Related papers: Quantum computation with indefinite causal structu…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
Classical circuit complexity characterizes parallel computation in purely combinatorial terms, ignoring the physical constraints that govern real hardware. The standard classes $\mathbf{NC}$, $\mathbf{AC}$, and $\mathbf{TC}$ treat unlimited…
Identifying causal order from restricted projective data is generally nontrivial. When two quantum players interact only through an unobserved environment, the available local measurement statistics are typically not tomographically…
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…
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…
Physical processes in the quantum regime possess non-classical properties of quantum mechanics. However, methods for quantitatively identifying such processes are still lacking. Accordingly, in this study, we develop a framework for…
We investigate quantum correlations in time in different approaches. We assume that temporal correlations should be treated in an even-handed manner with spatial correlations. We compare the pseudo-density matrix formalism with several…
In this article we set out to understand the significance of the process matrix formalism and the quantum causal modelling programme for ongoing disputes about the role of causation in fundamental physics. We argue that the process matrix…
Interacting many-body systems with explicitly accessible spatio-temporal correlation functions are extremely rare, especially in the absence of integrability. Recently, we identified a remarkable class of such systems and termed them…
In general relativity, `causal structure' refers to the partial order on space-time points (or regions) that encodes time-like relationships. Recently, quantum information and quantum foundations saw the emergence of a `causality…
The recently developed framework for quantum theory with no global causal order allows for quantum processes in which operations in local laboratories are neither causally ordered nor in a probabilistic mixture of definite causal orders.…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
The constraints arising for a general set of causal relations, both classically and quantumly, are still poorly understood. As a step in exploring this question, we consider a coherently controlled superposition of "direct-cause" and…
Closed timelike curves (CTCs) appear in many solutions of the Einstein equation, even with reasonable matter sources. These solutions appear to violate causality and so are considered problematic. Since CTCs reflect the global properties of…
The D-CTC condition is a condition originally proposed by David Deutsch as a condition on states of a quantum communication network that contains "backward time-steps" in some of its branches. It has been argued that this is an analogue for…
We study quantum processes, as one parameter families of differentiable completely positive and trace preserving (CPTP) maps. Using different representations of the generator, and the Sylvester criterion for positive semi-definite matrices,…
Discrete time crystals (DTCs) are nonequilibrium phases of matter with exotic observable dynamics. Among their remarkable features is their response to a periodic drive at a fraction of its frequency. Current successful experiments are…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
The proposed theory of causally structured discrete fields studies integer values on directed edges of a self-similar graph with a propagation rule, which we define as a set of valid combinations of integer values and edge directions around…
Modern machine learning (ML) methods typically fail to adequately capture causal information. Consequently, such models do not handle data distributional shifts, are vulnerable to adversarial examples, and often learn spurious correlations.…