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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

In early days of quantum theory it was believed that the results of measurements performed on two distant physical systems should be uncorrelated thus their quantum state should be separable it means described by a simple tensor product of…

Quantum Physics · Physics 2012-10-26 Marian Kupczynski

Causal knowledge is vital for effective reasoning in science, as causal relations, unlike correlations, allow one to reason about the outcomes of interventions. Algorithms that can discover causal relations from observational data are based…

Machine Learning · Statistics 2019-11-12 Anish Dhir , Ciarán M. Lee

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

A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…

Quantum Physics · Physics 2015-06-26 Antonio Cassa

The measurement process of observables in a quantum system comes out to be an unsovable problem which started in the early times of the development of the theory. In the present note we consider the measured system part of an open system…

Quantum Physics · Physics 2023-12-21 Jean Richert , Tarek Khalil

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

A causal input-output system may be described by a function space for inputs, a function space for outputs, and a causal operator mapping the input space into the output space. A particular representation of the state of such a system at…

Dynamical Systems · Mathematics 2010-09-28 Demetrios Serakos

The unrivaled robustness of topologically ordered states of matter against perturbations has immediate applications in quantum computing and quantum metrology, yet their very existence poses a challenge to our understanding of phase…

Strongly Correlated Electrons · Physics 2022-09-27 Amit Jamadagni , Hendrik Weimer

This paper establishes the existence of observable footprints that reveal the "causal dispositions" of the object categories appearing in collections of images. We achieve this goal in two steps. First, we take a learning approach to…

Machine Learning · Statistics 2017-11-01 David Lopez-Paz , Robert Nishihara , Soumith Chintala , Bernhard Schölkopf , Léon Bottou

Quantum nonseparability is a central feature of quantum mechanics, and raises important philosophical questions. Interestingly, a particular theoretical development of quantum mechanics, called the process matrix formalism (PMF), features…

Quantum Physics · Physics 2025-01-22 Laurie Letertre

Standard quantum mechanics undeniably violates the notion of separability that classical physics accustomed us to consider as valid. By relating the phenomenon of quantum nonseparability to the all-important concept of potentiality, we…

Quantum Physics · Physics 2008-11-25 Vassilios Karakostas

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

In relativistic Quantum Field Theory (QFT) ideal measurements of certain observables are physically impossible without violating causality. This prompts two questions: i) can a given observable be ideally measured in QFT, and ii) if not, in…

Quantum Physics · Physics 2022-01-14 I. Jubb

Explaining observations in terms of causes and effects is central to all of empirical science. Correlations between entangled quantum particles, however, seem to defy such an explanation. To recover a causal picture in this case, some of…

Quantum Physics · Physics 2016-09-05 M. Ringbauer , C. Giarmatzi , R. Chaves , F. Costa , A. G. White , A. Fedrizzi

Causal discovery, the task of automatically constructing a causal model from data, is of major significance across the sciences. Evaluating the performance of causal discovery algorithms should ideally involve comparing the inferred models…

Artificial Intelligence · Computer Science 2021-08-26 Maxime Peyrard , Robert West

Causality underpins all logical reasoning. However, the causal structure in quantum processes can be far from intuitive, often differing from its classical counterpart in relativity, which is defined by the light cone. In particular, in…

Quantum Physics · Physics 2026-01-21 Hong-Yi Wang , Haifeng Tang , Xiao-Liang Qi

After two decades of research on indefinite causality, a philosophical lesson emerges: the tension between operational quantum theory and dynamical spacetime physics is unbridgeable if one believes both types of theories to be fundamental.…

Quantum Physics · Physics 2025-12-30 Alexei Grinbaum

In quantum causality and quantum information, there is a vast landscape of abstract quantum protocols permitting cyclic or non-acyclic causal structures between operations, including frameworks for indefinite causal order and higher-order…

Quantum Physics · Physics 2026-05-12 Matthias Salzger , V. Vilasini

A property of a system is called actual, if the observation of the test that pertains to that property, yields an affirmation with certainty. We formalize the act of observation by assuming that the outcome correlates with the state of the…

Quantum Physics · Physics 2015-06-26 Sven Aerts