Entanglement Theory: a Quantum Odyssey, from the Generalised Quantum Stein's Lemma to Quantum Gravity

Introduction

Quantum entanglement fuels the most important quantum information processing protocols and is central to modern physics. However, the most profound questions concerning its operational meaning remain unanswered.

Key Questions

Most importantly, we do not know how efficiently mixed-state entanglement can be:

1. manipulated
2. detected
3. whether it is possible to formulate a thermodynamical theory of entanglement revolving around a unique entropic measure
4. how entanglement can be exploited to reveal quantum features of gravity in experiments with gravitationally interacting quantum systems.

A single key statement connects all these questions, the Generalised Quantum Stein's Lemma (GQSL) from quantum hypothesis testing.

Research Gap

I have uncovered [Lami and Regula, Nature Physics 19, 184 (2023); BBGLPRT, Nature Physics, in press (2023)] a fatal flaw in the original proof of the GQSL, which is now regarded as one of the most important open problems in entanglement theory.

Project Objectives

This project addresses questions (i)-(iv) in a unified way through the GQSL. The road map includes five key objectives:

1. Solve the GQSL with techniques from quantum Shannon theory.
2. Expand its scope from entanglement to other quantum resources and from states to processes.
3. Design new entanglement measures and use them to obtain tight constraints on entanglement manipulation.
4. Determine the ultimate performances of quantum communication networks and characterize entanglement in many-body systems.
5. Investigate quantum gravitational experiments systematically with the formalism of quantum hypothesis testing, formulating a complete proposal of a new type of 'dynamical' quantum gravitational experiment.

Conclusion

Thanks to my strong track record in quantum information theory, entanglement theory, and their applications to fundamental physics problems, I am in an ideal position to complete this project, whose goal is to build new bridges connecting these three key areas.