Multiqubit entanglement engineering via projective measurements

So far, various multiphoton entangled states have been observed experimentally by using different experimental setups. We present a scheme to realize many stochastic local operations and classical communication inequivalent states of three and four qubits via projective measurements on suitable entangled states. We demonstrate how these states can be observed experimentally in a single setup and study the feasibility of implementation with present-day technology.

Figure 1

Three-tangle ${\tau }_3$ for the states of Eq. (1) without (solid line) and with (dashed line) application of the transformation ${\mathcal{T}}_{+}\otimes {\mathcal{T}}_{+}\otimes {\mathcal{T}}_{+}$ (where ${\alpha }^{\prime }=\cos {\theta }^{\prime }$ and ${ϵ}^{\prime }=0$).

Figure 2

(Color online) Schematic experimental setup for the observation of the state $\mid D_4^{\left(2\right)}⟩$ (innermost section, dashed frame). The weak coherent beam, the 4:1 beam splitter as well as the detection in an additional mode $e$ are needed for the proposed experimental implementation of the five photon states $\mid {\Delta }_5⟩$ (details see text).

Figure 3

(Color online) Experimental density matrices for the measured $W_3$ (a) and ${\overline{W}}_3$ (b) states. The density matrices for the ${\mathrm{GHZ}}_3$ states of (c) and (d) are calculated from the measured $G_3^{+}$ and $G_3^{-}$ states. Displayed is the real part of the corresponding density matrix.

Figure 4

Coherence between the weak coherent beam and the SPDC photons. (a) Interference of the two possibilities how to obtain an $HV$ coincidence. (b) Enhanced emission (cloning) due to the bosonic nature of photons. The solid line shows a Gaussian fit to the data points, giving an enhancement of $1.52\pm 0.03$.

Figure 5

(Color online) Calculated fidelity of $W_4$ (a) and ${\mathrm{GHZ}}_4^{+}$ (b) states when considering only five-photon contributions [Eq. (9)]. Calculated fidelity of $W_4$ (c) and ${\mathrm{GHZ}}_4^{+}$ (d) states when considering also six-photon contributions. All calculations assume a strength of the SPDC source of $\mid z_{\mathrm{dc}}\mid =0.17$, which we experimentally observed for our setup.