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We describe a new class of models of quantum space-time based on energetic causal sets and show that under natural conditions space-time emerges from them. These are causal sets whose causal links are labelled by energy and momentum and…

General Relativity and Quantum Cosmology · Physics 2016-02-22 Marina Cortês , Lee Smolin

In theories of communication, it is usually presumed that the involved parties perform actions in a fixed causal order. However, practical and fundamental reasons can induce uncertainties in the causal order. Here we show that a maximal…

Quantum Physics · Physics 2019-11-20 Ding Jia , Fabio Costa

Time has a fundamentally different character in quantum mechanics and in general relativity. In quantum theory events unfold in a fixed time order while in general relativity temporal order is influenced by the distribution of matter. When…

Quantum Physics · Physics 2020-06-17 Magdalena Zych , Fabio Costa , Igor Pikovski , Caslav Brukner

In the classical world, physical events always happen in a fixed causal order. However, it was recently revealed that quantum mechanics allows events to occur with indefinite causal order (ICO). In this study, we use an optical quantum…

In quantum computing, the nonstabilizerness of quantum operations is crucial for understanding and quantifying quantum speedups. In this study, we explore the phenomena of nonstabilizerness of the quantum SWITCH, a novel structure that…

Quantum Physics · Physics 2024-07-31 Yin Mo , Chengkai Zhu , Zhiping Liu , Mingrui Jing , Xin Wang

Quantum theory allows for the superposition of causal orders between operations, i.e., for an indefinite causal order; an implication of the principle of quantum superposition. Since a higher theory might also admit this feature, an…

Quantum Physics · Physics 2024-11-08 Kuntal Sengupta

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 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

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

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

Quantum superposition, a cornerstone of quantum mechanics, enables systems to exist in multiple states simultaneously, giving rise to probabilistic outcomes. In quantum information science, conditional entropy has become a key metric for…

General Physics · Physics 2024-10-21 Daegene Song

Quantum mechanics allows the occurrence of events without having any definite causal order. Here, it is shown that the application of two different thermal channels in the causally inseparable order can enhance the potential to extract…

Quantum Physics · Physics 2020-09-23 Tamal Guha , Mir Alimuddin , Preeti Parashar

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

The superposition of causal order shows promise in various quantum technologies. However, the fragility of quantum systems arising from environmental interactions, leading to dissipative behavior and irreversibility, demands a deeper…

The questions we raise in this letter are as follows: What is the most general representation of a quantum state at a single point in time? Can we adapt the current formalisms to situations where the order of quantum operations is…

Quantum Physics · Physics 2024-06-21 Onur Pusuluk , Zafer Gedik , Vlatko Vedral

Wave--particle duality is a cornerstone of quantum mechanics, traditionally formulated under definite causal order. We investigate how complementarity is modified when the temporal order of operations is coherently superposed, as in the…

Quantum Physics · Physics 2026-03-31 Mohd Asad Siddiqui , Md Qutubuddin , Tabish Qureshi

In standard quantum theory, the causal relations between operations are fixed. One can relax this notion by allowing for dynamical arrangements, where operations may influence the causal relations of future operations, as certified by…

Quantum Physics · Physics 2025-10-23 Veronika Baumann , Ämin Baumeler , Eleftherios-Ermis Tselentis

Quantum supermaps are transformations that map quantum operations to quantum operations. It is known that quantum supermaps which respect a definite, predefined causal order between their input operations correspond to fixed-order quantum…

Quantum Physics · Physics 2023-06-21 Julian Wechs , Hippolyte Dourdent , Alastair A. Abbott , Cyril Branciard

Understanding the causal influences that hold among parts of a system is critical both to explaining that system's natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is…

Quantum Physics · Physics 2018-01-22 Jean-Philippe W. MacLean , Katja Ried , Robert W. Spekkens , Kevin J. Resch

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…