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· 1 citation· ⚡1
Affine modular linear hashing is one of the simplest classical hash families. For a prime $p>u$, the hash function is obtained by choosing $s,t$ uniformly from $\mathbb{Z}_p$ and mapping each key $x \in \{0,\ldots,u-1\}$ to one of $n$ bins by $h(x) = [(sx+t) \bmod p] \bmod n$. Despite its simplicity, the maximum load o...
Ainesh Bakshi, A. Conway, Hanna Komlós et al.· 1 citation
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
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