Systematic errors in current quantum state tomography tools

Abstract

Common tools for obtaining physical density matrices in experimental quantum state tomography are shown here to cause systematic errors. For example, using maximum likelihood or least squares optimization for state reconstruction, we observe a systematic underestimation of the fidelity and an overestimation of entanglement. A solution for this problem can be achieved by a linear evaluation of the data yielding reliable and computational simple bounds including error bars.

8 pages, 8 figures

References in corpus (18)

• Scalable multi-particle entanglement of trapped ions
• Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor
• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Efficient quantum state tomography
• Direct Fidelity Estimation from Few Pauli Measurements
• Complete universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits
• Concurrence of arbitrary dimensional bipartite quantum states
• Complete methods set for scalable ion trap quantum information processing
• Experimental Observation of Four-Photon Entangled Dicke State with High Fidelity
• Permutationally invariant quantum tomography
• Estimating entanglement measures in experiments
• Randomized Benchmarking of Multi-Qubit Gates
• Permutationally invariant state reconstruction
• Imperfect measurements settings: implications on quantum state tomography and entanglement witnesses
• Optimal error regions for quantum state estimation
• Precision-guaranteed quantum tomography
• When quantum tomography goes wrong: drift of quantum sources and other errors
• Effect of nonnegativity on estimation errors in one-qubit state tomography with finite data

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• Readout error mitigated quantum state tomography tested on superconducting qubits
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