Testing Real Quantum Theory in an Optical Quantum Network

Quantum theory is commonly formulated in complex Hilbert spaces. However, the question of whether complex numbers need to be given a fundamental role in the theory has been debated since its pioneering days. Recently it has been shown that tests in the spirit of a Bell inequality can reveal quantum predictions in entanglement swapping scenarios that cannot be modeled by the natural real-number analog of standard quantum theory. Here, we tailor such tests for implementation in state-of-the-art photonic systems. We experimentally demonstrate quantum correlations in a network of three parties and two independent EPR sources that violate the constraints of real quantum theory by over 4.5 standard deviations, hence disproving real quantum theory as a universal physical theory.

Figure 1

The entanglement swapping scenario. Two sources, that may at most be classically correlated, distribute an entangled pair between Alice and Bob, and Bob and Charlie, respectively. Alice, Bob, and Charlie each select one of three, four, and six inputs, respectively, and perform corresponding quantum measurements on their respective shares. Each measurement gives one of two possible outcomes.

Figure 2

Schematic of the experiment. The setup consists of two EPR sources, $S_1$ and $S_2$, and three measurement nodes, Alice, Bob, and Charlie. In each EPR source, the laser pulse is injected into a Sagnac loop interferometer containing a PPLN crystal to produce a pair of photons in Bell state $|{\mathrm{\Phi }}^{+}⟩$ via the SPDC process [38]. The EPR source delivers the signal photon to Bob and the idler photon to Alice (Charlie). Bob performs measurement with the two signal photons, which prepares Alice and Charlie in a Bell state. Alice and Charlie measure the idler photons according to the inputs from the quantum random number generator. PPG in EPR source $S_1$ triggers the PPG in EPR source $S_2$; DHWP: HWP for dual wavelength; SPBS: spatial PBS; $D_1$, $D_2$, $D_3$, $D_4$, $D_5$, $D_6$, $D_7$, $D_8$ are superconducting nanowire single-photon detectors (SNSPDs); FPBS: fibre PBS; DWDM: dense wavelength division multiplexer.

Figure 3

Experimental results. The ideal (a) and experimentally measured (b) values $S_{xzy}={\mathrm{\Sigma }}_{a,c=\pm 1}acp(a,b=1,c|x,y,z)$. (c) The values of $W$ in different scenarios. $W_{\mathrm{RQT}}$: real quantum theory, $W_{\text{C}\mathrm{QT}}$: complex quantum theory, $W_{\mathrm{EXP}}$: experimental result in our optical quantum network. (d) An emulation of the experiment based on complex quantum theory. The value of the red dot is given by $W_{\mathrm{EXP}}-W_{\mathrm{RQT}}$. Error bars shown in (c) and (d) represent 1 standard deviation in the experiment.