Quantum state tomography with quantum shot noise

We propose a scheme for a complete reconstruction of one- and two-particle orbital quantum states in mesoscopic conductors. The conductor in the transport state continuously emits orbital quantum states. The orbital states are manipulated by electronic beam splitters and detected by measurements of average currents and zero frequency current shot-noise correlators. We show how, by a suitable complete set of measurements, the elements of the density matrices of the one- and two-particle states can be directly expressed in terms of the currents and current correlators.

Figure 1

(Color online) Schematic of the setup. A mesoscopic conductor acting as a source $S$ [thick red (dark gray) box] is connected via four leads, $A1,A2,B1$, and $B2$, to regions $A$ and $B$ (dashed boxes) each containing two reservoirs $+$ and $-$, a beam splitter [green (gray) cross] and a side gate (thin open box), which induces a phase shift ${\varphi }_A$ or ${\varphi }_B$. Two particles [red (dark gray) dots] emitted from the source are shown.

Figure 2

(Color online) Left: Table with scattering parameters at $A$ for the four different settings. Right: Schematic of an elementary mesoscopic source $S$ [thick red (dark gray) box, see Fig. 1]. Two reservoirs biased at $eV$, 1 and 2, and two grounded reservoirs, 3 and 4, are connected via beam splitters to the four leads going out towards $A$ and $B$. Scattering between upper and lower leads, e.g., $A1$ and $A2$, is not possible.