Landauer current and mutual information

We study quantum evolution of the mutual information of a quantum dot connected to left and right leads initially maintained at chemical potentials ${\mu }_L$ and ${\mu }_R$, respectively, within the noninteracting resonant-level model. The full nonequilirbium mixed state density matrix of the whole system is written down exactly, and the mutual information of the dot with respect to the leads is computed. A strong and direct correlation is found between the Landauer current and the mutual information at all times, the steady-state values in particular displaying a quadratic relationship at high temperatures. Strikingly, it is found that one can obtain a maximal mutual information by simply applying a sufficiently large “source-drain” voltage $V_{\mathrm{SD}}$ even at high temperatures.

Figure 1

The intimate relationship between current and mutual information between the dot and the leads, $S$. Each of them is plotted as a function of time $t$ for just one set of parameters shown.

Figure 2

Figure shows (a) the steady-state value of $S_{\infty }$ as a function of the steady-state value of current $I_{\infty }$, and (b) $S_{\infty }$ as a function of the steady-state quantum fluctuations in current ${\nu }_{\infty }$. A range of data is presented for temperatures going all the way from $T=0.1$ to $T=10$, the increasing direction of temperature being pointed by the arrow. At each temperature, $V_{\mathrm{SD}}$ was varied from 0 to 10 and the steady-state values were plotted against each other.