Abstract
Precise characterization of quantum devices is usually achieved with quantum tomography. However, most methods which are currently widely used in experiments, such as maximum likelihood estimation, lack a well-justified error analysis. Promising recent methods based on confidence regions are difficult to apply in practice or yield error bars which are unnecessarily large. Here, we propose a practical yet robust method for obtaining error bars. We do so by introducing a novel representation of the output of the tomography procedure, the quantum error bars. This representation is (i)concise, being given in terms of few parameters, (ii)intuitive, providing a fair idea of the "spread" of the error, and (iii)useful, containing the necessary information for constructing confidence regions. The statements resulting from our method are formulated in terms of a figure of merit, such as the fidelity to a reference state. We present an algorithm for computing this representation and provide ready-to-use software. Our procedure is applied to actual experimental data obtained from two superconducting qubits in an entangled state, demonstrating the applicability of our method.
Highlights
Introduction.—Recent experimental developments have demonstrated increasingly precise manipulation and control of quantum systems, paving the way towards the hopeful implementation of a quantum computer [1,2,3,4,5,6,7,8,9,10,11,12]
Our main result is a novel representation of the output of the tomography procedure—a summary of what the tomographic data tells us about the state of the system—which we call quantum error bars
The quantum error bars are designed to mimic the role of classical error bars
Summary
We do so by introducing a novel representation of the output of the tomography procedure, the quantum error bars This representation is (i) concise, being given in terms of few parameters, (ii) intuitive, providing a fair idea of the “spread” of the error, and (iii) useful, containing the necessary information for constructing confidence regions. In the realistic regime where finite data are collected, the error bars provided by most methods which are widely applied in current experiments [19,22,23,24] are typically ill justified and may lead to deceiving conclusions [25,26,27] To remedy this problem, Blume-Kohout [27] and Christandl and Renner [28] resort to confidence regions.
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