Multiplexed quantum memories and high-dimensional entanglement can improve the performance of quantum repeaters by promoting the entanglement generation rate and the quantum communication channel capacity. Here, we experimentally generate a high-dimensional entangled state between a photon and a collective spin wave excitation stored in the multiplexed atomic quantum memory. We verify the entanglement dimension by the quantum witness and the entanglement of formation. Then we use the high-dimensional entangled state to test the violation of the Bell-type inequality. Our work provides an effective method to generate multidimensional entanglement between the flying photonic pulses and the atomic quantum interface.
I. INTRODUCTIONLong distance quantum communication requires quantum entanglement distributed over two end nodes of a quantum communication channel [1][2][3]. Due to the optical absorption and other noise in the channel, the error of direct communication increases exponentially with the distance, thus reduces the key rates in quantum key distribution. To overcome this problem, the quantum repeater protocol has been proposed, where a series of entanglement generation and swapping operations are performed to extend the entanglement to farther and farther nodes with only polynomial cost [4]. The practical utilization of a quantum repeater requires quantum memories [5,6]. Pioneering works have been demonstrated toward the implementation of a quantum repeater with atomic quantum memory. For example, photonic qubits have been stored as collective spin wave excitations in the atomic ensemble [7][8][9]; entanglement between the memory and transmitting photons has also been realized [10][11][12].Several methods have been proposed to further improve the quantum repeater protocol. One is to use multiplexed quantum memories, which significantly reduce the required time to establish entanglement in the quantum communication channel [13][14][15]. Another possibility is to explore high-dimensional entanglement in the quantum network [16,17], which increases the capacity of the communication channel and thus enhances the quantum communication efficiency [18]. High-dimensional entanglement also has plenty of applications beyond quantum communication, such as quantum teleportation with high capacity [19][20][21], quantum distillation [22,23] and robust Bell tests [24,25]. Recently, many efforts have been devoted to creating high-dimensional entanglement sources in different systems, like rare-earth-doped crystals [26- * Present address: 32], integrated devices [25,32] and atomic systems [33][34][35]. Moreover, the photonic qudits possessing the highdimensional entanglement have been stored in quantum memory elements, based on atomic ensembles [36,37] or rare-earth-doped crystals [9,26,38].