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In quantum mechanics events can happen in no definite causal order: in practice this can be verified by measuring a causal witness, in the same way that an entanglement witness verifies entanglement. Indefinite causal order can be observed…

Quantum Physics · Physics 2018-11-05 K. Goswami , C. Giarmatzi , M. Kewming , F. Costa , C. Branciard , J. Romero , A. G. White

Classically the causal order of two timelike separated events A and B is fixed -- either A before B or B before A. This is no longer true in quantum theory, where it is possible to encounter superpositions of causal orders. The quantum…

In the past decade, the toolkit of quantum information has been expanded to include processes in which the basic operations do not have definite causal relations. Originally considered in the context of the unification of quantum mechanics…

Quantum Physics · Physics 2024-07-22 Lee A. Rozema , Teodor Strömberg , Huan Cao , Yu Guo , Bi-Heng Liu , Philip Walther

Understanding the physical world fundamentally relies on the assumption that events are temporally ordered, with past events serving as causes for future ones. However, quantum mechanics permits events to occur in a superposition of causal…

Quantum Physics · Physics 2025-08-07 Dengke Qu , Quan Lin , Lei Xiao , Xiang Zhan , Peng Xue

Our common understanding of the physical world deeply relies on the notion that events are ordered with respect to some time parameter, with past events serving as causes for future ones. Nonetheless, it was recently found that it is…

It was recently realised that quantum theory allows for so-called causally nonseparable processes, which are incompatible with any definite causal order. This was first suggested on a rather abstract level by the formalism of process…

Quantum Physics · Physics 2016-05-20 Cyril Branciard

Recent developments in the formalisation of quantum causal structures have made it possible to test and compare hypotheses about causal structure empirically, rather than being a-priori assumptions. Such differences in causal structure may…

Quantum Physics · Physics 2026-05-28 Declan Maguire , Fabio Costa

The study of causal relations has recently been applied to the quantum realm, leading to the discovery that not all physical processes have a definite causal structure. While indefinite causal processes have previously been experimentally…

In classical physics, events follow a definite causal order: the past influences the future, but not the reverse. Quantum theory, however, permits superpositions of causal orders -- so-called indefinite causal orders -- which can provide…

Quantum Physics · Physics 2026-04-29 Carla M. D. Richter , Michael Antesberger , Huan Cao , Philip Walther , Lee A. Rozema

Quantum mechanics allows for coherent control over the order in which different processes take place on a target system, giving rise to a new feature known as indefinite causal order. Indefinite causal order provides a resource for quantum…

Quantum causality extends the conventional notion of fixed causal structure by allowing channels and operations to act in an indefinite causal order. The importance of such an indefinite causal order ranges from the foundational---e.g.…

Quantum Physics · Physics 2020-09-29 K. Goswami , J. Romero

A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…

Probability · Mathematics 2011-09-22 Graham Brightwell , Malwina Luczak

Recent frameworks describing quantum mechanics in the absence of a global causal order admit the existence of causally indefinite processes, where it is impossible to ascribe causal order for events A and B. These frameworks even allow for…

Quantum Physics · Physics 2021-05-11 Simon Milz , Dominic Jurkschat , Felix A. Pollock , Kavan Modi

The quantum switch, the canonical example of a process with indefinite causal order, has been claimed to provide various advantages over processes with definite causal orders for some particular tasks in the field of quantum metrology. In…

Quantum Physics · Physics 2024-06-27 Raphaël Mothe , Cyril Branciard , Alastair A. Abbott

The idea that events obey a definite causal order is deeply rooted in our understanding of the world and at the basis of the very notion of time. But where does causal order come from, and is it a necessary property of nature? We address…

Quantum Physics · Physics 2013-02-15 Ognyan Oreshkov , Fabio Costa , Caslav Brukner

When transforming pairs of independent quantum operations according to the fundamental rules of quantum theory, an intriguing phenomenon emerges: some such higher-order operations may act on the input operations in an indefinite causal…

Quantum Physics · Physics 2022-02-08 Jessica Bavaresco , Mateus Araújo , Časlav Brukner , Marco Túlio Quintino

Quantum theory is compatible with scenarios in which the order of operations is indefinite. Experimental investigations of such scenarios, all of which have been based on a process known as the quantum switch, have provided demonstrations…

Quantum Physics · Physics 2023-06-12 Tein van der Lugt , Jonathan Barrett , Giulio Chiribella

Quantum theory is in principle compatible with scenarios where physical processes occur in an indefinite order, potentially yielding advantages in a broad range of information processing tasks. However, advantages in communication, the most…

Quantum Physics · Physics 2026-03-26 Xuanqiang Zhao , Benchi Zhao , Cyril Branciard , Giulio Chiribella

Operations performing on quantum batteries are extended to scenarios where we no longer force the existence of definite causal order of occurrence between distinct processes. In contrast to standard theories, the so called indefinite causal…

Quantum Physics · Physics 2021-05-27 Yuanbo Chen , Yoshihiko Hasegawa

Recently, the possible existence of quantum processes with indefinite causal order has been extensively discussed, in particular using the formalism of process matrices. Here we give a new perspective on this question, by establishing a…

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