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In a recent article [X. Lai et al., Phys. Rev. Lett. 133, 033601 (2024)], the coherence time of degenerate entangled photon pairs (biphotons) generated via backward spontaneous four-wave mixing in a cold atomic ensemble was shown to be immune to optical loss and dephasing. This finding is crucial for practical applications in quantum information processing, quantum communication, and networking, where loss is inevitable. However, in studying the underlying mechanism for this loss- and dephasing-insensitive biphoton coherence time, the previous article did not take quantum noise into account. In this work, we employ the Heisenberg-Langevin approach to study this effect and provide a rigorous theoretical proof of the symmetry-protected biphoton coherence by taking quantum noise into consideration, as compared to the perturbation theory in the interaction picture. 

We report the observation of symmetry protected two-photon coherence time of biphotons generated from backward spontaneous four-wave mixing in laser-cooled 87Rb atoms. When biphotons are nondegenerate, nonsymmetric photonic absorption loss results in exponential decay of the temporal waveform of the two-photon joint probability amplitude, leading to shortened coherence time. In contrast, in the case of degenerate biphotons, when both paired photons propagate with the same group velocity and absorption coefficient, the two-photon coherence time, protected by space-time symmetry, remains unaffected by medium absorptive losses. Our experimental results validate these theoretical predictions. This outcome highlights the pivotal role of symmetry in manipulating and controlling photonic quantum states. 

One fundamental goal of quantum networks is to provide node-to-node entanglement distribution. In this work, we develop a simulator, called A 2 Tango, for entanglement generation between two remote atom-ensemble nodes in a quantum network following Briegel, Dur, Cirac and Zoller (BDCZ) protocol. We encode quantum information to the two spatial modes of local atomic-ensemble spin waves and polarization states of single photons. The basic operations include atom-photon entanglement generation, quantum memory write-read operations, two-photon Bell-state measurement, and quantum state tomography. We model multi-photon events during the local excitation and propagation to account for their induced error in entanglement generation and distribution. We investigate the entanglement generation rate and fidelity as functions of the parameters which are realizable in experiments. Our work improves the open-sourced SeQUeNCe simulator and inspires the development of future quantum networks.