For an explicit prefix/tree family of quantum states, adaptive local Pauli tomography achieves polynomial copy complexity while non-adaptive strategies require exponentially many copies.
Sample-optimal tomography of quantum states
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
It is a fundamental problem to decide how many copies of an unknown mixed quantum state are necessary and sufficient to determine the state. Previously, it was known only that estimating states to error $\epsilon$ in trace distance required $O(dr^2/\epsilon^2)$ copies for a $d$-dimensional density matrix of rank $r$. Here, we give a theoretical measurement scheme (POVM) that requires $O (dr/ \delta ) \ln (d/\delta) $ copies of $\rho$ to error $\delta$ in infidelity, and a matching lower bound up to logarithmic factors. This implies $O( (dr / \epsilon^2) \ln (d/\epsilon) )$ copies suffice to achieve error $\epsilon$ in trace distance. We also prove that for independent (product) measurements, $\Omega(dr^2/\delta^2) / \ln(1/\delta)$ copies are necessary in order to achieve error $\delta$ in infidelity. For fixed $d$, our measurement can be implemented on a quantum computer in time polynomial in $n$.
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quant-ph 2verdicts
UNVERDICTED 2representative citing papers
1D translation-invariant Gibbs states at positive temperature exhibit superexponential decay of Belavkin-Staszewski conditional mutual information, enabling efficient learning from local measurements and tensor network approximations.
citing papers explorer
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An Exponential Advantage for Adaptive Tomography of Structured States under Pauli Basis Measurements
For an explicit prefix/tree family of quantum states, adaptive local Pauli tomography achieves polynomial copy complexity while non-adaptive strategies require exponentially many copies.
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Conditional Independence of 1D Gibbs States with Applications to Efficient Learning
1D translation-invariant Gibbs states at positive temperature exhibit superexponential decay of Belavkin-Staszewski conditional mutual information, enabling efficient learning from local measurements and tensor network approximations.