Partial projected ensembles from Haar-random states and scrambling circuits exhibit two information phases in Holevo information: exponential decay versus linear growth with system size, separated by sharp transitions and revealing a measurement-invisible quantum-correlated phase.
First note that, if the PER∪Eforms a Haar ensemble, then the PPE onRtrivially forms a gHSe
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Information phases of partial projected ensembles generated from random quantum states and scrambling dynamics
Partial projected ensembles from Haar-random states and scrambling circuits exhibit two information phases in Holevo information: exponential decay versus linear growth with system size, separated by sharp transitions and revealing a measurement-invisible quantum-correlated phase.