Nullspaces of entanglement breaking channels and applications

Abstract

Abstract Quantum entanglement breaking channels are a fundamental class of quantum operations; originally investigated for quantum information theoretic reasons, their study has since grown to touch on many aspects of quantum information science. Here we investigate the nullspace structures of entanglement breaking channels and we derive a pair of related applications. We show that every operator space of trace zero matrices is the nullspace of an entanglement breaking channel. We derive a test for mixed unitarity of quantum channels based on complementary channel behaviour and entanglement breaking channel nullspaces. We identify conditions that guarantee the existence of private algebras for certain classes of entanglement breaking channels.