[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Universal Multipartite D-Level Entanglement Witnesses for Realistic Measurement Settings

摘要： Entanglement is an essential resource in quantum information science [1] and its presence in any quantum system can be experimentally detected through entanglement witness operators [2]. In particular, measuring a negative expectation value of a witness with high statistical confidence provides a necessary and sufficient condition to confirm the generation of a genuine multipartite [3] and/or d-level entangled state [4]. In recent years, the experimental generation of complex quantum states has intensified the need for witnesses that are capable of detecting such systems and are experimentally optimal at the same time. This means that the witness should require the least measurement effort (in terms of number and complexity of the measurement settings), include only projections on single qudits, while at the same time possessing a high noise tolerance (Fig. 1a). However, “experimentally-friendly” witnesses capable of accomplishing these tasks have not been derived yet. Here, we provide a universal method to construct experimentally-optimal witnesses capable of detecting entanglement in any arbitrarily-complex quantum state that can be customized towards experimental restrictions and/or accessible measurement settings [5]. As an example, using our technique and exploiting the stabilizer formalism [6,7], we derive an entanglement witness for N-partite d-level cluster states that consists of only two measurement settings. We apply our method to experimentally measure the expectation value of a witness for a four-partite three-level optical cluster states [8]. Through projection measurements in an optical time/frequency photon system [9-10], we measured a witness expectation value -0.28±0.04<0 (Fig.1b), thus confirming the realization of genuine four-partite cluster state entanglement. Finally, we used the derived witness to investigate the white noise tolerance of multipartite d-level cluster states and demonstrate that this increases with the number of level. Our approach is completely universal and can be applied to any complex quantum state.