Comparison of confidence regions for quantum state tomography
arXiv:2303.07136 · doi:10.1088/1367-2630/ad06d9
Abstract
The quantum state associated to an unknown experimental preparation procedure can be determined by performing quantum state tomography. If the statistical uncertainty in the data dominates over other experimental errors, then a tomographic reconstruction procedure must express this uncertainty. A rigorous way to accomplish this is via statistical confidence regions in state space. Naturally, the size of this region decreases when increasing the number of samples, but it also depends critically on the construction method of the region. We compare recent methods for constructing confidence regions as well as a reference method based on a Gaussian approximation. For the comparison, we propose an operational measure with the finding, that there is a significant difference between methods, but which method is preferable can depend on the details of the state preparation scenario.
arXiv comment20 pages, 4 figures
References in corpus (20)
- Quantum state tomography via compressed sensing
- Efficient quantum state tomography
- Quantum state estimation
- Optimal, reliable estimation of quantum states
- Complete methods set for scalable ion trap quantum information processing
- Reliable Quantum State Tomography
- Iterative algorithm for reconstruction of entangled states
- Self-guided quantum tomography
- Permutationally invariant state reconstruction
- Systematic errors in current quantum state tomography tools
- Practical, Reliable Error Bars in Quantum Tomography
- Optimal error regions for quantum state estimation
- Precision-guaranteed quantum tomography
- A comparative study of estimation methods in quantum tomography
- Confidence Polytopes in Quantum State Tomography
- Quantum key distribution rates from semidefinite programming
- Bound entangled states fit for robust experimental verification
- Error regions in quantum state tomography: computational complexity caused by geometry of quantum states
- Effect of nonnegativity on estimation errors in one-qubit state tomography with finite data
- Fast and robust quantum state tomography from few basis measurements