Oded Regev

TL;DR: For all n ≥ 1, the authors gave an explicit construction of m × m matrices A1, …, An with m = 2⌊n∕2⌋ such that for any d and d × d matrices, it must be the case that d ≥ 2 √ n√ 2 ⌋−1.

Abstract: We study the simultaneous message passing (SMP) model of communication complexity, for the case where one party is quantum and the other is classical. We show that in an SMP protocol that computes some function with the first party sending q qubits and the second sending c classical bits, the quantum message can be replaced by a randomized message of O(qc) classical bits, as well as by a deterministic message of O(q c log q) classical bits. Our proofs rely heavily on earlier results due to Scott Aaronson. In particular, our results imply that quantum-classical protocols need to send Omega(sqrt{n/log n}) bits/qubits to compute Equality on n-bit strings, and hence are not significantly better than classical-classical protocols (and are much worse than quantum-quantum protocols such as quantum fingerprinting). This essentially answers a recent question of Wim van Dam. Our results also imply, more generally, that there are no superpolynomial separations between quantum-classical and classical-classical SMP protocols for functional problems. This contrasts with the situation for relational problems, where exponential gaps between quantum-classical and classical-classical SMP protocols are known. We show that this surprising situation cannot arise in purely classical models: there, an exponential separation for a relational problem can be converted into an exponential separation for a functional problem.

TL;DR: In this paper, Bar-Yossef, Jayram, and Kerenidis gave two new two-player games with Bell inequality violations that are stronger, fully explicit, and arguably simpler than earlier work.

TL;DR: A neural network model is presented that provides insights into RNA splicing, a fundamental process in the transfer of genomic information into functional biochemical products and whose predictive accuracy is on par with state-of-the-art models.