Quantifying nonclassicality: Global impact of local unitary evolutions

We show that only those composite quantum systems possessing nonvanishing quantum correlations have the property that any nontrivial local unitary evolution changes their global state. We derive the exact relation between the global state change induced by local unitary evolutions and the amount of quantum correlations. We prove that the minimal change coincides with the geometric measure of discord (defined via the Hilbert-Schmidt norm), thus providing the latter with an operational interpretation in terms of the capability of a local unitary dynamics to modify a global state. We establish that two-qubit Werner states are maximally quantum correlated, and are thus the ones that maximize this type of global quantum effect. Finally, we show that similar results hold when replacing the Hilbert-Schmidt norm with the trace norm.

Figure 1

Possible values of the impact power $P$ for an arbitrary initial state ${\rho }^{AB}$. The impact power is zero if the spectrum of the local Hamiltonian $H_A$ is degenerate: $E_0=E_1$ (yellow line). For $E_0\ne E_1$, the impact power can only take values between $P_{\min }$ and $P_{\max }$ (green-blue area). The impact power gap is the region between 0 and $P_{\min }$. Its width is measured by the amount of quantum correlations present in the initial state ${\rho }^{AB}$, as measured by the geometric measure of discord: $P_{\min }=2D_A^{\left(2\right)}$. See main text for details.