Heralded generation of multiphoton entanglement

We present a scheme, based only on linear optics and standard photon detection, that allows to generate heralded multiphoton entangled states of arbitrary photon number from spontaneous parametric downconversion (PDC) in the weak interaction regime. The scheme also works in the strong interaction regime, i.e., for the production of large photon numbers, when photon-number resolving detectors with nearly perfect quantum efficiency are used. In addition, the same setup can be used for quantum metrology as multiphoton interferometer with sensitivity at the Heisenberg limit.

Figure 1

Schematic setup for the heralded preparation of multiphoton maximally entangled states. $\left(\mathbf{a}\right)$ Conditional generation of two-photon Bell states. $\left(\mathbf{b}\right)$ Conditional generation of three-photon GHZ states. $\left(\mathbf{c}\right)$ Conditional generation of multiphoton states of the GHZ type.

Figure 2

Multiphoton interferometer for quantum metrology. $\left(\mathbf{a}\right)$ Eight-photon path-entangled NOON states can be generated by performing a polarization measurement in all of the output modes in the linear polarization basis $\mid \pm ⟩$ where the number of $\mid -⟩$ projections is odd. This results in pure eight-photon interference due to projection onto the (nonlocal) path-entangled eight-photon state $\mid \Psi ⟩=1∕\sqrt{2}(\mid 8{⟩}_{a2b2a4b4}\mid 0{⟩}_{a1b1a3b3}+\mid 0{⟩}_{a2b2a4b4}\mid 8{⟩}_{a1b1a3b3})$. $\left(\mathbf{b}\right)$ Generalized scheme for $4n$-photon NOON states.