Families of complex tensor trace-invariants with tree-like dominant pairings factorize at large N, allowing computation of typical multipartite Rényi entropies for uniform random states.
Tensor invariants for multipartite entanglement clas- sification
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Multi-entropy exhibits a structural obstruction to replica symmetry breaking in random tensor networks due to incompatible boundary permutations in the replica hypercube, unlike entanglement negativity.
Two methods are introduced for quantum circuits that directly measure local unitary invariants of three qubits, with demonstrations on IBM Quantum hardware for entanglement measures.
Third-order negativity is a necessary and sufficient criterion for full separability of tripartite pure states and extends to mixed states and qudits.
The authors extend tensorial free cumulants to arbitrary orders, connect prior frameworks, and compute non-trivial examples for Gaussian tensors with structured covariances.
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Large $N$ factorization of families of tensor trace-invariants
Families of complex tensor trace-invariants with tree-like dominant pairings factorize at large N, allowing computation of typical multipartite Rényi entropies for uniform random states.
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Properties of tensorial free cumulants
The authors extend tensorial free cumulants to arbitrary orders, connect prior frameworks, and compute non-trivial examples for Gaussian tensors with structured covariances.