The maximally mixed state in the translation-invariant subspace of a 1D ring is long-range entangled because the dimension of translationally symmetric short-range entangled states grows polynomially while the full subspace grows exponentially.
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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.
Haar random qubit states show vanishing fermionic non-Gaussianity for subsystems smaller than half the total size without symmetry, small but finite non-Gaussianity with U(1) symmetry, and extensive non-Gaussianity for larger subsystems.
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Mixed-State Long-Range Entanglement from Dimensional Constraints
The maximally mixed state in the translation-invariant subspace of a 1D ring is long-range entangled because the dimension of translationally symmetric short-range entangled states grows polynomially while the full subspace grows exponentially.
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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.
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Non-Gaussianity of random quantum states
Haar random qubit states show vanishing fermionic non-Gaussianity for subsystems smaller than half the total size without symmetry, small but finite non-Gaussianity with U(1) symmetry, and extensive non-Gaussianity for larger subsystems.