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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Non-entangling channels amplify existing entanglement only if they generate it probabilistically, yielding a channel Schmidt number and witness-preserving dual maps that enable Bell-like detection of entanglement generation.
Generalized coherent information acts as a sharp phase-transition indicator over the entire p-T plane in the 2D ±J random-bond Ising model, yielding a high-precision multicritical point estimate p_c=0.1092212(4) with reduced finite-size effects.
Hadamard states exhibit higher average multipartite entanglement than Haar-typical states via purity of balanced bipartitions, with hypergraph states (real alternating-sign coefficients) being especially promising for maximal entanglement due to simplicity and sampling likelihood.
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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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The entangling power of non-entangling channels
Non-entangling channels amplify existing entanglement only if they generate it probabilistically, yielding a channel Schmidt number and witness-preserving dual maps that enable Bell-like detection of entanglement generation.
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Revisiting Nishimori multicriticality through the lens of information measures
Generalized coherent information acts as a sharp phase-transition indicator over the entire p-T plane in the 2D ±J random-bond Ising model, yielding a high-precision multicritical point estimate p_c=0.1092212(4) with reduced finite-size effects.
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Multipartite entanglement of random states of qubits
Hadamard states exhibit higher average multipartite entanglement than Haar-typical states via purity of balanced bipartitions, with hypergraph states (real alternating-sign coefficients) being especially promising for maximal entanglement due to simplicity and sampling likelihood.