Experimental implementation of arbitrary entangled operations

Quantum entanglement lies at the heart of quantum mechanics in both fundamental and practical aspects. The entanglement of quantum states has been studied widely both theoretically and experimentally, however, the entanglement of operators has not been studied much experimentally in spite of its importance. Here, we propose a scheme to realize arbitrary entangled operations based on a coherent superposition of local operations with a non-zero probability of failure. Then, we experimentally implement several intriguing two-qubit entangled operations in photonic systems. We also discuss the generalization of our scheme to extend the number of superposed operations and the number of qubits. Due to the simplicity of our scheme, we believe that it can reduce the complexity or required resources of the quantum circuits and provide insights to investigate properties of entangled operations.