Quantum transport and entanglement: Interplay and dynamical manifestations

• Applicants: Professor Dr. Reinhold Egger; Professor Dr. Igor Gornyi
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 566472220

We explore the interplay and manifestations of many-body entanglement and quantum transport along three interrelated directions from a theoretical perspective. Our proposals are realizable in state-of-the-art experiments. First, we study how transport is expected to affect quantum mechanical entanglement in many body systems in the context of the so-called quantum Mpemba effect. In quantum quench protocols realizing the quantum Mpemba effect, one has the option to tune entanglement properties at will by modifying the transport current driven through the quantum system, thus realizing an "entanglement machine". We will explore different scenarios, in particular bridging the limits of open and closed quantum systems and investigating the possibility of an entanglement-based Mpemba effect. Second, we study how entanglement affects measurement induced transport.The challenging question posed here is whether entanglement may reveal itself through modifications of the measurement-induced dynamical steering of the system. What happens if one tries to move two particles that are prepared in an entangled state by means of measurements? Will they move faster or slower than two unentangled particles as considered before? Can one quantify the role of entanglement in measurement-induced transport in terms of entanglement-renormalized effective parameters of the system? For example, given an effective Langevin description, can one associate a mass with entanglement? Focusing initially on a two-particle model, we will compare the dynamics of entangled and unentangled particles under various measurement protocols, including weak measurements with ancillary degrees of freedom, and entangling measurements. We will quantify the influence of entanglement on transport, potentially through entanglement-renormalized parameters within a Langevin-type description of measurement-induced transport. Ultimately, this work will be extended to many-body systems in order to understand the broader impact of entanglement on measurement-induced transport in complex many-body quantum systems. Third, we will construct a theoretical framework to study entanglement transport in quantum many-body systems. We will analyze how entanglement transport is affected and may be manipulated through protocols involving quantum measurements with or without feedback. Since entanglement is not a conserved quantity, we are dealing with lossy transport. We will aim at identifying optimal constructs for local entanglement (“entanglement density”), devising a framework to describe the evolution of this density in representative setups and/or under various physical conditions. To ascertain that entanglement transport is not masked by other types of currents, our initial analysis will implement conditions of vanishing electric, heat, and (if relevant) spin current flow. Our long-distance goal is to construct a hydrodynamic theory of entanglement flow in quantum many-body systems.

• DFG Programme: Research Grants