Quantum Information Processing with Interacting Parties

Introduction

We are approaching an era where the capabilities of quantum hardware begin to meet the requirements of theoretical quantum protocols. Such times give new urgency to the Central Challenge of the theory of quantum information processing:

• For which tasks do quantum devices hold an advantage over their conventional counterparts?

Proposal Overview

My proposal addresses this challenge in the context of information processing with interacting parties, which is the natural setting for problems in cryptography, communication, and distributed computing.

We take a two-pronged approach, with each prong addressing an essential facet of interactive information processing while sharing a common focus on efficiency. A desired impact is to kick-start a new pragmatic trend that focuses on efficiency in areas where the main goal so far has been an information-theoretic understanding of ultimate quantum capabilities.

Work Package 1: Entanglement

The first work package deals with the uniquely quantum resource of entanglement, which is responsible for most quantum advantages in multi-party settings.

We will propose new tools (e.g., entanglement-preserving reductions) that will allow us to systematically identify scenarios where the generally elusive quantum advantages can be detected and realized efficiently.

Additionally, we will address major outstanding challenges, including:

1. The Parallel Repetition question.
2. Finding a simple task capable of distinguishing two competing models of entanglement.

The latter is our most ambitious goal, which would provide an alternative proof for Connes' Embedding Problem and lay theoretical groundwork for an experiment capable of identifying the right mathematical description of reality.

Work Package 2: Schur-Weyl Duality

The second work package will leverage Schur-Weyl duality to devise efficient algorithms for symmetric problems with quantum input.

We will put forth new error reduction algorithms for black-box devices (e.g., quantum majority vote) and propose highly efficient explicit quantum circuits for key subroutines like quantum Schur sampling.