General Theory of quantum holography based on two-photon Interference

As a kind of quantum phenomenon, Hong-Ou-Mandel (HOM) interference is more robust against phase noise. Because of this feature, robust quantum holography emerges, through which wave function of interested photon can be retrieved according to HOM interference pattern. For better understanding and developing this method, we derive a theoretical framework of robust HOM holography. In the quantum holography scheme, test state and reference state interfere at beam splitter (BS). Then, degree of freedom (DOF) resolved detections (such as spatial resolved detection, temporal resolved detection or spectrum resolved detection) are used at the BS output ports, respectively. Based on the single photon detection results, the DOF resolved coincidence counts are postselected, producing interference patterns. The information of the test states is retrieved from the patterns. According to different test states and reference states, four combinations are analysed, including measuring the wave function of single photon state by using standard single photon state or coherent state and measuring the wave function of coherent state through using standard single photon state or coherent state. In all cases, information of the test states is reflected in normalized second-order correlation function or interference patterns in similar forms. Specially, the wave function of test states can be directly retrieved from the interference patterns, with no complex algorithm required. Besides, phase noise from environment has no influence on this kind quantum holography. Comparison between traditional holography and quantum holography is made and analysed.