Necessary and Sufficient Conditions for the Trumping Relation

Understand

Entanglement catalysis allows one to convert certain entangled states into others by the temporary involvement of another entangled state (so-called catalyst), where after the conversion the catalyst is returned to the same state.

• For bipartite pure entangled states that can be transformed in this way with unit probability, the respective Schmidt coefficients are said to satisfy the trumping relation, a mathematical relation which is an extension of the majorization relation.
• This article provides all necessary and sufficient conditions for the trumping relation in terms of the Schmidt coefficients.
• The coefficients should satisfy strict inequalities for the entropy of entanglement and for power means excluding the special power 1.