Optimal error regions for quantum state estimation
arXiv:1302.4081 · doi:10.1088/1367-2630/15/12/123026
Abstract
Rather than point estimators, states of a quantum system that represent one's best guess for the given data, we consider optimal regions of estimators. As the natural counterpart of the popular maximum-likelihood point estimator, we introduce the maximum-likelihood region---the region of largest likelihood among all regions of the same size. Here, the size of a region is its prior probability. Another concept is the smallest credible region---the smallest region with pre-chosen posterior probability. For both optimization problems, the optimal region has constant likelihood on its boundary. We discuss criteria for assigning prior probabilities to regions, and illustrate the concepts and methods with several examples.
13 pages, 5 figures, 1 table, 23 references; title changed; v2 corrects some short-comings of v1 and reports additional details
References in corpus (5)
- Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
- Knowledge and ignorance in incomplete quantum state tomography
- Incomplete quantum state estimation: a comprehensive study
- Robust error bars for quantum tomography
- Numerical Estimation Schemes for Quantum Tomography
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- Systematic errors in current quantum state tomography tools
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- Quantum state estimation with informationally overcomplete measurements
- Statistical Methods for Quantum State Verification and Fidelity Estimation
- Device-independent point estimation from finite data and its application to device-independent property estimation
- Quantum State Tomography of a Single Qubit: Comparison of Methods
- Monte Carlo sampling from the quantum state space. II
- Very strong evidence in favor of quantum mechanics and against local hidden variables from a Bayesian analysis
- Monte Carlo sampling from the quantum state space. I
- High posterior density ellipsoids of quantum states
- Confidence Polytopes in Quantum State Tomography
- Adaptive quantum tomography
- Quantum key distribution rates from semidefinite programming
- Bound entangled states fit for robust experimental verification
- Optimal error intervals for properties of the quantum state
- Uncertainty Quantification for Matrix Compressed Sensing and Quantum Tomography Problems
- Quantum Model Averaging
- On determining which quantum measurement performs better for state estimation
- Error regions in quantum state tomography: computational complexity caused by geometry of quantum states
- Practical and reliable error bars for quantum process tomography
- Informationally Incomplete Quantum Tomography
- Proper error bars for self-calibrating quantum tomography
- Using prior expansions for prior-data conflict checking
- Efficient Bayesian credible-region certification for quantum-state tomography
- Reliable experimental quantification of bipartite entanglement without reference frames
- Bayesian error regions in quantum estimation I: analytical reasonings
- Provable quantum state tomography via non-convex methods
- Comparison of confidence regions for quantum state tomography
- Probing Bayesian credible regions intrinsically: a feasible error certification for physical systems
- Evidence-based certification of quantum dimensions
- User-friendly confidence regions for quantum state tomography
- Bayesian error regions in quantum estimation II: region accuracy and adaptive methods
- User-specified random sampling of quantum channels and its applications
- Systematic errors in direct state measurements with quantum controlled measurements
- The initial system-bath state via the maximum-entropy principle
- Analysing multiparticle quantum states
- Relative-belief inference in quantum information theory
- Checking the Model and the Prior for the Constrained Multinomial
- State learning from pairs of states