Abstract
We present a new characterization of quantum theory in terms of simple physical principles that is different from previous ones in two important respects: first, it only refers to properties of single systems without any assumptions on the composition of many systems; and second, it is closer to experiment by having absence of higher-order interference as a postulate, which is currently the subject of experimental investigation. We give three postulates—no higher-order interference, classical decomposability of states, and strong symmetry—and prove that the only non-classical operational probabilistic theories satisfying them are real, complex, and quaternionic quantum theory, together with three-level octonionic quantum theory and ball state spaces of arbitrary dimension. Then we show that adding observability of energy as a fourth postulate yields complex quantum theory as the unique solution, relating the emergence of the complex numbers to the possibility of Hamiltonian dynamics. We also show that there may be interesting non-quantum theories satisfying only the first two of our postulates, which would allow for higher-order interference in experiments while still respecting the contextuality analogue of the local orthogonality principle.
Highlights
Quantum theory currently underpins much of modern physics and is essential in many other scientific fields and countless technological applications
Our results hint at possible physical properties of conceivable alternative theories against which quantum theory can be tested in interference experiments, and which may be of independent mathematical interest
We show that one additional assumption brings us into the realm of Jordan algebra state spaces
Summary
Quantum theory currently underpins much of modern physics and is essential in many other scientific fields and countless technological applications. Any system of this kind—if it exists—has a set of ‘filtering’ operations that represent an orthomodular lattice known from quantum logic [38], but these filters do not necessarily preserve the purity of states as they do in quantum theory (equivalently, the lattice does not satisfy the ‘covering law’) These systems still satisfy the principle of ‘consistent exclusivity’ [54], bringing their contextuality behavior close to quantum theory, despite the appearance of (non-quantum) third-order interference. In this way, our results hint at possible physical properties of conceivable alternative theories against which quantum theory can be tested in interference experiments, and which may be of independent mathematical interest. Reversible processes, the subject of postulate 2, are even more crucial in classical and quantum thermodynamics
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