Behavior of Quantum Correlations under Local Noise

We characterize the behavior of quantum correlations under the influence of local noisy channels. Intuition suggests that such noise should be detrimental for quantumness. When considering qubit systems, we show for which channels this is indeed the case: The amount of quantum correlations can only decrease under the action of unital channels. However, nonunital channels (e.g., such as dissipation) can create quantum correlations for some initially classical states. Furthermore, for higher-dimensional systems even unital channels may increase the amount of quantum correlations. Thus, counterintuitively, local decoherence can generate quantum correlations.

Figure 1

Quantum channels on a single qubit: The upper figure shows a unital quantum channel ${\Lambda }_u$ (green arrow) which maps the maximally mixed state $\frac{1}{2}\mathbb{1}$ onto itself: ${\Lambda }_u(\frac{1}{2}\mathbb{1})=\frac{1}{2}\mathbb{1}$. Two orthogonal states $|{\psi }_1⟩$ and $|{\psi }_2⟩$ with collinear Bloch vectors are mapped onto the states ${\rho }_1={\Lambda }_u(|{\psi }_1⟩⟨{\psi }_1|)$ and ${\rho }_2={\Lambda }_u(|{\psi }_2⟩⟨{\psi }_2|)$ with collinear Bloch vectors. The lower figure shows a nonunital quantum channel ${\Lambda }_{nu}$ (yellow arrow) which maps the maximally mixed state onto the state $\sigma ={\Lambda }_{nu}(\frac{1}{2}\mathbb{1})\ne \frac{1}{2}\mathbb{1}$. The Bloch vectors of ${\sigma }_1={\Lambda }_{nu}(|{\psi }_1⟩⟨{\psi }_1|)$ and ${\sigma }_2={\Lambda }_{nu}(|{\psi }_2⟩⟨{\psi }_2|)$ add up to twice the nonzero Bloch vector of $\sigma$; see the main text.