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A survey on the complexity of learning quantum states
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We survey various recent results that rigorously study the complexity of learning quantum states. These include progress on quantum tomography, learning physical quantum states, alternate learning models to tomography and learning classical functions encoded as quantum states. We highlight how these results are paving the way for a highly successful theory with a range of exciting open questions. To this end, we distill 25 open questions from these results.
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Cited by 2 Pith papers
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No low-degree tests for quantum states
Testing degree-d phase states requires at least Ω(binomial(⌊m/2⌋,⌊(d−1)/2⌋)) copies, and degree-2 states require Ω(m), so no efficient quantum low-degree test exists in the studied regime.
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A general estimation framework for continuous-variable systems
In continuous-variable quantum estimation, informational completeness is not enough: stable reconstruction needs a positive lower frame bound in a σ-regularized geometry, and quasiprobability singularities (the P func...
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