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When Does Adaptivity Help for Quantum State Learning?
We give an adaptive algorithm that outputs a state which is $\gamma$-close in infidelity to $\rho$ using only $\tilde{O}(d^3/\gamma)$ copies, which is optimal for incoherent measurements.
Tight Bounds for Quantum State Certification with Incoherent Measurements
When $\sigma$ is the maximally mixed state $\frac{1}{d} I_d$, this is known as mixedness testing.
The Algorithmic Phase Transition of Random $k$-SAT for Low Degree Polynomials
We prove that the class of low degree polynomial algorithms cannot find a satisfying assignment at clause density $(1 + o_k(1)) \kappa^* 2^k \log k / k$ for a universal constant $\kappa^* \approx 4. 911$.
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