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“…Such a translation enriches the understanding of the "non-causal" worldjust as the translation between Bell non-locality and contextuality [68][69][70][71][72][73] (see Budroni et al [74] for a recent preprint on that topic)-and speculatively brings forward experimental setups to violate causal order (cf. Oreshkov [75], Purves and Short [8], Wechs et al [9], and Wechs, Branciard, and Oreshkov [76]).…”

Section: Open Questionsmentioning

confidence: 96%

Unlimited non-causal correlations and their relation to non-locality

Baumeler

Gilani

Rashid

2022

Quantum

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Non-causal correlations certify the lack of a definite causal order among localized space-time regions. In stark contrast to scenarios where a single region influences its own causal past, some processes that distribute non-causal correlations satisfy a series of natural desiderata: logical consistency, linear and reversible dynamics, and computational tameness. Here, we present such processes among arbitrary many regions where each region influences every other but itself, and show that the above desiderata are altogether insufficient to limit the amount of "acausality" of non-causal correlations. This leaves open the identification of a principle that forbids non-causal correlations. Our results exhibit qualitative and quantitative parallels with the non-local correlations due to Ardehali and Svetlichny.

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“…A more sophisticated version of this view was developed by Oreshkov [39] (see also [55]). The idea is that we can start by representing the experiment of interest with a circuit with a feedback loop.…”

Section: Figmentioning

confidence: 99%

Causal structure in the presence of sectorial constraints, with application to the quantum switch

Ormrod¹,

Vanrietvelde²,

Barrett³

2022

Preprint

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Existing work on quantum causal structure assumes that one can perform arbitrary operations on the systems of interest. But this condition is often not met. Here, we extend the framework for quantum causal modelling to cases where a system can suffer sectorial contraints, that is, restrictions on the orthogonal subspaces of its Hilbert space that may be mapped to one another. Our framework (a) proves that a number of different intuitions about causal relations turn out to be equivalent; (b) shows that quantum causal structures in the presence of sectorial constraints can be represented with a directed graph; and (c) defines a fine-graining of the causal structure in which the individual sectors of a system bear causal relations, which provides a more detailed analysis than its coarse-grained counterpart. As an example, we apply our framework to purported photonic implementations of the quantum switch to show that while their coarse-grained causal structure is cyclic, their fine-grained causal structure is acyclic. We therefore conclude that these experiments realize indefinite causal order only in a weak sense. Notably, this is the first argument to this effect that is not rooted in the assumption that the causal relata must be localized in spacetime.

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Existence of processes violating causal inequalities on time-delocalised subsystems

Cited by 4 publications

References 36 publications

Projective characterization of higher-order quantum transformations

Projective characterization of higher-order quantum transformations

Unlimited non-causal correlations and their relation to non-locality

Causal structure in the presence of sectorial constraints, with application to the quantum switch

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