Enhancing the Violation of the Einstein-Podolsky-Rosen Local Realism by Quantum Hyperentanglement

Mermin’s observation [Phys. Rev. Lett. 65, 1838 (1990)] that the magnitude of the violation of local realism, defined as the ratio between the quantum prediction and the classical bound, can grow exponentially with the size of the system is demonstrated using two-photon hyperentangled states entangled in polarization and path degrees of freedom, and local measurements of polarization and path simultaneously.

Figure 1

(a) Parametric source of polarization-momentum hyperentangled two-photon states. The zero-order $\lambda /4$ wave plate placed between $M$ and the BBO crystal intercepts twice both back-reflected $\lambda$ and ${\lambda }_p$ beams and rotates by $\pi /2$ the polarization of the back-reflected field at $\lambda$ while leaving the polarization state of the UV pump beam virtually undisturbed. The orthogonal section of the emission cone identifies the entanglement ring ($e$ ring). Phase settings $\theta =0$, $\pi$ are obtained by micrometric translation of $M$. (b) Spatial coupling of input mode sets $l_u-l_d$ and $r_u-r_d$ on the BS plane. The BS output modes, $l_u^{\prime }$, $l_d^{\prime }$, $r_u^{\prime }$, and $r_d^{\prime }$ are analyzed each by a half-wave plate (HW) and a polarization beam splitter (PBS). Glass plates on modes $r_u$ and $r_d$ are used in order to measure momentum observables.