Author

Ainesh Bakshi

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Preprint Sep 2026

Optimal spectrum estimation

We prove that the spectrum of an unknown $d$-dimensional quantum state can be estimated to error $\varepsilon$ in total variation distance using \[ O\!\left(d^2\min\left\{ \frac{1}{(\varepsilon\log d)^4},\; \frac{1}{(\varepsilon\log d)^2} \right\}\right) \] copies. This matches the recent lower bound of Wang. When rest...

Ainesh Bakshi, A. Singh, Xin-Yu Tan · 3 citations · ⚡2

Preprint Aug 2026

Lower Bounds for Linear Hashing via Arithmetic Kakeya

It is shown that, for sufficiently large $p, the expected maximum loads in the modular and real settings are essentially the same, giving an alternative route to an $n^{1/3+o(1)}$ upper bound, and the Kakeya conjecture for upper Minkowski dimension is proved.

Ainesh Bakshi, A. Conway, Hanna Komlós et al. · 1 citation

Preprint Aug 2026

On the Approximability of Boolean Max-$k$-CSP

A polynomial time algorithm is obtained that achieves a $(k/2^k)-approximation, improving on the previous best guarantee of $0.626612\; k/2^k$, and is an extension of a recently established Gaussian comparison inequality used to resolve the Weak Simplex Conjecture in coding theory.

Ainesh Bakshi · 1 citation