Quantum Entanglement Criteria & Measures

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Abstractions about detecting and quantifying quantum entanglement, covering separability tests (Peres-Horodecki Criterion, Reduction Criterion), entangled-state constructions (Greenberger-Horne-Zeilinger State), and distinguishability or correlation measures like the Diamond Norm and Reflected Entropy.

5 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Diamond norm — The completely bounded trace norm of a linear map on matrices, maximizing output trace norm after arbitrary ancillary extension and operationally measuring one-use distinguishability of quantum channels.
• Greenberger–Horne–Zeilinger state — A multipartite entangled state formed by a coherent superposition of all subsystems in one basis state and all in its complementary basis state.
• Peres–Horodecki criterion — Test bipartite quantum-state separability by partially transposing one subsystem and checking positivity, a necessary condition in all dimensions and a sufficient one only for 2×2 and 2×3 systems.
• Reduction criterion — Certify a necessary condition for bipartite separability by requiring both reduced-state operators tensored with identity minus the joint density operator to remain positive semidefinite.
• Reflected entropy — A mixed-state correlation measure obtained by canonically purifying a bipartite density operator and taking entanglement entropy across the reflected subsystem split.