Decoherence to quantum theory from a causally-indefinite post-quantum theory

TL;DR

This paper introduces a hyper-decoherence process that derives standard quantum theory from a higher-order quantum framework, challenging existing no-go theorems and raising questions about the nature of causality and purity in quantum theory.

Contribution

It presents a hyper-decoherence map that bypasses previous constraints, suggesting a possible physical process from causally-indefinite theories to standard quantum mechanics.

Findings

The hyper-decoherence map satisfies the axioms of hyper-decoherence.

It evades the no-go theorem by relaxing signalling constraints.

The map may indicate a genuine causal transition or require re-evaluation of hyper-decoherence axioms.

Abstract

We find a process satisfying the axioms of hyper-decoherence which produces standard quantum theory from the theory of quantum boxes (higher-order quantum theory with the non-signalling tensor product). This hyper-decoherence map evades the no-go theorem of Lee and Selby by relaxing constraints on signalling to the past and the uniqueness of purifications. We discuss some natural opposing conclusions: that the existence of this map might be evidence of a genuine hyper-decoherence process producing causal quantum theory from its causally-indefinite higher-order theory; or that it serves as an indication that the axioms of hyper-decoherence might need careful re-consideration, especially regarding the subtle albeit central role that purity plays.