Related papers: Causality in Higher Order Process Theories
In recent years, various frameworks have been proposed for the study of quantum processes with indefinite causal order. In particular, quantum circuits with quantum control of causal order (QC-QCs) form a broad class of physical supermaps…
Univalent homotopy type theory (HoTT) may be seen as a language for the category of $\infty$-groupoids. It is being developed as a new foundation for mathematics and as an internal language for (elementary) higher toposes. We develop the…
Causal modelling provides a powerful set of tools for identifying causal structure from observed correlations. It is well known that such techniques fail for quantum systems, unless one introduces `spooky' hidden mechanisms. Whether one can…
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…
Quantum resources exist in a hierarchy of multiple levels. At order zero, quantum states are transformed by linear maps (channels, or gates) in order to perform computations or simulate other states. At order one, gates and channels are…
We explore the sense in which the existing constructions for higher-order maps on quantum theory based on causality constraints and compositionality constraints respectively, coincide. More precisely, we construct a functor F : Caus(C) ->…
We study the signalling structure of higher order quantum maps from an order-theoretic perspective, building on the combinatorial characterization of higher order types by Bisio and Perinotti. We have shown in a previous work…
We propose Universal Causality, an overarching framework based on category theory that defines the universal property that underlies causal inference independent of the underlying representational formalism used. More formally, universal…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the…
This paper presents a framework for Quantum causal modeling based on the interpretation of causality as a relation between an observer's probability assignments to hypothetical or counterfactual experiments. The framework is based on the…
Homotopy type theory (HoTT) can be seen as a generalisation of structural set theory, in the sense that 0-types represent structural sets within the more general notion of types. For material set theory, we also have concrete models as…
Causality is one of the most fundamental notions in physics. Generalized probabilistic theories (GPTs) and the process matrix framework incorporate it in different forms. However, a direct connection between these frameworks remains…
The Causaloid framework is an operational approach aimed to house both the radical aspects of General Relativity -- dynamic causal structure, and Quantum Theory -- indefiniteness, to provide a scaffolding that might be suitable for Quantum…
We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. We define causaltopes, our chosen portmanteau of "causal polytopes", for…
We study higher order quantum maps in the context of a *-autonomous category of affine subspaces. We show that types of higher order maps can be identified with certain Boolean functions that we call type functions. By an extension of this…
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…
Existing work on quantum causal structure assumes that one can perform arbitrary operations on the systems of interest. But this condition is often not met. Here, we extend the framework for quantum causal modelling to situations where a…
Can a large system be fully characterized using its subsystems via inductive reasoning? Is it possible to completely reduce the behavior of a complex system to the behavior of its simplest "atoms"? In the following paper we answer these…
The process matrix framework [O. Oreshkov, F. Costa, and C. Brukner, Nature Communications {\bf3}, 1092 (2012)] can describe general physical theory where locally operations are described by completely-positive maps but globally no fixed…