A hyper-decoherence map is constructed that produces standard quantum theory from quantum boxes theory, evading the Lee-Selby no-go theorem via relaxations on past signalling and purification uniqueness.
Purity co-preservation within the non-deterministic state space does not hold for our ex- ample for the same reasons outlined by Lee and Selby in
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Decoherence to quantum theory from a causally-indefinite post-quantum theory
A hyper-decoherence map is constructed that produces standard quantum theory from quantum boxes theory, evading the Lee-Selby no-go theorem via relaxations on past signalling and purification uniqueness.