  We propose a framework to characterize entanglement with quantum discord,
both asymmetric and symmetric, over state extensions. In particular, we show
that the minimal Bures distance of discord over state extensions is equivalent
to Bures distance of entanglement. This equivalence places quantum discord at a
more primitive position than entanglement conceptually in the sense that
entanglement can be interpreted as an irreducible part of discord over all
state extensions. Based on this equivalence, we also offer an operational
meaning of Bures distance of entanglement by connecting it to quantum state
discriminations. Moreover, for the relative entropy part, we prove that the
entanglement measure introduced by Devi and Rajagopal [A. R. U. Devi and A. K.
Rajagopal, Phys. Rev. Lett. 100, 140502 (2008)] is actually equivalent to the
relative entropy of entanglement. We also provide several quantifications of
entanglement based on discord measures.

Quantum Physics