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Multipartite quantum channels realisable in a spacetime obey the no-superluminal-signalling constraints imposed by relativistic causality. But what about the converse: Can every channel that exhibits no superluminal signalling also be realised through relativistically valid dynamics? To our knowledge, only special cases of this question have been studied. For bipartite channels, the answer has been found to be negative in general (Beckman et al., 2001), though we will argue that counterexamples must necessarily involve a form of fine-tuning. Another special case of the question has been extensively explored under the name of nonlocal quantum computation in the context of position-based cryptography. We will pose and motivate the question in generality, conjecture a positive answer for all but the fine-tuned channels, and present results towards proving it, drawing on insights from nonlocal quantum computation and the new field of causally faithful circuit decompositions of unitary transformations (see also Tuesday). Beyond their relevance to spacetime realisability, the circuit decompositions involved in addressing the question also find applications in quantum causal modelling.

Supermaps are higher-order transformations that take maps as input. We explore quantum algorithms that implement supermaps of unitary operations using multiple calls to a black-box unitary operation. We investigate how the causal structure and spacetime symmetry of these unitary black-boxes affect their performance in implementing higher-order quantum operations. We analyze several tasks, inversion, complex conjugation, and transposition of black-box unitaries.

In this talk, we first present a detailed analysis of the classical geometry of generic null hypersurfaces. We then reformulate the Einstein equations as conservation laws for the intrinsic geometric data on these hypersurfaces. Following this, we derive the symplectic structure and the corresponding Poisson bracket. Upon quantizing this phase space, we propose that the projected Einstein tensor obeys the operator product expansion of the stress tensor in a conformal field theory along null time. This hypothesis is supported by explicit computations in simplified scenarios, such as the absence of radiation and within the framework of perturbative gravity. Notably, we discover a non-vanishing central charge, which counts the local geometric degrees of freedom and diverges in the classical limit. We suggest that this central charge is a fundamental principle underlying the emergence of time in quantum gravity. If time permits, we will conclude by introducing a mesoscopic model of quantum gravity on null hypersurfaces, based on the concept of the "embadon," an operator that creates localized bits of area on cuts.

Generalizations of Bell's theorem, particularly within quantum networks, are now being analyzed through the causal inference lens. However, the use of interventions, a central concept in causality theory, remains unexplored. As will be discussed, if we are not limited to observational data and can intervene in our experimental setup, we can witness quantum violations of classical causal bounds even when no Bell-like violation is possible. Through interventions, the quantum behavior of a system, that would seem classical otherwise, can be demonstrated. We will then present a photonic experiment implementing those ideas and consider applications of this framework for measurement-based quantum computation, quantification of causality in quantum gates and quantum network protocols.