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A minimax estimator has the minimum possible error ("risk") in the worst case.
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Without a doubt there are other reasonable definitions that would lead to different answers. Examples are given by Refs. Ng and Englert 2012 ; Flammia2012 , who each obtain substantially different conclusions by choosing different loss functions. We expect future work to consider other variations, and we hope that our results and discussion will help to inform and guide such future work
2012
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C. Ferrie and R. Blume-Kohout, Estimating the bias of a noisy coin , AIP Conference Proceeding 1443
2012
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H. K. Ng and B.-G. Englert, A simple minimax estimator for quantum states , International Journal of Quantum Information 10
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M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information . Cambridge University Press (2010)
2010
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R. Blume-Kohout, Optimal, reliable estimation of quantum states , New Journal of Physics 12
Cited in the paper.
R. Blume-Kohout, Hedged maximum likelihood quantum state estimation , Physical Review Letters 105
Cited in the paper.
A rebit is a system with a 2-dimensional real Hilbert space, containing states | ψ ⟩ = sin θ | 0 ⟩ + cos θ | 1 ⟩ \left|\psi\right\rangle=\sin\theta\left|0\right\rangle+\cos\theta\left|1\right\rangle . Alternatively, consider a qubit with the constraint ⟨ σ y ⟩ = 0 \left\langle\sigma_{y}\right\rangle=0
Cited in the paper.
Bayesian mean is known to provide optimal accuracy on average over a known prior distribution of ρ \rho , for certain important error metrics d ( ρ : ρ ^ ) d(\rho:\hat{\rho})
Cited in the paper.
Cited in the paper.
S. T. Flammia, D. Gross, Y.-K. Liu and Jens Eisert, Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators , New Journal of Physics 14
2012
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D. Mahler, L. A. Rozema, A. Darabi, C. Ferrie, R. Blume-Kohout, and A. Steinberg, Adaptive quantum state tomography improves accuracy quadratically , Physical Review Letters 111
2013
Later among the works it cites.