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Distributed Entanglement
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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.
Forward citations
Cited by 12 Pith papers
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Qubit-qubit-qutrit quantum correlations in $H \to f \bar f V$
In h→τ^-τ^+ Z decays, the spin state is genuinely qubit-qubit-qutrit entangled almost everywhere, violates Bell inequalities throughout, and carries up to 1.95 bits of non-local magic.
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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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Surviving correlations across a horizon: reflected entropy for bosonic fields in non-inertial frames and black hole spacetimes
Bosonic Alice-Bob reflected entropy saturates at nonzero floors (1.757 bits for Bell, 0.315 for GHZ) at infinite acceleration, while the inter-wedge reflected entropy diverges linearly in the squeezing parameter.
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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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Probing the Hierarchy of Genuine Multipartite Entanglement with Generalized Latent Entropy
A generalized latent-entropy measure orders k-uniform states, maxes out on AME states, shows odd-party random states saturate it, and distinguishes SYK variants.
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A Refined Algorithm For the EPR model
A refined algorithm for the EPR model using homogeneous and quasi-homogeneous fractional matchings achieves improved approximation ratios on regular graphs, e.g., 0.872 for 2-regular graphs.
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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 g...
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Bell states for fermions in loop quantum gravity
In loop quantum gravity, a surface-normal fermion spin observable can be used to construct CHSH-type correlations that are violated by fermion states coupled to quantum geometry.
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Testing APS conjecture on regular graphs
The FED algorithm's energy estimates on Henning-Yeo regular graphs never exceed the APS conjecture's predicted bound, so the tests find no violation.
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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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Les Houches Lecture Notes on Tensor Networks
A well-organized five-lecture review of tensor networks (MPS/PEPS/MPO) covering algorithms, phase classification, string-nets, strange correlators, and dualities; it contains no new research results.
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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.
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