Related papers: Non-causal computation
We show that the computational power of the non-causal circuit model, i.e., the circuit model where the assumption of a global causal order is replaced by the assumption of logical consistency, is completely characterized by the complexity…
Causality serves as an abstract notion of time for concurrent systems. A computation is causal, or simply valid, if each observation of a computation event is preceded by the observation of its causes. The present work establishes that this…
The aim of this paper is to discuss a recent result which shows that probabilistic inference in the presence of (unknown) causal mechanisms can be tractable for models that have traditionally been viewed as intractable. This result was…
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…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
Quantum processes with indefinite causal structure emerge when we wonder which are the most general evolutions, allowed by quantum theory, of a set of local systems which are not assumed to be in any particular causal order. These processes…
Causal reasoning is essential to science, yet quantum theory challenges it. Quantum correlations violating Bell inequalities defy satisfactory causal explanations within the framework of classical causal models. What is more, a theory…
Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order…
Requiring that the causal structure between different parties is well-defined imposes constraints on the correlations they can establish, which define so-called causal correlations. Some of these are known to have a "dynamical" causal order…
In sequential circuits, the current output may depend on both past and current inputs. However, certain kinds of sequential circuits do not refer to all of the past inputs to generate the current output; they only refer to a subset of past…
Boolean circuits abstract away from physical details to focus on the logical structure and computational behaviour of digital components. Although such circuits have been studied for many decades, compositionality has been widely ignored or…
We develop a correspondence between the theory of sequential algorithms and classical reasoning, via Kreisel's no-counterexample interpretation. Our framework views realizers of the no-counterexample interpretation as dynamic processes…
Over the past decade, a number of quantum processes have been proposed which are logically consistent, yet feature a cyclic causal structure. However, there is no general formal method to construct a process with an exotic causal structure…
In distributed systems where strong consistency is costly when not impossible, causal consistency provides a valuable abstraction to represent program executions as partial orders. In addition to the sequential program order of each…
The causal structure of a unitary transformation is the set of relations of possible influence between any input subsystem and any output subsystem. We study whether such causal structure can be understood in terms of compositional…
Non-causal correlations certify the lack of a definite causal order among localized space-time regions. In stark contrast to scenarios where a single region influences its own causal past, some processes that distribute non-causal…
In an ordinary quantum algorithm the gates are applied in a fixed order on the systems. The introduction of indefinite causal structures allows to relax this constraint and control the order of the gates with an additional quantum state. It…
Complex information-processing systems, for example quantum circuits, cryptographic protocols, or multi-player games, are naturally described as networks composed of more basic information-processing systems. A modular analysis of such…
The difficulty of explaining non-local correlations in a fixed causal structure sheds new light on the old debate on whether space and time are to be seen as fundamental. Refraining from assuming space-time as given a priori has a number of…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…