Entanglement catalysis

A catalyst is an auxiliary state enabling a conversion while being returned according to a specified convention. Exact uncorrelated return requires an output $\sigma\otimes\tau$ with the original catalyst $\tau$. Correlated catalysis may return only the marginal $\tau$, and approximate return allows a perturbation. These are inequivalent resource theories.

For pure bipartite states, Jonathan–Plenio discovered exact catalysis; catalytic majorization/trumping criteria characterize the relevant Schmidt-vector conversions, including their support and strict-inequality conditions. Kondra–Datta–Streltsov's entropy criterion concerns approximate pure-bipartite conversion with the catalyst marginal returned and allowed output correlations, not arbitrary exact mixed-state or multipartite conversion. Van Dam–Hayden embezzlement shows why unconstrained catalyst dimension and arbitrarily small return error can otherwise trivialize conversion obstructions.

Related preprint progress (August 2026): Ao–Philip–Streltsov provide monotones and an irreversibility example under the larger class of PPT operations with correlated catalysts. E6 records this same paper's evidence and provenance; it is not a second independent advance.

Useful benchmarks fix source/target families, trace-distance accuracy, allowed correlations and catalyst dimension or entanglement cost. Necessary-and-sufficient criteria in these controlled settings remain the incremental target.

Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.