Experimental demonstration of adaptive quantum state estimation

Summary form only given. Quantum theory is inherently statistical. This entails repetition of experiments over a number of identically prepared quantum objects, for example, quantum states, if one wants to know the “true state” or the “true value” of the parameter that specifies the quantum state. Such an estimation procedure is particularly important for quantum communication and quantum computation, and is also indispensable to quantum metrology [1,2]. In applications, one needs to design the estimation procedure in such a way that the estimated value of the parameter should be close to the true value (consistency), and that the uncertainty of the estimated value should be as small as possible (efficiency) for a given limited number of samples. In order to realize these requirements, Nagaoka advocated an adaptive quantum state estimation (AQSE) procedure [3], and recently Fujiwara proved the strong consistency and asymptotic efficiency for AQSE [4]. In this paper, we report the first experimental demonstration of AQSE using photons[5]. The angle of a half wave plate (HWP) that initializes the linear polarization of input photons is estimated using AQSE (Fig. 1). sequence of AQSE is carried out with 300 input photons, and the sequence is repeated 500 times for four different settings of HWP. The statistical analysis of these results verifies the strong consistency and asymptotic efficiency of AQSE. Recently, it has been mathematically proven that the precision of AQSE outperforms the conventional state tomography [6]. It is thus expected that AQSE will provide a useful methodology in the broad area of quantum information processing, communication, and metrology. This work was supported in part by JSPS Quantum Cybernetics, JSPS-Kakenhi, JST-CREST, FIRST Program, Special Coordination Funds for Promoting Science and Technology, Research Foundation for Opto-Science and Technology.