Complexity of formation, unlike complexity of purification, shows distinct and timescale-matching signatures of both decoherence and recoherence in a Gaussian two-field de Sitter model.
Einstein's Equations from Varying Complexity
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A recent proposal equates the circuit complexity of a quantum gravity state with the gravitational action of a certain patch of spacetime. Since Einstein's equations follow from varying the action, it should be possible to derive them by varying complexity. I present such a derivation for vacuum solutions of pure Einstein gravity in three-dimensional asymptotically anti-de Sitter space. The argument relies on known facts about holography and on properties of Tensor Network Renormalization, an algorithm for coarse-graining (and optimizing) tensor networks.
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Probing the self-coherence of primordial quantum fluctuations with complexity
Complexity of formation, unlike complexity of purification, shows distinct and timescale-matching signatures of both decoherence and recoherence in a Gaussian two-field de Sitter model.