Nonlocal polarization interferometer for entanglement detection

We report a nonlocal interferometer capable of detecting entanglement and identifying Bell states statistically. This is possible due to the interferometer's unique correlation dependence on the antidiagonal elements of the density matrix, which have distinct bounds for separable states and unique values for the four Bell states. The interferometer consists of two spatially separated balanced Mach-Zehnder or Sagnac interferometers that share a polarization-entangled source. Correlations between these interferometers exhibit nonlocal interference, while single-photon interference is suppressed. This interferometer also allows for a unique version of the Clauser-Horne-Shimony-Holt–Bell test where the local reality is the photon polarization. We present the relevant theory and experimental results.

Figure 1

The two-photon interferometer is composed of two balanced Mach-Zehnder interferometers sharing a polarization-entangled source. Nonlocal interference effects are observed, while single-photon interference is suppressed.

Figure 2

Nonlocal interference observed for an orthogonal polarization event VA1HB1 is due to indistinguishable cases (a) and (b).

Figure 3

Nonlocal interference observed for an identical polarization event HA1HB1 is due to indistinguishable cases (a) and (b).

Figure 4

Sagnac interferometer setup including a directionally dependent phase modulator and dual-polarization circulator.

Figure 5

Separable- and entangled-state bounds for parameters $f+f^{*}$ and $d+d^{*}$, with corresponding measurement values for the four Bell states indicated by dots and diamonds.

Figure 6

Expected and observed values for the correlation coefficients ${\mathcal{E}}_{HH}$, ${\mathcal{E}}_{VV}$, ${\mathcal{E}}_{HV}$, and ${\mathcal{E}}_{VH}$ in the standard configuration for each Bell state. Standard deviations for these coefficients are $\le 0$.06.

Figure 7

(a) Variation of phase $\theta$ in state $\psi \left(\theta \right)\propto HV+e^{i\theta }VH$ using a liquid-crystal wave plate. (b) Variation of phase $\gamma$ in state $\varphi \left(\gamma \right)\propto HH+e^{i\gamma }VV$ using a liquid-crystal wave plate.

Figure 8

A typical CHSH Bell test. An entangled photon pair is shared between Alice and Bob, whose local measurement settings, or local realities $a_0,a_1,b_0,$ and $b_1$, are randomly chosen by a symmetric beam splitter.

Figure 9

Separable- and entangled-state bounds for parameters ${\mathcal{S}}_{\psi }$ and ${\mathcal{S}}_{\varphi }$, with corresponding measurement values for the four prepared Bell states indicated by dots and diamonds.

Figure 10

Expected and observed values for the correlation coefficients ${\mathcal{E}}_{HH}$, ${\mathcal{E}}_{VV}$, ${\mathcal{E}}_{HV}$, and ${\mathcal{E}}_{VH}$ in the CHSH configuration for each Bell state. Standard deviations for these coefficients are $\le 0.06$.

Figure 11

The NPI Sagnac experiment includes a polarization-entangled source dependent on the spectral indistinguishability of the signal and idler photons. Bell states were generated by polarization rotation and phase modulation in the path to Alice's interferometer.