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There exists a growing literature on the so-called physical Church-Turingthesis in a relativistic spacetime setting. The physical Church-Turing thesisis the conjecture that no computing device that is physically realizable (evenin principle) can exceed the computational barriers of a Turing machine. Bysuggesting a concrete implementation of a beyond-Turing computer in a spacetimesetting, Istv\'an N\'emeti and Gyula D\'avid (2006) have shown how anappreciation of the physical Church-Turing thesis necessitates the confluenceof mathematical, computational, physical, and indeed cosmological ideas. Inthis essay, I will honour Istv\'an's seventieth birthday, as well as hislongstanding interest in, and his seminal contributions to, this field goingback to as early as 1987 by modestly proposing how the concrete implementationin N\'emeti and D\'avid (2006) might be complemented by aquantum-information-theoretic communication protocol between the computingdevice and the logician who sets the beyond-Turing computer a task such asdetermining the consistency of Zermelo-Fraenkel set theory. This suggests thateven the foundations of quantum theory and, ultimately, quantum gravity mayplay an important role in determining the validity of the physicalChurch-Turing thesis.

A quantum-information-theoretic complement to a general-relativistic implementation of a beyond-Turing computer