Statistical estimation of the quality of quantum-tomography protocols

Abstract

We present a complete methodology for testing the performances of quantum tomography protocols. The theory is validated by several numerical examples and by the comparison with experimental results achieved with various protocols for whole families of polarization states of qubits and ququaters including pure, mixed, entangled and separable.

20 pages, 20 figures

References in corpus (15)

• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Research on Hidden Variable Theories: a review of recent progresses
• Permutationally invariant quantum tomography
• Diluted maximum-likelihood algorithm for quantum tomography
• Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection
• Choice of Measurement Sets in Qubit Tomography
• Knowledge and ignorance in incomplete quantum state tomography
• Experimental Polarization State Tomography using Optimal Polarimeters
• Experimental quantum process tomography of non trace-preserving maps
• Quantum process tomography with coherent states
• Transition Probability (Fidelity) and Its Relatives
• Generalized tomographic maps
• Tomographic test of Bell's inequality for a time-delocalized single photon
• Optimal estimation of entanglement in optical qubit systems
• Properties of entangled photon pairs generated by a CW laser with small coherence time: theory and experiment

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