Experimental construction of optical multiqubit cluster states from Bell states

Cluster states serve as the central physical resource for one-way quantum computing. We here present an experimental demonstration of the efficient cluster-state construction scheme proposed by Browne and Rudolph. In our experiment, three-photon cluster states with high purity are created from two Bell states via a qubit “fusion” operation, showing a strong violation of a three-particle Mermin inequality of $\mid ⟨A⟩\mid =3.10\pm 0.03$. In addition, the entanglement properties of the cluster states are examined under ${\sigma }_z$ and ${\sigma }_x$ measurements on a qubit. This scheme could be extended to any desired number of qubits and represents an essential step for the optical one-way quantum computation.

Figure 1

(a). The nondeterministic qubit fusion operation. $D2$ stand for a polarization discriminating photon detector. Two photons of different spatial modes are mixed in a PBS, the output in mode $3^{\prime }$ is accepted only when $D2$ receives exactly one photon. (b). A successful Type-I fusion combines two linear clusters of length $n$ and $m$ into a new one of length $(n+m-1)$.

Figure 2

(Color online) Experimental setup for generating a three-photon cluster state from two pairs of maximally entangled photons produced by Type-II spontaneous parametric down conversion. The half wave plate (HWP) used in paths 2 and 4 are used to locally transform the photon from $H∕V$ basis to +/− basis and the four polarizers P1, P2, P3, P4 are used for necessary polarization analysis. In the experiment, we managed to obtain an average twofold coincidence of $2.2\times {10}^4{\mathrm{s}}^{-1}$.

Figure 3

(Color online) (a) Experimental data under eight different polarization settings. Two desired terms $+H+$ and $-V-$ are prominent while other six are strongly depressed on average to around 3% of these desired ones. (b) Experimental data in the diagonal basis showing the two components are in a coherent superposition. Maximum interference occurs at zero delay between the two incoming photons.

Figure 4

(Color online) Experimental results showing polarization correlation between photon 1 and 4, under a ${\sigma }_z$ and ${\sigma }_x$ measurement of photon 3. (a). Data obtained under a ${\sigma }_z$ measurement. The coincident counts when $P1$ was set at $-45°$ were so strongly suppressed that they are close to zero; while counts when $P1$ was set at 45° are the most prominent, twice as when $P1$ was set at 90° and with a fringe of visibility $0.93\pm 0.03$. The experimental results clearly agree that the state obtained is ${\mid +⟩}_1\otimes {\mid +⟩}_4$. (b). Data obtained under a ${\sigma }_x$ measurement. The two sinusoidal curves with a visibility of $0.79\pm 0.03$ demonstrate that photons 1 and 4 are in an entangled state as ${\mid +⟩}_1{\mid +⟩}_4+{\mid -⟩}_1{\mid -⟩}_4$.