Asymmetric broadcasting of quantum correlations

In this work, we exhaustively investigate $1 \rightarrow 2$ local and non local broadcasting of entanglement and correlations (optimal and non-optimal) using asymmetric Pauli cloners, with the most general two qubit state as a resource. We exemplify the broadcasting of entanglement using Maximally Entangled Mixed States and demostrate the variation of broadcasting range with the amount of entanglement in resource state as well as the asymmetry in the cloner. We show that it is impossible to optimally broadcast quantum correlations that go beyond entanglement (Geometric Discord) with the help of these asymmetric Pauli cloning machines. We introduce the concept of asymmetry in correlations to quantify the degree of variation in the amount of correlation present in the output pairs obtained after broadcasting. We also study the problem of $1 \rightarrow 3$ broadcasting of entanglement using non-maximally entangled state (NME) as a resource. We adopt two different strategies : successive application of $1 \rightarrow 2$ optimal cloning machines and application of $1 \rightarrow 3$ optimal cloning machines. Interestingly, we show that $1 \rightarrow 3$ optimal cloner does a better job at broadcasting than the successive application of $1 \rightarrow 2$ cloners. Finally, we create an example to show that there are local unitaries, which when applied on non-maximally entangled state locally give us a better range of broadcasting, that surpasses the best possible range obtained using cloning machines. This result opens up a new direction in exploration of methods to perform broadcasting which may outperform standard broadcasting strategies implemented through cloning transformations.