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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 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

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

Researchers have long been aiming to understand how the characteristics of Quantum Theory and General Relativity combine to account for regimes in their interface. One reason why this is a hard task is how differently the theories approach…

Quantum Physics · Physics 2023-10-05 Bruna Sahdo

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 this "map" we are going to present the concept of indefinite causal order and make a quick journey through its different flavours. We will start with a broad conceptual motivation for studying indefinite causal order, based on the…

Quantum Physics · Physics 2025-06-06 Jorge Escandón-Monardes

It was recently found that the indefinite causal order in the quantum switch can be certified device-independently when assuming the impossibility of superluminal influences. Here we strengthen this result in two ways. First, we give a…

Quantum Physics · Physics 2024-12-04 Tein van der Lugt , Nick Ormrod

Treating the time of an event as a quantum variable, we derive a scheme in which superpositions in time are used to perform operations in an indefinite causal order. We use some aspects of a recently developed space-time-symmetric formalism…

Quantum Physics · Physics 2022-07-13 David Felce , Nicetu Tibau Vidal , Vlatko Vedral , Eduardo O. Dias

Can causal relations be subject to quantum indefiniteness, similar to other physical properties? The process-matrix framework formalises this possibility: valid processes are defined by what local laboratories can implement, without…

Quantum Physics · Physics 2026-05-29 Jacopo Surace , Shintaro Minagawa , Ravi Kunjwal

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

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…

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

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…

We explore indefinite causal order between events in the context of quasiclassical spacetimes in superposition. We introduce several new quantifiers to measure the degree of indefiniteness of the causal order for an arbitrary finite number…

General Relativity and Quantum Cosmology · Physics 2025-10-07 Samuel Fedida , Anne-Catherine de la Hamette , Viktoria Kabel , Časlav Brukner

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

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

Time-reversal symmetry is a prevalent feature of microscopic physics, including operational quantum theory and classical general relativity. Previous works have studied indefinite causal structure using the language of operational quantum…

Quantum Physics · Physics 2024-06-27 Luke Mrini , Lucien Hardy

Quantum processes can exhibit scenarios beyond a fixed order of events. We propose information inequalities that, when violated, constitute sufficient conditions to certify quantum processes without a fixed causal order -- causally…

Quantum Physics · Physics 2025-05-21 Matheus Capela , Kaumudibikash Goswami

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 suggested that causal structures are both dynamical, because of general relativity, and indefinite, due to quantum theory. The process matrix formalism furnishes a framework for quantum mechanics on indefinite causal…

Quantum Physics · Physics 2018-03-28 Esteban Castro-Ruiz , Flaminia Giacomini , Časlav Brukner
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