Quantum computation is the unique reversible circuit model for which bits are balls

The computational efficiency of quantum mechanics can be characterized in terms of the qubit circuit model, which is defined by a few simple properties: each computational gate is a reversible transformation in a connected matrix group; single wires carry quantum bits, i.e. states of a three-dimensional Bloch ball; states on two or more wires are uniquely determined by local measurement statistics and their correlations. In this paper, we ask whether other types of computation are possible if we relax one of those characteristics (and keep all others), namely, if we allow wires to be described by d-dimensional Bloch balls, where d is different from three. Theories of this kind have previously been proposed as possible generalizations of quantum physics, and it has been conjectured that some of them allow for interesting multipartite reversible transformations that cannot be realized within quantum theory. However, here we show that all such potential beyond-quantum models of computation are trivial: if d is not three, then the set of reversible transformations consists entirely of single-bit gates, and not even classical computation is possible. In this sense, qubit quantum computation is an island in theoryspace.Quantum Computing and Foundations: alternatives to quantum theory are excludedThe standard quantum formalism is the only one compatible with the possibility to perform any kind of computation (even classical ones). Marius Krumm and Markus P. Müller from University of Vienna have shown that, if one modifies the standard way of describing two-level systems in quantum mechanics (the “qubits”) impossible conclusions are reached. In standard quantum theory, a qubit is mathematically described as an entity living in a 3-dimensional ball; now, the authors showed that, if they were described by balls living in more than 3 dimensions, not only quantum mechanics but even classical mechanics couldn’t allow any kind of computation, like the ones that your laptop is currently performing. Such extensions of quantum theory are then demonstrated to be impossible by the authors.