研究目的
Investigating the feasibility and number of measurement configurations required to perform quantum tomography of a multimode multiphoton Fock state using linear optics and photon counting.
研究成果
The study demonstrates that quantum tomography of multimode multiphoton states can be achieved using linear optics and photon counting with a finite number of measurement configurations. It provides a lower bound on the number of configurations required and shows that this bound can be saturated with random linear optics configurations. The results have implications for quantum information processing and quantum metrology.
研究不足
The approach is limited to states with a definite number of photons and requires a finite number of measurement configurations. The complexity of the reconstruction increases with the number of photons and modes, and the method may not be optimal in terms of the number of configurations used.
1：Experimental Design and Method Selection:
The study employs linear optics and photon counting to perform quantum state tomography. It involves configuring an M-mode linear optical interferometer followed by photon counting to measure multiple copies of the quantum state.
2：Sample Selection and Data Sources:
The experiment considers arbitrary states of N indistinguishable photons in M modes, including mixtures of states with fixed but possibly different numbers of photons.
3：List of Experimental Equipment and Materials:
The setup includes linear optical interferometers and photon-counting detectors. The specific models and brands are not mentioned.
4：Experimental Procedures and Operational Workflow:
The procedure involves measuring the state using different configurations of the interferometer and recording the photon counts. The number of configurations required is derived and shown to be achievable with random linear optics configurations.
5：Data Analysis Methods:
The analysis involves reconstructing the state from the measurement outcomes using a pseudo-inverse method that minimizes the least-square error. The complexity of the reconstruction is analyzed in terms of the Hilbert space dimension.
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