Continuous-variable optical quantum state tomography
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This review covers latest developments in continuous-variable quantum-state tomography of optical fields and photons, placing a special accent on its practical aspects and applications in quantum information technology. Optical homodyne tomography is reviewed as a method of reconstructing the state of light in a given optical mode. A range of relevant practical topics are discussed, such as state-reconstruction algorithms (with emphasis on the maximum-likelihood technique), the technology of time-domain homodyne detection, mode matching issues, and engineering of complex quantum states of light. The paper also surveys quantum-state tomography for the transverse spatial state (spatial mode) of the field in the special case of fields containing precisely one photon.
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Connecting Quantum Tomography and Quantum Retrodiction
The Petz recovery map equals the gradient of the log-likelihood in maximum-likelihood tomography, unifying retrodiction and state reconstruction via a shared iterative procedure.
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