An Improved Sample Complexity Lower Bound for (Fidelity) Quantum State Tomography

Abstract

We show that $\Omega (rd/\epsilon )$ copies of an unknown rank-$r$, dimension-$d$ quantum mixed state are necessary in order to learn a classical description with $1-\epsilon$ fidelity. This improves upon the tomography lower bounds obtained by Haah, et al. and Wright (when closeness is measured with respect to the fidelity function).

arXiv comment3 pages. Comments welcome

References in corpus (4)

• Optimal Cloning of Pure States
• Coding Theorem and Strong Converse for Quantum Channels
• Optimal Cloning of Pure States, Judging Single Clones
• Optimal state estimation for d-dimensional quantum systems

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• Hückel Molecular Orbital Theory on a Quantum Computer: A Scalable System-Agnostic Variational Implementation with Compact Encoding
• Empirical Sample Complexity of Neural Network Mixed State Reconstruction
• Quantum Tensor Product Decomposition from Choi State Tomography
• Hardness of observing strong-to-weak symmetry breaking
• Certifying nonstabilizerness in quantum processors
• The additivity of states uniquely determined by marginals
• Sample Optimal and Memory Efficient Quantum State Tomography
• Performance Guarantees for Quantum Neural Estimation of Entropies