Broadcasting of quantum correlations in qubit-qudit systems

TL;DR

This paper explores the broadcasting of quantum correlations like entanglement, discord, and coherence in higher-dimensional qubit-qudit systems using cloning machines, revealing new possibilities and limitations in resource generation.

Contribution

It extends the study of quantum resource broadcasting beyond 2x2 systems, characterizing states and protocols in 2x3 and higher dimensions, including the generation of entangled states with positive partial transpose.

Findings

Broadcasting ranges for MEMS and TPCS are determined.

Generation of entangled states with positive partial transpose in 3x3 systems.

Impossibility of optimal broadcasting of quantum correlations beyond entanglement in 2xd 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 $2\otimes3$ 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.