Research ArticleCONDENSED MATTER PHYSICS

All-photonic quantum teleportation using on-demand solid-state quantum emitters

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Science Advances  14 Dec 2018:
Vol. 4, no. 12, eaau1255
DOI: 10.1126/sciadv.aau1255
  • Fig. 1 On-demand photon source and quantum teleportation setup.

    (A) The radiative recombination of XX-X states provides two photons entangled in polarization if the energetic splitting of the X state, the fine structure splitting (FSS), is sufficiently low. The on-demand generation occurs via a resonant laser tuned to half the energy of the XX state. EB indicates the XX binding energy. (B) Population of the XX state as a function of the pulse area. The experimental data (circles) are modeled as an exponentially damped sine-squared function (purple curve) to determine the depicted preparation fidelity. (C) The autocorrelation measurements for the XX and X transition of a representative QD. (D) The experimental setup for quantum teleportation. A pulsed laser [titanium sapphire (TiSa)] is used to excite two times the QD, which then emits an early pair (PE) and a late pair (PL) of entangled photons separated by Δt in time. The XX and X photons are then spectrally separated by a filter (F). The early XE and late XL pass a HOM Mach-Zehnder consisting of two beam splitters (BSs), performing the Bell state measurement. Polarizers (POLs) and variable retarders (VRs) are used to define the XL input state and XXE detection state accordingly. The three-photon correlation measurement is then recorded as a function of arrival times τ with avalanche photodiodes (APDs).

  • Fig. 2 Indistinguishability and degree of entanglement of QD1.

    (A) The two-photon interference measurement using copolarized settings. The histograms envelope function (bold red) is the sum of five Lorentzian peaks fitted to the HOM quintuplet. The resulting raw two-photon interference visibility is VX = 65(2) %. (B) XX-X cross-correlation measurements for different polarization detection bases: rectilinear (V, H), diagonal (D, A), and circular basis (R, L).

  • Fig. 3 Measurement of the teleportation fidelity using QD1.

    (A) Normalized third-order correlation of a D-polarized X input state for copolarized (left) and cross-polarized (right) detection of the XX photons. (B) Integrated coincidences for both detection bases for different excitation cycles (top) and the corresponding calculated teleportation fidelity (bottom). (C) Teleportation fidelities for a full set of orthogonal input states. The classical limit is highlighted as a dashed orange line.

  • Fig. 4 Single-qubit tomography and theoretical modeling of experimental data.

    (A) Real and imaginary parts of the measured density matrix of the quantum teleportation using QD2. The reference frame is chosen with respect to the diagonal input state. (B) Calculated average teleportation fidelity based on our model. The change in teleportation fidelity is shown for vanishing FSS (perfect entanglement fidelity) and varying visibility and for perfect visibility and varying FSS. The teleportation fidelity as a function of the entanglement fidelity is additionally calculated from the two-photon state’s evolution using the average X lifetime of Embedded Image ps. Each of the panels contains the expected ideal behavior (dashed line) compared with the real experimental conditions (solid line), considering polarization-dependent, relative phase shifts introduced by the optical setup. (C) The average teleportation fidelity of all measured QDs (green dot) and their predicted theoretical value (blue circle).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/12/eaau1255/DC1

    Theory

    Fig. S1. Lifetime and full third-order correlation.

    Fig. S2. Teleportation measurements on QD1.

    Fig. S3. Classical teleporter.

    Fig. S4. Single-qubit density matrices for QD2.

    Table S1. Lifetimes of measured QDs.

    Table S2. Compiled experimental and theoretical results of all QDs under investigation.

  • Supplementary Materials

    This PDF file includes:

    • Theory
    • Fig. S1. Lifetime and full third-order correlation.
    • Fig. S2. Teleportation measurements on QD1.
    • Fig. S3. Classical teleporter.
    • Fig. S4. Single-qubit density matrices for QD2.
    • Table S1. Lifetimes of measured QDs.
    • Table S2. Compiled experimental and theoretical results of all QDs under investigation.

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