Experimental entanglement-assisted weak measurement of phase shift

Weak value amplification is a popular method in quantum metrology for enhancing the sensitivity at the expense of the signal intensity. Recently, it was suggested that the trade-off between signal intensity and sensitivity can be improved by using an entangled auxiliary system. Here, we experimentally investigate such entanglement-assisted weak measurement of small conditional phase shifts induced by an interaction between ancilla and meter qubits. We utilize entangled photon pairs and implement the required three-qubit quantum logic circuit with linear optics. The circuit comprises a two-qubit controlled phase gate and a three-qubit controlled-controlled phase gate with fully tunable conditional phase shifts. We fully characterize the output states of our circuit by quantum state tomography and perform a comprehensive analysis of the trade-off between the measurement sensitivity and the success probability of the protocol. The observed experimental results are in good qualitative agreement with theoretical predictions, but the overall performance of our setup is limited by various experimental imperfections. We provide a detailed theoretical analysis of the influence of dephasing of the entangled ancilla state, which is one of the main sources of imperfections in the experiment. We also discuss the ultimate scaling with the dimension of the entangled ancilla system.