Rahul Jain

A Direct Product Theorem for One-Way Quantum Communication

2020 · arXiv (Cornell University)

We prove a direct product theorem for the one-way entanglement-assisted quantum communication complexity of a general relation $f\subseteq\mathcal{X}\times\mathcal{Y}\times\mathcal{Z}$. For any $\varepsilon, ζ> 0$ and any $k\geq1$, we show that \[ \mathrm{Q}^1_{1-(1-\varepsilon)^{Ω(ζ^6k/\log|\mathcal{Z}|)}}(f^k) = Ω\left(k\left(ζ^5\cdot\mathrm{Q}^1_{\varepsilon + 12ζ}(f) …

Quantum Measurement Adversary

2023 · IEEE Transactions on Information Theory

Multi-source extractors are functions that extract uniform randomness from multiple (weak) sources of randomness. Quantum multi-source extractors were considered by Kasher and Kempe (2010) (for the quantum independent adversary and the quantum bounded storage adversary), …