Table 1 Phase settings for the on-chip preparation of all six eigenstates of the three Pauli operators and all four Bell states.

From: Integrated high-fidelity preparation and analysis of photonic two-qubit states for quantum network nodes

State/basis

\(\phi _\text {P11}\)

\(\phi _\text {P12}\)

\(\phi _\text {P21}\)

\(\phi _\text {P22}\)

\(\phi _\text {PCR}\)

\(\phi _\text {P23}\)

Fidelity (%)

Purity (%)

\(|H,V\rangle\)

\(\pi\)

0

0

0

\(\pi\)

\(\pi\)

99.274(15)

99.98(3)

\(|+,-\rangle\)

\(\pi /2\)

\(\pi\)

\(\pi /2\)

0

\(\pi\)

\(\pi\)

99.553(14)

99.40(3)

\(|+_\text {i},-_\text {i}\rangle\)

\(\pi /2\)

\(3\pi /2\)

\(\pi /2\)

\(\pi /2\)

\(\pi\)

\(\pi\)

99.13(2)

98.84(5)

\(|\Phi ^+\rangle\)

\(\pi /2\)

\(\pi\)

\(\pi /2\)

0

0

0

98.13(7)

97.70(14)

\(|\Phi ^-\rangle\)

\(\pi /2\)

0

\(\pi /2\)

0

0

0

97.00(7)

98.09(15)

\(|\Psi ^+\rangle\)

\(\pi /2\)

0

\(\pi /2\)

0

0

\(\pi\)

98.25(6)

98.36(13)

\(|\Psi ^-\rangle\)

\(\pi /2\)

\(\pi\)

\(\pi /2\)

0

0

\(\pi\)

97.39(7)

97.57(15)

\(|C\rangle\)

\(\pi /2\)

0

\(\pi /2\)

0

0

\(\pi /2\)

90.0(16)

91(3)

XX

\(\pi /2\)

0

\(\pi /2\)

0

\(\pi\)

\(\pi\)

-

-

YY

\(\pi /2\)

\(\pi /2\)

\(\pi /2\)

\(\pi /2\)

\(\pi\)

\(\pi\)

-

-

ZZ

\(\pi\)

0

\(\pi\)

0

\(\pi\)

\(\pi\)

-

-

  1. The phase shifters P1H, P1V, P2H, and P2V are set to compensate for imbalances introduced by the two-dimensional grating couplers (2DGCs) during the experiments. The chip layout and phase shifter locations are shown in Fig. 1.
  2. The states prepared on-chip are coupled out of the chip using 2DGCs and analysed by two off-chip full quantum state tomography units. From the measured coincidence counts, the density matrix of each state is recovered using maximum likelihood estimation. Here, the determined fidelity (see Eq. 3) and purity (see Eq. 4) of each state are given. Additionally, the phase settings to prepare a two-qubit cluster state \(|C\rangle\), which is sent from the sender chip to the receiver chip, and the determined fidelity and purity are given.
  3. We also list the phase settings for setting the on-chip bases X, Y, and Z.