Graphical Algebraic Geometry creates universal diagrammatic languages for commutative algebras and affine varieties that also characterize the qudit ZH calculus for quantum computation.
Distributed Entanglement
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Consider three qubits A, B, and C which may be entangled with each other. We show that there is a trade-off between A's entanglement with B and its entanglement with C. This relation is expressed in terms of a measure of entanglement called the "tangle," which is related to the entanglement of formation. Specifically, we show that the tangle between A and B, plus the tangle between A and C, cannot be greater than the tangle between A and the pair BC. This inequality is as strong as it could be, in the sense that for any values of the tangles satisfying the corresponding equality, one can find a quantum state consistent with those values. Further exploration of this result leads to a definition of the "three-way tangle" of the system, which is invariant under permutations of the qubits.
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UNVERDICTED 6representative citing papers
Concurrence minima in neutrino oscillations identify low-entanglement energy regions that, when aligned with NOνA and T2K data, yield tighter joint constraints on sin²θ₂₃, δ_CP, and Δm²₃₁.
Genuine multi-entropy in heavy local quenches in 2D holographic CFTs is kinematically fixed to logarithms of rational functions of time, independent of heavy operator dimension, due to global saddle selection in the geodesic network.
Harmony is a new entanglement measure for two qubits expressed as a simple function of the density operator that detects separability and maximal entanglement and is monogamous for three-qubit states.
Third-order negativity is a necessary and sufficient criterion for full separability of tripartite pure states and extends to mixed states and qudits.
Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.
citing papers explorer
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Graphical Algebraic Geometry: From Ideals and Varieties to Quantum Calculi
Graphical Algebraic Geometry creates universal diagrammatic languages for commutative algebras and affine varieties that also characterize the qudit ZH calculus for quantum computation.
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Quantum Information as a New Lens for Precision Neutrino Physics
Concurrence minima in neutrino oscillations identify low-entanglement energy regions that, when aligned with NOνA and T2K data, yield tighter joint constraints on sin²θ₂₃, δ_CP, and Δm²₃₁.
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Multi-entropy in heavy local quenches
Genuine multi-entropy in heavy local quenches in 2D holographic CFTs is kinematically fixed to logarithms of rational functions of time, independent of heavy operator dimension, due to global saddle selection in the geodesic network.
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Harmony for 2-Qubit Entanglement
Harmony is a new entanglement measure for two qubits expressed as a simple function of the density operator that detects separability and maximal entanglement and is monogamous for three-qubit states.
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Separability from Multipartite Measures
Third-order negativity is a necessary and sufficient criterion for full separability of tripartite pure states and extends to mixed states and qudits.
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Entanglement Certification $-$ From Theory to Experiment
Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.