Augmented Index and Quantum Streaming Algorithms for DYCK(2)

TL;DR

This paper introduces quantum information theoretic tools to establish lower bounds on quantum information complexity, leading to new insights into quantum streaming algorithms for the DYCK(2) language.

Contribution

It develops new quantum tools for analyzing information complexity and applies them to derive lower bounds for quantum streaming algorithms for DYCK(2).

Findings

Lower bounds on quantum information complexity for Augmented Index.

Quantum generalization of Jain and Nayak's argument.

Space complexity lower bounds for quantum streaming algorithms for DYCK(2).

Abstract

We show how two recently developed quantum information theoretic tools can be applied to obtain lower bounds on quantum information complexity. We also develop new tools with potential for broader applicability, and use them to establish a lower bound on the quantum information complexity for the Augmented Index function on an easy distribution. This approach allows us to handle superpositions rather than distributions over inputs, the main technical challenge faced previously. By providing a quantum generalization of the argument of Jain and Nayak [IEEE TIT'14], we leverage this to obtain a lower bound on the space complexity of multi-pass, unidirectional quantum streaming algorithms for the DYCK(2) language.