Causally nonseparable processes admitting a causal model

Feix, Adrien; Araújo, Mateus; Brukner, Časlav

doi:10.1088/1367-2630/18/8/083040

Cited by 38 publications

(58 citation statements)

References 27 publications

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“…In fact, we will see that the natural generalization of condition (51) to the multipartite case is not equivalent to the condition that a process is causal (the same holds also for other possible generalizations that we will discuss later). Very recently, the same was shown to hold also in the bipartite case, by Feix, Araújo, and Brukner [38].…”

mentioning

confidence: 58%

Causal and causally separable processes

2016

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confidence: 58%

Causal and causally separable processes

2016

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“…Our use of the notation p here is consistent e.g. with that of [14,15,18,22,27,34,35,43,44], and would instead correspond to the notation  in [17] (also used in [2]).…”

Section: A23 Particular Cases Withmentioning

confidence: 98%

“…To generate random process matrices, one could follow the hit-and-run approach of [43]. Although this approach is guaranteed to sample process matrices uniformly, the high dimensionality of the space of valid process matrices (in this scenario it is 7597-dimensional) renders this approach intractable.…”

Section: Appendix D Equivalence Between Oreshkov and Giarmatziʼs Extmentioning

confidence: 99%

On the definition and characterisation of multipartite causal (non)separability

2019

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The concept of causal nonseparability has been recently introduced, in opposition to that of causal separability, to qualify physical processes that locally abide by the laws of quantum theory, but cannot be embedded in a well-defined global causal structure. While the definition is unambiguous in the bipartite case, its generalisation to the multipartite case is not so straightforward. Two seemingly different generalisations have been proposed, one for a restricted tripartite scenario and one for the general multipartite case. Here we compare the two, showing that they are in fact inequivalent. We propose our own definition of causal (non)separability for the general case, which-although a priori subtly different -turns out to be equivalent to the concept of 'extensible causal (non)separability' introduced before, and which we argue is a more natural definition for general multipartite scenarios. We then derive necessary, as well as sufficient conditions to characterise causally (non)separable processes in practice. These allow one to devise practical tests, by generalising the tool of witnesses of causal nonseparability. J Wechs et ali.e. the unitaries are applied in a 'superposition of orders'. The output state is then sent to a third party C (Charlie) who can measure the control qubit, and possibly also the target system. The protocol just described can straightforwardly be generalised to the case where A and Bʼs operations are general quantum instruments instead of unitaries. This so-called quantum switch can be understood as a quantum supermap [23], or higher order transformation, that maps A and Bʼs local operations to the overall global transformation. It cannot be realised by inserting the local operations into a circuit with a well-defined causal order, and therefore constitutes a new resource for quantum computation that goes beyond causally ordered quantum circuits [4]. It has attracted particular interest as a consequence of being readily implementable, and indeed several implementations have been experimentally realised [24-28]. Consequent work has sought to clarify whether such implementations can New J. Phys. 21 (2019) 013027 J Wechs et al New J. Phys. 21 (2019) 013027 J Wechs et al 12 1 2 (which may be empty), respectively, one must have 18 New J. Phys. 21 (2019) 013027 J Wechs et al W k M k 1 1 is causally separable. 30 New J. Phys. 21 (2019) 013027 J Wechs et al

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“…Proof. It has been shown in [34] that the process matrix of example 1 can be mixed with a certain amount of white noise and still be causally non-separable. In detail, the process matrix…”

Section: Probability Of Successmentioning

confidence: 99%

“…1 [34], this means that there are process matrices that violate causal inequalities and can be implemented with a success probability of more than 50%. , Figure 6.…”

Section: Probability Of Successmentioning

confidence: 99%

Entanglement, non-Markovianity, and causal non-separability

Milz

Pollock

et al. 2018

New J. Phys.

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Quantum mechanics, in principle, allows for processes with indefinite causal order. However, most of these causal anomalies have not yet been detected experimentally. We show that every such process can be simulated experimentally by means of non-Markovian dynamics with a measurement on additional degrees of freedom. In detail, we provide an explicit construction to implement arbitrary a causal processes. Furthermore, we give necessary and sufficient conditions for open system dynamics with measurement to yield processes that respect causality locally, and find that tripartite entanglement and nonlocal unitary transformations are crucial requirements for the simulation of causally indefinite processes. These results show a direct connection between three counter-intuitive concepts: entanglement, non-Markovianity, and causal non-separability.

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Causally nonseparable processes admitting a causal model

Cited by 38 publications

References 27 publications

Causal and causally separable processes

Causal and causally separable processes

On the definition and characterisation of multipartite causal (non)separability

Entanglement, non-Markovianity, and causal non-separability

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