Quantum teleportation of single-electron states

We consider a scheme for on-demand teleportation of a dual-rail electron qubit state, based on single-electron sources and detectors. The scheme has a maximal efficiency of 25%, which is limited both by the shared entangled state as well as the Bell-state measurement. We consider two experimental implementations, realizable with current technology. The first relies on surface acoustic waves, where all the ingredients are readily available. The second is based on Lorentzian voltage pulses in quantum Hall edge channels. As single-electron detection is not yet experimentally established in these systems, we consider a tomographic detection of teleportation using current correlators up to (and including) third order. For both implementations, we take into account environmental effects.

Figure 1

Schematic view of the original teleportation protocol (a) and our proposed setup for single-electron teleportation (b). (a) Alice and Bob are each given one-half of an entangled state $\left|\varphi \right.〉$. Alice also receives an unknown qubit state $\left|\psi \right.〉$. She performs a measurement on the combined state of the qubit and her part of the entangled state and sends the result to Bob. Based on the measurement outcome, Bob performs a unitary operation on his part of the entangled state to recover the unknown qubit from the postmeasurement state $\left|{\psi }^{\prime }\right.〉$. (b) The ${\mathcal{S}}_i$ denote single-electron sources, ${\mathcal{G}}_i$ empty inputs (grounded contacts in the implementation based on levitons). Beamsplitters are labeled by $S$ and phase-shifters by $\phi$ and $\theta$. The A and ${\mathrm{A}}^{\prime }$ modes propagate to Alice while the B and ${\mathrm{B}}^{\prime }$ propagate to Bob. Electrons are detected by Alice at four detectors at ${\mathrm{A}}_0^{\pm }$ and at ${\mathrm{A}}_1^{\pm }$. The aim of the experiment is to transfer a superposition of ${\mathrm{A}}^{\prime }$ modes to a superposition of ${\mathrm{B}}^{\prime }$ modes. Bob can perform state tomography on his part of the post-measurement state in order to verify teleportation. He selects which component of the Bloch vector to measure by adjusting $S^{\mathrm{B}}$ and $\theta$.

Figure 2

Illustration of the experimental setup using levitons in chiral edge states, using a Corbino disk geometry. Electrons are generated at the sources (red) and travel along the edges of the disk, with the possible trajectories indicated by lines. The QPCs (blue) act as beamsplitters and facilitate scattering between the two edges. Phase differences $\phi$ and $\theta$ are introduced along two of the paths and their sum, which is what the observables of interest depend on, can be tuned by a magnetic flux $\mathrm{\Phi }$. Current measurements are performed at six different detectors (purple). We note that the same physical contacts may serve as the grounded contacts (green) and the detectors (purple).

Figure 3

Teleportation fidelity for the $++$ outcome as a function of temperature for different leviton widths. The horizontal line denotes the classical limit of ${\mathcal{F}}_{\mathrm{tel}}=2/3$.