Work

Bottlenecks in Quantum Channels and Finite Temperature Phases of Matter

Year: 2026

Type: article

Abstract: We prove an analog of the "bottleneck theorem," well-known for classical Markov chains, for Markovian quantum channels. In particular, we show that if two regions (subspaces) of Hilbert space are separated by a region that has very low weight in the channel's steady state, then states initialized on one side of this barrier will take a long time to relax, putting a lower bound on the mixing time in terms of an appropriately defined "quantum bottleneck ratio." Importantly, this bottleneck ratio involves not only the probabilities of the relevant subspaces, but also the size of off-diagonal matrix elements between them. For low temperature quantum many-body systems, we use the bottleneck theorem to bound the performance of any quasilocal Gibbs sampler. This leads to a new perspective on thermally stable quantum phases in terms of a decomposition of the Gibbs state into multiple components separated by bottlenecks. As a concrete application, we show rigorously that weakly perturbed commuting projector models with extensive energy barriers (which include certain classical and quantum expander codes) have exponentially large mixing times.

Source: Physical Review Letters

DOI: 10.1103/y9z2-52rl

Authors: Tibor Rakovszky, Benedikt Placke, Nikolas P. Breuckmann, Vedika Khemani

Institutions: Budapest University of Technology and Economics, Stanford University, University of Oxford, University of Bristol

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green