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arXiv:quant-ph/0602150 · Physical Review A

Tomographic test of Bell’s inequality for a time-delocalized single photon

Milena D’Angelo, Alessandro Zavatta, Valentina Parigi, Marco Bellini

Published Nov 29, 2006• 37 citations
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Abstract

Time-domain balanced homodyne detection is performed on two well-separated temporal modes sharing a single photon. The reconstructed density matrix of the two-mode system is used to prove and quantify its entangled nature, while the Wigner function is employed for an innovative tomographic test of Bell's inequality based on the theoretical proposal by Banaszek and Wodkiewicz [Phys. Rev. Lett. 82, 2009 (1999)]. Provided some auxiliary assumptions are made, a clear violation of the Banaszek-Bell inequality is found.

DOI
10.1103/physreva.74.052114

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Time-domain balanced homodyne detection is performed on two well-separated temporal modes sharing a single photon. The reconstructed density matrix of the two-mode system is used to prove and quantify its entangled nature, while the Wigner function is employed for an innovative tomographic test of Bell's inequality based on the theoretical proposal by Banaszek and Wodkiewicz [Phys. Rev. Lett. 82, 2009 (1999)]. Provided some auxiliary assumptions are made, a clear violation of the Banaszek-Bell inequality is found.
We have developed a technique for dual-temporal-mode, ultrafast, time-domain, balanced homodyne detection. We have tested it by performing homodyne measurements on pairs of picosecond-duration temporal modes (or “time bins”) carrying a delocalized single photon. The experimental homodyne data have been used to reconstruct both the density matrix and the two-mode Wigner function of the delocalized state, thus showing the correlations existing between the pair of temporal modes carrying the single photon.
Bell’s inequality plays an important role in quantum mechanics. Many experiments have been made to test the Bell’s inequality by using various bipartite entangled sources. However, the maximal violation of the Bell inequality (i.e., the Cirel’son’s limit) has not been reached yet, due to various practically-existing imperfections (e.g., entangled source is not the pure maximally-entangled state, and the measurement settings used are not the best ones). In this paper, we investigate experimentally an approach to enhance the violation degree of Bell’s inequality with the commercialized entangled photons by optimizing the measurement settings for the experimentally-reconstructed density matrix of the entangled photons. It is shown that the measurement setting related to the pure entangled state can not get maximally violation generally. However, upon the density matrix reconstructed by tomographic technique, optimal measurement settings can be found. With these optimal settings, we consequently found that the violation degree of the Bell’s inequality can be increased. This suggests a possible approach to optimize the test of Bell’s inequality.
We present a review of our recent studies concerning remotely prepared entangled bits (ebits) made of a single photon coherently delocalized between two well-separated temporal modes (or time bins). The preparation scheme represents a remotely tunable source for tailoring arbitrary ebits, whether maximally or non-maximally entangled, which is highly desirable for applications in quantum information technology. The remotely prepared ebit is analyzed by performing both single-mode and two-mode homodyne tomography with the ultra-fast balanced homodyne detection scheme recently developed in our lab. Beside the non-classical behavior typical of single-photon Fock states (negative values around the origin), the reconstructed two-mode Wigner function is found to be characterized by an intriguing phase and by correlations between the two distant time bins sharing the single photon.
e present a review of our recent studies concerning remotely prepared entangled bits (ebits) made of a single photon coherently delocalized between two well-separated temporal modes (or time bins). The preparation scheme represents a remotely tunable source for tailoring arbitrary ebits, whether maximally or non-maximally entangled, which is highly desirable for applications in quantum information technology. The remotely prepared ebit is analyzed by performing both single-mode and two-mode homodyne tomography with the ultra-fast balanced homodyne detection scheme recently developed in our lab. Beside the non-classical behavior typical of single-photon Fock states (negative values around the origin), the reconstructed two-mode Wigner function is found to be characterized by an intriguing phase and by correlations between the two distant time bins sharing the single photon.