Heralded Three-Photon Entanglement from a Single-Photon Source on a Photonic Chip

In the quest to build general-purpose photonic quantum computers, fusion-based quantum computation has risen to prominence as a promising strategy. This model allows a ballistic construction of large cluster states which are universal for quantum computation, in a scalable and loss-tolerant way without feed forward, by fusing many small $n$-photon entangled resource states. However, a key obstacle to this architecture lies in efficiently generating the required essential resource states on photonic chips. One such critical seed state that has not yet been achieved is the heralded three-photon Greenberger-Horne-Zeilinger (3-GHZ) state. Here, we address this elementary resource gap, by reporting the first experimental realization of a heralded 3-GHZ state. Our implementation employs a low-loss and fully programmable photonic chip that manipulates six indistinguishable single photons of wavelengths in the telecommunication regime. Conditional on the heralding detection, we obtain the desired 3-GHZ state with a fidelity $0.573\pm 0.024$. Our Letter marks an important step for the future fault-tolerant photonic quantum computing, leading to the acceleration of building a large-scale optical quantum computer.

Figure 1

The heralded generation scheme for a 3-GHZ state. Six single photons are prepared at the input ports of a linear optical circuit, where we can describe the initial input quantum state as $|{\psi }_{\mathrm{in}}⟩=|1011010110⟩$ with 0 and 1 being the number of photons in each mode. The photonic circuit (depicted in the light cyan background color), which contains twelve beams splitters of three different transmissions—$1/2$ (black), $1/4$ (blue), $2/3$ (orange), and two $\pi$-phase shifters (purple)—implements a required unitary transformation $U$ for a 3-GHZ state. The 3-GHZ state in dual-rail encodings (a single photon appearing in only one of the two spatial modes describes a qubit such as $Q_1$, $Q_2$, and $Q_3$) is heralded in the modes (1–6) by a measurement pattern in the last four modes (7–10). Three phase-tunable Mach-Zehnder interferometers of phases ${\phi }_i$ and ${\theta }_i$ ($i=1$, 2, 3) are used to perform quantum state measurements on the created GHZ state.

Figure 2

The experimental setup. A single $\mathrm{InAs}/\mathrm{GaAs}$ quantum dot, resonantly coupled to an open microcavity, is used to produce pulsed resonance fluorescence single photons. The wavelength of these single photons in near infrared is then converted into a telecom wavelength of 1550 nm with a quantum frequency converter by coupling a continuous wave laser and single photons into a periodically poled lithium niobate waveguide. Five pairs of Pockels cells and polarizing beam splitters are employed to actively translate a stream of single photons into six spatial modes. Optical fibers of different lengths are used to precisely compensate time delays. The six indistinguishable single photons are then fed into a 12-modes programmable linear-optical quantum circuit, which allows the preparation and measurement of a heralded three-qubit dual-rail encoded GHZ state. The single photons at the output ports of the photonic circuit are detected by superconducting nanowire single-photon detectors. All coincidences are recorded by a coincidence count unit (not shown).

Figure 3

Characterization of the single-photon source and the photonic quantum circuit. (a) The purity of the single-photon source of telecom wavelength is evaluated by a second-order correlation function $g^2(0)$. The observed antibunched peak at zero-time delay reveals $g^2(0)=0.026(6)$. (b) Measurement of the photon indistinguishability by performing a Hong-Ou-Mandel interferometer between photon 1 and photon 2 (3, 4, 5, or 6). The corresponding measured indistinguishabilities are 0.883(7), 0.86(1), 0.86(3), 0.88(1), 0.87(3), respectively. The error bars indicates 1 standard deviation, deduced from propagated Poissonian counting statistics of the raw photon detection events. (c)–(d) Amplitude (c) and phase (d) of the ideal unitary transformation matrix (black wire frames) and their experimental reconstructions (colored bars). We send six single photons into the used six input ports of the photonic circuit, and measure the normalized amplitude and phase for each input-output combination.

Figure 4

Experimental results of the generated heralded three-qubit GHZ state. (a) Six-photon coincidence counts measured in the dual-rail basis $|0{⟩}_d/|1{⟩}_d$ accumulated for 23 h. (b) Expectation values of $⟨M_{\theta }^{\otimes 3}⟩$ with phase shift being $\theta =k\pi /3$ ($k=0$, 1, 2), each obtained from the measurement in the basis of $(|0{⟩}_d\pm e^{i\theta }|1{⟩}_d)/\sqrt{2}$. Error bars indicate 1 standard deviation calculated from Poissonian counting statistics of the raw detection events.