Broadcasting of quantum correlations in qubit-qudit systems
Rounak Mundra, Dhrumil Patel, Indranil Chakrabarty, Nirman Ganguly, Sourav Chatterjee · Physical Review A · 2019
Quantum mechanical properties like entanglement, discord, and coherence act as fundamental resources in various quantum information processing tasks. Consequently, the technique of generating more resources from a few, typically termed as broadcasting, serves as a promising candidate for the design of quantum networks. One way to broadcast resources could be using a cloning operation. In this article, broadcasting of quantum resources beyond $2\ensuremath{\bigotimes}2$ systems is investigated. In particular, in $2\ensuremath{\bigotimes}3$ dimensions, a class of states not useful for broadcasting of entanglement is characterized considering an optimal universal Heisenberg cloning machine. The broadcasting ranges for maximally entangled mixed states and two-parameter class of states are obtained to exemplify our protocol. A significant derivative of our protocol is that the cloning operation generates a qutrit ($3\ensuremath{\bigotimes}3$) entangled pair with positive partial transpose on one of the local sides, and an absolutely separable qubit ($2\ensuremath{\bigotimes}2$) pair on the other side of the input bipartite $2\ensuremath{\bigotimes}3$-dimensional resource state. Moving beyond entanglement, in $2\ensuremath{\bigotimes}d$ dimensions, the impossibility to optimally broadcast quantum discord and quantum coherence (${l}_{1}$ norm) is established. However, some significant illustrations are provided to highlight that nonoptimal broadcasting of discord and coherence is still possible.