Quantifying the information distribution of quantum information masking

Quantum information masking encodes an arbitrary quantum state into a multipartite system such that the original information of input states is completely unknown to local subsystems. In this work, we investigate the quantitative distribution of quantum information masking. We regard quantum information maskers as quantum broadcasting channels and propose the Holevo’s quantity as a measure of the information carried by local subsystems. Based on the theory of quantum channels, we first give necessary and sufficient conditions for the existence of perfect quantum information masking. Then, we investigate information recovery from the union of local subsystems. We find a close connection between quantum information masking and codes for quantum erasing channels, by which the no-masking theorem is rediscovered from the point of view of information transmission. Finally, we discuss the storage behavior of quantum information and propose that quantum information can reside in the correlations of subsystems in a redundant way. Our work deepens the understanding of the way that quantum information resides.