Photonic Implementation of Quantum Gravity Simulator

Abstract

Detecting gravity mediated entanglement can provide evidence that the gravitational field obeys quantum mechanics. We report the result of a simulation of the phenomenon using a photonic platform. The simulation tests the idea of probing the quantum nature of a variable by using it to mediate entanglement, and yields theoretical and experimental insights. We employed three methods to test the presence of entanglement: Bell test, entanglement witness and quantum state tomography. We also simulate the alternative scenario predicted by gravitational collapse models or due to imperfections in the experimental setup and use quantum state tomography to certify the absence of entanglement. Two main lessons arise from the simulation: 1) which--path information must be first encoded and subsequently coherently erased from the gravitational field, 2) performing a Bell test leads to stronger conclusions, certifying the existence of gravity mediated nonlocality.

Figures (3)

• Figure 1: Two masses in path superposition interacting gravitationally become entangled. Two massive particles with embedded magnetic spin are put into a spin-dependent path superposition. They are then left to Free Fall, where they interact via the gravitational field only. Then, the path superposition is undone and measurements are performed on the spins. During the Free Fall, each branch of the superposition accumulates a different phase, which entangles the two particles.
• Figure 2: The quantum circuit simulator (a) and its photonic implementation (b).a) Two qubits, $\ket{s_1}$ and $\ket{s_2}$, represent the spin degrees of freedom, while two qubits, $\ket{g_1}$ and $\ket{g_2}$, represent the geometry. Each stage of the experiment is mapped into quantum gates acting on the qubits. b) The simulator is implemented by using the path and polarization degrees of freedom of two photons. The spin qubits of the simulator are encoded in the polarization degree of freedom of the photons, while the geometry degrees of freedom are encoded in the photon paths. The two photons are independently prepared in a superposition of horizontal and vertical polarization and each one passes through a beam displacer (BD), which completely entangles the path of each photon with its polarization. The CZ gate is implemented thanks to bosonic interference, due to the indistinguishability of the photons, at the beam splitter (BS). Two half-waveplates (HWP) momentarily make the polarization of all paths equal in order to allow the realization of the Control-Phase (CZ) gate on this degree of freedom. Finally, the qubit state is restored by two other half-waveplates and the paths are recombined by final BDs, which disentangles path and polarization. Finally, the polarizations of the photons are measured by means of quarter- and half-waveplates (QWP and HWP)and polarizing beam splitter (PBS) followed by single photon detectors (APDs).
• Figure 3: Results of the simulator, without and with decoherence.a) Expectation values of the operators used for CHSH test on the spin qubits. The lighter colored parts in each bar (hardly visible) represent the Poissonian experimental errors associated to each observable. The orange dashed bars are the values expected from an ideal maximally entangled state. b) Real and imaginary parts of the measured density matrix of the spin qubits. c) Measured values of the entanglement witness $\mathcal{W}$ as function of the degree of decoherence $\eta$. The latter corresponds to the relative time delay of different polarization normalized to the coherence time of the photons. The purple shaded area indicates the region where the witness certifies the entanglement of the state. The dashed black line represents the theoretical curve from the model of the experimental setup. Error bars are due to Poissonian statistics of the measured events. d) Real and imaginary parts of the measured density matrix of the polarization state of the spin qubits, where the state has experienced maximum decoherence effects ($\eta=1$) introduced by a delay between linear polarizations greater than the photon coherence time. The off-diagonal terms are completely suppressed, and the state is separable.