We study prediction of one unmeasured copy of an unknown finite-dimensional pure quantum state after independently measuring the observed copies with the one-copy Haar POVM. For the resulting fixed separable observation, the Bayes predictive state under quantum relative-entropy loss is the full-rank posterior mean. We...
Naqueeb Ahmad Warsi, Ayanava Dasgupta, Masahito Hayashi· 0 citations
We study unbiased estimation of scalar-valued polynomial functionals of quantum states from independent copies. We establish an equivalence between the first-order marginal of a permutation-invariant finite-copy observable and the functional gradient. We then prove that, among unbiased permutation-invariant estimators,...
Ayanava Dasgupta, Naqueeb Ahmad Warsi, Premanshu Chatterjee· 0 citations
We study unbiased estimation of scalar-valued polynomial functionals of quantum states from independent copies. We establish an equivalence between the first-order marginal of a permutation-invariant finite-copy observable and the functional gradient. We then prove that, among unbiased permutation-invariant estimators,...
Ayanava Dasgupta, Naqueeb Ahmad Warsi, Premanshu Chatterjee· 0 citations
We study Haar-Bayesian prediction of one unmeasured copy of an unknown finite-dimensional pure quantum state after an arbitrary collective measurement on $n$ observed copies. Performance is evaluated by quantum relative entropy. For a fixed measurement, the Bayes predictive state is the posterior mean and the optimized...
Masahito Hayashi, Ayanava Dasgupta, Naqueeb Ahmad Warsi· 1 citation
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