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Separability of Mixed States: Necessary and Sufficient Conditions

9 Pith papers cite this work. Polarity classification is still indexing.

9 Pith papers citing it
abstract

We provide necessary and sufficient conditions for separability of mixed states. As a result we obtain a simple criterion of separability for $2\times2$ and $2\times3$ systems. Here, the positivity of the partial transposition of a state is necessary and sufficient for its separability. However, it is not the case in general. Some examples of mixtures which demonstrate the utility of the criterion are considered.

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UNVERDICTED 9

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representative citing papers

Separability and entanglement of resonating valence-bond states

cond-mat.str-el · 2022-12-22 · unverdicted · novelty 6.0

Proves exact separability for disconnected subsystems in dimer RK states and exponentially suppressed entanglement for RVB states on arbitrary lattices, with negativity expressed via partition functions.

Separability from Multipartite Measures

quant-ph · 2026-05-03 · unverdicted · novelty 5.0 · 2 refs

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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Showing 4 of 4 citing papers after filters.

  • Logarithmic negativity typically equals exact entanglement cost quant-ph · 2026-07-01 · unverdicted · none · ref 9 · internal anchor

    Logarithmic negativity equals exact entanglement cost under PPT-preserving operations for large random induced mixed states.

  • Separability from Multipartite Measures quant-ph · 2026-05-03 · unverdicted · none · ref 19 · 2 links

    Third-order negativity is a necessary and sufficient criterion for full separability of tripartite pure states and extends to mixed states and qudits.

  • Bipartite entanglement harvesting with multiple detectors quant-ph · 2026-04-15 · unverdicted · none · ref 51

    Multiple Unruh-DeWitt detectors harvest more vacuum entanglement when arranged in specific configurations, with harvested negativity scaling linearly in linear chains.

  • On the existence of fully inseparable biseparable Gaussian states quant-ph · 2026-05-27 · unverdicted · none · ref 46 · internal anchor

    Numerical evidence from projections and witnesses on specific Gaussian families leads to the conjecture that full inseparability implies genuine multipartite entanglement for all Gaussian states.