The space of logically consistent classical processes without causal order

Baumeler, Ämin; Wolf, Stefan

doi:10.1088/1367-2630/18/1/013036

Cited by 64 publications

(120 citation statements)

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“…Note added-While finishing writing up this manuscript, we became aware that the concept of causal polytopes introduced here was also referred to (with proper reference to our work) in [14], where the emphasis was put on multipartite scenarios, and in [42], where the authors also introduced, for the multipartite case as well, larger polytopes of logically consistent but possibly noncausal classical processes.…”

Section: Resultsmentioning

confidence: 99%

The simplest causal inequalities and their violation

et al. 2015

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In a scenario where two parties share, act on and exchange some physical resource, the assumption that the parties' actions are ordered according to a definite causal structure yields constraints on the possible correlations that can be established. We show that the set of correlations that are compatible with a definite causal order forms a polytope, whose facets define causal inequalities. We fully characterize this causal polytope in the simplest case of bipartite correlations with binary inputs and outputs. We find two families of nonequivalent causal inequalities; both can be violated in the recently introduced framework of process matrices, which extends the standard quantum formalism by relaxing the implicit assumption of a fixed causal structure. Our work paves the way to a more systematic investigation of causal inequalities in a theory-independent way, and of their violation within the framework of process matrices.This approach is more powerful as it can detect all causally nonseparable process matrices, while not all causally nonseparable process matrices can violate a causal inequality [13,14]. Furthermore, physical implementations of certain (multipartite) causally nonseparable process matrices, and of corresponding causal witnesses that detect their causal nonseparability, have been proposed [13][14][15] and even realized experimentally [16], while it is still not known whether there actually exist any physically realizable process that violates a causal inequality. Nevertheless, the device-independent approach is still of interest as it relaxes the requirement to trust the functioning and the operations implemented by one's devices in an experiment. It is furthermore also theoryindependent: causal inequalities can in principle be tested, and correlations with no definite causal order can be identified whatever the description of the physical resource is-whether we use the process matrix framework or any other theory to be discovered in the future. A related open question is whether the ability to violate causal inequalities can-in analogy with Bell nonlocality [17]-be exploited as a resource, just like causally nonseparable process matrices provide advantages for information-theoretical [18], computational [19], and communication complexity [20] tasks.Our paper aims at providing a better understanding of the device-independent characterization of correlations that are compatible with a definite causal order or not. We show that bipartite correlations with a definite causal order form a convex polytope, whose facets correspond to causal inequalities (section 2). We characterize this causal polytope in the simplest scenario where the two parties observe correlations with binary inputs and outputs, which gives us two families of new causal inequalities. We then investigate their possible violation in the framework of process matrices, and find that these can indeed be violated (section 3). This provides an example of 'noncausal' process matrix correlations in a simpler scenario than that considered i...

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Section: Resultsmentioning

confidence: 99%

The simplest causal inequalities and their violation

et al. 2015

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“…It is known that for two parties, non-causal logically consistent classical processes do not exist [26,36]. For three parties or more, however, such processes do exist [30,37]. We describe two non-causal logically consistent classical processes.…”

Section: Non-causal Classical Processesmentioning

confidence: 98%

“…, Theorem 6.  [30] By using the logically consistent classical process framework, game 3 can be won perfectly. The logically consistent classical processE to perfectly win game 3 is…”

Section: Proofmentioning

confidence: 99%

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Device-independent test of causal order and relations to fixed-points

Baumeler¹,

Wolf²

2016

New J. Phys.

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Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency.The assumption of a fixed causal order between a set of parties, together with free randomness, implies device-independent inequalities-just as the assumption of locality does. It is known that local validity of quantum theory is consistent with violating such inequalities. Moreover, for three parties or more, even the (stronger) assumption of local classical probability theory plus logical consistency allows for violating causal inequalities. Here, we show that a classical environment (with which the parties interact), possibly containing loops, is logically consistent if and only if whatever the involved parties do, there is exactly one fixed-point, the latter being representable as a mixture of deterministic fixedpoints. We further show that the non-causal view allows for a model of computation strictly more powerful than computation in a world of fixed causal orders. Historical background on space, time, and causalityThe debate about as how fundamental space and time are to be seen has a long history in within natural philosophy. In pre-Socratic time, the opposite standpoints on the question have arisen in the views of Parmenides as opposed to Heraclitus: for the latter, the stage set by a fundamental space-time structure is where the play of permanent change-for him synonymous to existence-happens. Parmenides' world view, on the other hand, is static and such that space and, in particular, time emerge only subsequently and only subjectively. The described opposition can be seen as a predecessor of the famous debate between Newton and Leibniz [13], centuries later. Whereas Newton starts from an initially given and static space-time, Leibniz was criticising that view: space, for instance, is for him merely relational and not absolute. The course of occidental science decided to go for Newtonʼs (overly successful) picture, until Leibniz' relational view was finally adopted by Mach. Indeed, Machʼs principle states that inertial forces are purely relational, and it was the crystallisation point of Einsteinʼs general relativity although the latter did, in the end, not satisfy the principle; however, it does propose a dynamic space-time structure (still absolute, though) in which, additionally, space and time become closely intertwined where they have been seen independently in Newtonʼs picture.

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“…A more interesting example is the quantum switch, where according to event A's causal reference frame, event B is in a controlled superposition of being in the future or in the past (and vice-versa). In section 4, we study a new example of a causal inequality violating pure tripartite process, obtained by taking the time-reverse of a known non-causal classical process [27,28]. We point out some curious features in the causal frame description of this process, which may explain why such processes do not have a known realisation in the laboratory.…”

Section: Introductionmentioning

confidence: 99%

Observer-dependent locality of quantum events

Guérin

Brukner

2018

New J. Phys.

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In general relativity, the causal structure between events is dynamical, but it is definite and observerindependent; events are point-like and the membership of an event A in the future or past light-cone of an event B is an observer-independent statement. When events are defined with respect to quantum systems however, nothing guarantees that the causal relationship between A and B is definite. We propose to associate a causal reference frame corresponding to each event, which can be interpreted as an observerdependent time according to which an observer describes the evolution of quantum systems. In the causal reference frame of one event, this particular event is always localised, but other events can be 'smeared out' in the future and in the past. We do not impose a predefined causal order between the events, but only require that descriptions from different reference frames obey a global consistency condition. We show that our new formalism is equivalent to the pure process matrix formalism (Araújo et al 2017 Quantum 1 10). The latter is known to predict certain multipartite correlations, which are incompatible with the assumption of a causal ordering of the events-these correlations violate causal inequalities. We show how the causal reference frame description can be used to gain insight into the question of realisability of such strongly non-causal processes in laboratory experiments. As another application, we use causal reference frames to revisit a thought experiment Zych et al (arXiv:1708.00248) where the gravitational time dilation due to a massive object in a quantum superposition of positions leads to a superposition of the causal ordering of two events.

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The space of logically consistent classical processes without causal order

Cited by 64 publications

References 46 publications

The simplest causal inequalities and their violation

The simplest causal inequalities and their violation

Device-independent test of causal order and relations to fixed-points

Observer-dependent locality of quantum events

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