On Quantum No-Broadcasting

We address the issue of one-side local broadcasting for correlations in a quantum bipartite state, and conjecture that the correlations can be broadcast if and only if they are classical-quantum, or equivalently, the quantum discord, as defined by Ollivier and Zurek (Phys Rev Lett 88:017901, 2002), vanishes. We prove this conjecture when the reduced state is maximally mixed and further provide various plausible arguments supporting this conjecture. Moreover, we demonstrate that the conjecture implies the following two elegant and fundamental no-broadcasting theorems: (1) The original no-broadcasting theorem by Barnum et al. (Phys Rev Lett 76:2818, 1996), which states that a family of quantum states can be broadcast if and only if the quantum states commute. (2) The no-local-broadcasting theorem for quantum correlations by Piani et al. (Phys Rev Lett 100:090502, 2008), which states that the correlations in a single bipartite state can be locally broadcast if and only if they are classical. The results provide an informational interpretation for classical-quantum states from an operational perspective and shed new lights on the intrinsic relation between non-commutativity and quantumness.