Quantum-state tomography is a crucial ingredient in quantum-computations and engineering. Measurement of state fidelity is fundamental for determination of the performance of various quantum protocols and their specific implementations. Tomography can be also used in error correction protocols . Principally, tomography of two types of quantum objects needs to be performed. The first measurements can be done over photons which are good transmitters of quantum information. The other on “atomic” systems, which offers the ability to manipulate the information. Atomic gasses are among the most promises candidates for quantum-information processing and storage. Typically, this task is performed in ultra-cold gasses , where various relaxation processes are mitigated. At the same time, hot atomic vapours also offer various advantages, like the simplicity of ensemble preparing (lack of cooling apparatus or fact that in paraffin-coated cells all interactions are averaged over the volume of the cell).
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