Deriving quantum theory from its local structure and reversibility

TL;DR

This paper explores whether the global structure of quantum theory can be derived from local properties and reversibility, concluding that for identical qubits, continuous reversible interactions imply the theory is quantum.

Contribution

It demonstrates that imposing dynamical reversibility on theories with quantum-like local structure uniquely recovers quantum theory for identical qubits.

Findings

Theories with quantum-like local structure and continuous reversible interactions are equivalent to quantum theory.

Tripartite correlations can differ from quantum, but bipartite correlations are simulatable in quantum.

Reversibility constrains the global structure, leading to quantum theory for identical qubits.

Abstract

We investigate the class of physical theories with the same local structure as quantum theory, but a potentially different global structure. It has previously been shown that any bipartite correlations generated by such a theory must be simulatable in quantum theory, but that this does not hold for tripartite correlations. Here we explore whether imposing an additional constraint on this space of theories - that of dynamical reversibility - will allow us to recover the global quantum structure. In the particular case in which the local systems are identical qubits, we show that any theory admitting at least one continuous reversible interaction must be identical to quantum theory.