Research ArticleAPPLIED SCIENCES AND ENGINEERING

Quantum interference enables constant-time quantum information processing

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Science Advances  19 Jul 2019:
Vol. 5, no. 7, eaau9674
DOI: 10.1126/sciadv.aau9674
  • Fig. 1 Photonic implementation of a fractional QKT.

    (A) HOM interference of photon number states on a variable BS, followed by two photon-counting detectors, (B) Setup: Ti:Sa, titanium-sapphire laser pump (blue); BS, 50:50 BS; τ, optical phase delay; SPDC, periodically poled potassium titanyl phosphate nonlinear spontaneous parametric down-conversion waveguide chip that produces photon number–correlated states (red); VC, variable coupler; DAQ, data acquisition unit.

  • Fig. 2 HOM interference and QKT on a Bloch sphere.

    (A to D) Two-mode Fock states (blue) correspond to Dicke states (black)—the basis of spin-S2 states. HOM interference turns Dicke states into a superposition of them. This coincides with a rotation Rθ,ϕ in the Dicke state basis. The two most distinct cases are shown: the rotation Rπ2,π2 of the pole S2;S2 and of the great circle state S2;0. (E to H) Q-function representation of (A to D). HOM interference implements a rotation on the Bloch sphere by θ=π2 around Sx of input Sz-eigenbasis Dicke states and thus the full QKT (compare Eq. 2). The sequence (x0, x1,…, xS) is (1, 0, 0, …, 0) in (A) and (0, …, 1, …, 0) in (C). The QKT transfers the input—a position eigenstate—into the same state but in Sy basis—a momentum eigenstate.

  • Fig. 3 Photon number statistics resulting from Fock state |l, S − l〉 interference.

    The probabilities of detecting ∣k〉 and ∣Sk〉 photons behind the BS for input (A) ∣0,3〉, (B) ∣0,4〉, (C) ∣0,5〉, (D) ∣1,2〉, (E) ∣2,2〉, and (F) ∣2,3〉. The BS reflectivities are r = 0.05 (green), 0.2 (red), 0.5 (blue), and 0.95 (gray). Vertical bars represent theoretical values for an ideal system, while dots are values determined in experiment. The states in (A) to (C) encode sequences (x0 = 1, x1 = 0, …, xS = 0), and states in (D) to (F) encode (0, 1, 0, 0), (0, 0, 1, 0, 0), and (0, 0, 1, 0, 0, 0), respectively. The measured probabilities set their QKTs (∣X02, ∣X12, …, ∣XS2), Xk2=l=0SAS(r)(k,l)·xl2 of fractionality α = 0.28 (green), 0.60 (red), 1.00 (blue), and 1.72 (gray).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/7/eaau9674/DC1

    Fig. S1. Symmetric Kravchuk polynomials kn(1/2)(x, N) and functions ϕn(1/2)(x, N).

    Fig. S2. Basis states for a 16-point KT.

    Fig. S3. Basis states for a 16-point discrete FT.

    Fig. S4. KT versus DFT.

    Fig. S5. Example of FFT and KT image processing.

    Fig. S6. HOM dip.

    Fig. S7. Photon number statistics resulting from Fock state ∣l, Sl〉 interference.

    Table S1. Second-order interferometric visibilities in HOM interference.

    References (3040)

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Symmetric Kravchuk polynomials kn(1/2)(x, N) and functions ϕn(1/2)(x, N).
    • Fig. S2. Basis states for a 16-point KT.
    • Fig. S3. Basis states for a 16-point discrete FT.
    • Fig. S4. KT versus DFT.
    • Fig. S5. Example of FFT and KT image processing.
    • Fig. S6. HOM dip.
    • Fig. S7. Photon number statistics resulting from Fock state ∣l, Sl〉 interference.
    • Table S1. Second-order interferometric visibilities in HOM interference.
    • References (3040)

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