Broadcasting of quantum correlations in qubit-qudit systems

Abstract

Quantum mechanical properties like entanglement, discord and coherence act as fundamental resources in various quantum information processing tasks. Consequently, generating more resources from a few, typically termed as broadcasting is a task of utmost significance. One such strategy of broadcasting is through the application of cloning machines. In this article, broadcasting of quantum resources beyond $2\otimes 2$ systems is investigated. In particular, in $2\otimes 3$ dimension, a class of states not useful for broadcasting of entanglement is characterized for a choice of optimal universal Heisenberg cloning machine. The broadcasting ranges for maximally entangled mixed states (MEMS) and two parameter class of states (TPCS) are obtained to exemplify our protocol. A significant derivative of the protocol is the generation of entangled states with positive partial transpose in $3\otimes 3$ dimension and states which are absolutely separable in $2\otimes 2$ dimension. Moving beyond entanglement, in $2\otimes d$ dimension, the impossibility to optimally broadcast quantum correlations beyond entanglement (QCsbE) (discord) and quantum coherence ($l_1$-norm) is established. However, some significant illustrations are provided to highlight that non-optimal broadcasting of QCsbE and coherence are still possible.