Research ArticleQuantum Mechanics

A quantum Fredkin gate

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Science Advances  25 Mar 2016:
Vol. 2, no. 3, e1501531
DOI: 10.1126/sciadv.1501531
  • Fig. 1 Experimental arrangement and truth table measurements.

    (A) The quantum Fredkin gate circuit. The states of the target qubits are either swapped or not swapped, depending on the state of the control qubit. (B) Concept of our experiment. Two SPDC photon sources allow production of path entanglement such that modes R and Y are entangled with modes B and G. The SWAP operation is carried out on the path modes, depending on the control photon’s state, such that arrival of the control photon indicates a system state of α|HC|ψ〉T1|φ〉T2 + β|VC|φ〉T1|ψ〉T2. (C) The experimental arrangement. Entangled photons are produced via SPDC (see Materials and Methods). Entering the gate via a single-mode fiber, the two target photons are sent through a PBS. The path-entangled state in Eq. 1 is produced after each target photon enters a displaced Sagnac interferometer and the which-path information is erased on an NPBS. QWPs and HWPs encode the polarization state in Eq. 2. The control consists of a polarization beam displacer interferometer. The desired control state is encoded onto modes 1R and 1B and coherently recombined. A tilted HWP is used to set the phase of the output state. Successful operation is heralded by fourfold coincidence events between the control, target, and trigger detectors. (D) Ideal (transparent bars) and measured (solid bars) truth table data for our gate. A total of 620 fourfold events were measured for each of the eight measurements, giving Embedded Image.

  • Fig. 2 Real (left) and imaginary (right) parts of the reconstructed density matrices for our four GHZ states.

    Fidelity and purity were calculated for each state. (A) Embedded Image: F = 0.88 ± 0.01 and P = 0.79 ± 0.02. (B) Embedded Image: F = 0.90 ± 0.01 and P = 0.83 ± 0.02. (C) Embedded Image: F = 0.93 ± 0.01 and P = 0.87 ± 0.02. (D) Embedded Image: F = 0.92 ± 0.01 and P = 0.85 ± 0.02.

  • Fig. 3 Measured correlations for violations of Mermin’s and Svetlichny’s inequalities.

    (A) Mermin’s inequality resulting in SM = 3.58 ± 0.06, a violation by 24 SD. (B) Svetlichny’s inequality with SSv = 4.88 ± 0.13, a violation by 7 SD. Error bars were calculated from Poissonian counting statistics.

  • Fig. 4 Estimations of nonlinear functionals of a single-qubit state with the quantum Fredkin gate.

    (A) Circuit diagram of the network. (B) Measurements of the overlap of two single-qubit states, |〈T1| T2〉|2. The fringe visibility or overlap was measured for states |0〉T1|0〉T2 (black), Embedded Image (red), and |0〉T1|1〉T2 (blue), with values of 0.82 ± 0.02, 0.52 ± 0.02, and 0.05 ± 0.01, respectively. (C) Measurements of state purity. We measure a visibility of 0.82 ± 0.02 for a pure state and 0.03 ± 0.02 for a maximally mixed state.

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Erasing the which-path information.
    • Section S2. Generation of three-photon GHZ states.
    • Fig. S1. HOM dip measurements.

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