Causally faithful circuits for relativistic realisability, or: What can you do in a spacetime?

          @misc{ pirsa_PIRSA:24090098,
            doi = {10.48660/24090098},
            url = {https://pirsa.org/24090098},
            author = {van der Lugt, Tein},
            keywords = {Quantum Foundations, Quantum Information},
            language = {en},
            title = {Causally faithful circuits for relativistic realisability, or: What can you do in a spacetime?},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {sep},
            note = {PIRSA:24090098 see, \url{https://pirsa.org}}
          }
          

Abstract

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.