Towards Quantum Experiments with Human Eyes as Detectors Based on Cloning via Stimulated Emission

We show theoretically that a large Bell inequality violation can be obtained with human eyes as detectors, in a “micro-macro” experiment where one photon from an entangled pair is greatly amplified via stimulated emission. The violation is robust under photon loss. This leads to an apparent paradox, which we resolve by noting that the violation proves the existence of entanglement before the amplification. The same is true for the micro-macro experiments performed so far with conventional detectors. However, we also prove that there is genuine micro-macro entanglement even for high loss.

Figure 1

A single-photon qubit is amplified through cloning via stimulated emission in a nonlinear crystal ($\chi$). The clones are split into two orthogonal polarization modes, and each mode is detected by a naked human eye. The polarization basis can be varied with the help of a wave plate ($\varphi$).

Figure 2

Efficiency $\epsilon$ and visibility $V$, as defined in the text, of the human-eye detection method for amplified single-photon qubits, as a function of the mean photon number after amplification $⟨N_{\mathbf{a}}⟩$ (thick lines). The efficiency has a maximum of $\epsilon =0.61$ for $⟨N_{\mathbf{a}}⟩=288$. The visibility never drops below $\frac{1}{\sqrt{2}}$, which is relevant for Bell experiments in the micro-macro setting of Refs. 7, 8; cf. text and Fig. 3. We also show $V$ and $\epsilon$ for the case of additional losses after the amplification, corresponding to overall transmission factors $\frac{\eta }{2}$ (thin lines) and $\frac{\eta }{4}$ (dashed lines).

Figure 3

We consider the micro-macro entanglement scenario of Refs. 7, 8, but with human-eye detectors for the macro system.