Measuring the continuous variable quantum entanglement with a parametric amplifier assisted homodyne detection

Traditional method for measuring continuous-variable quantum entanglement relies on balanced homodyne detections, which are sensitive to vacuum quantum noise coupled in through losses resulted from many factors such as detector's quantum efficiency and mode mismatching between detected field and local oscillator. In this paper, we propose and analyze a new measurement method, which is realized by assisting the balanced homodyne detections with a high gain phase sensitive parametric amplifier. The employment of the high gain parametric amplifier helps to tackle the vacuum quantum noise originated from detection losses. Moreover, because the high gain parametric amplifier can couple two fields of different types in a phase sensitive manner, the proposed scheme can be used to reveal quantum entanglement between two fields of different types by using only one balanced homodyne detection. Furthermore, detailed analysis shows that in the multi-mode case, the proposed scheme is also advantageous over the traditional method. Such a new measurement method should find wide applications in quantum information and quantum metrology involving measurement of continuous variables.