Necessary conditions on effective quantum entanglement catalysts

Quantum catalytic transformations play important roles in the transformation of quantum entangled states under local operations and classical communications (LOCC). The key problems in catalytic transformations are the existence and the bounds on the catalytic states. We present the necessary conditions of catalytic states based on a set of points given by the Schmidt coefficients of the entangled source and target states. The lower bounds on the dimensions of the catalytic states are also investigated. Moreover, we give a detailed protocol of quantum mixed state transformation under entanglement-assisted LOCC.

Automated summary

Quantum catalytic transformations are crucial in converting quantum entangled states under local operations and classical communications (LOCC). The key issues lie in the existence and limits of catalytic states, with necessary conditions based on the Schmidt coefficients of entangled source and target states. Investigation into lower bounds on dimensions of catalytic states is conducted, along with a detailed protocol for quantum mixed state transformation under entanglement-assisted LOCC.