Universal Time-Entanglement Trade-Off in Open Quantum Systems

We demonstrate a surprising connection between pure steady-state entanglement and relaxation time scales in an extremely broad class of Markovian open systems, where two (possibly many-body) systems interact locally with a common dissipative environment. As steady-state entanglement increases, there is generically an emergent strong symmetry that leads to a dynamical slowdown. Using this, we can prove rigorous bounds on relaxation times set by steady-state entanglement [1]. This time diverges for maximal entanglement. To test our bound, we consider the dynamics of a random ensemble of local Lindbladians that support pure steady states, finding that the bound does an excellent job of predicting how the dissipative gap varies with the amount of entanglement. Moreover, we show that (surprisingly) this bound does not apply to fermions. We use this insight to find a new set of adaptive schemes for many-body entanglement generation [2]. Our work provides general insights into how dynamics and entanglement are connected in open systems and has specific relevance to quantum reservoir engineering.



[1] A. Pocklington and A. A. Clerk PRX Quantum 5, 040305 (2024)

[2] A. Pocklington and A. A. Clerk arXiv:2409.06012 (2024)