Optimal quantum tomography for states, measurements, and transformations

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We label the four spaces in such a way that W g , h ∈ ℬ ⁡ ( ℋ 1 ⊗ ℋ 3 ⊗ ℋ 2 ⊗ ℋ 4 ) W_{g,h}\in\mathcal{B}(\mathcal{H}_{1}\otimes\mathcal{H}_{3}\otimes\mathcal{H}_{2}\otimes\mathcal{H}_{4}) , with ℋ 1 = ℋ o ​ u ​ t \mathcal{H}_{1}=\mathcal{H}_{out} and ℋ 2 = ℋ i ​ n \mathcal{H}_{2}=\mathcal{H}_{in}

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