Broadcasting of Quantum Correlations: Possibilities & Impossibilities

In this work, we extensively study the problem of broadcasting of quantum correlations. This includes broadcasting of quantum entanglement as well as correlations that go beyond the notion of entanglement. It is quite well known from the "No-Broadcasting theorem" that perfect broadcasting of quantum correlation is not possible. However it does not rule out the possibility of partial broadcasting of correlations where we can get lesser correlated states from a given correlated state. In order to have a holistic view of broadcasting, we investigate this problem by starting with most general representation of two qubit mixed states in terms of the Bloch vectors. As a cloning transformation we have used universal symmetric optimal Buzek-Hillery (B-H) cloner both locally and nonlocally. More specifically, we obtain a set of ranges in terms of Bloch vectors for which broadcasting of entanglement will be possible. In addition to the idea of broadcasting of entanglement for general two qubit mixed states, we explore broadcasting of quantum correlations that go beyond entanglement with the help of both local and nonlocal cloners. Remarkably, we find that it is impossible to even partially broadcast such correlations by using both local and nonlocal quantum copying machines. Taking two different types Buzek-Hillery quantum cloners (state dependent and state independent) we analytically prove the impossibility of even partial broadcasting of correlation. Lastly, we generalize this impossibility result for any symmetric or asymmetric cloning machines as well. This result brings out a fundamental difference between the correlation defined from the perspective of entanglement and the correlation measure which claims to go beyond entanglement.
Comment: 18 pages, 6 figures, 6 tables. arXiv admin note: text overlap with arXiv:quant-ph/0607067 by other authors. Accepted in Physical Review A