24 Feb 2025 | Ainesh Bakshi, Allen Liu, Ankur Moitra, Ewin Tang
The paper "High-Temperature Gibbs States are Unentangled and Efficiently Preparable" by Ainesh Bakshi, Allen Liu, Ankur Moitra, and Ewin Tang from MIT and UC Berkeley, respectively, explores the properties of thermal states in quantum many-body systems. The main findings are:
1. **Sudden Death of Thermal Entanglement**: The authors prove that for a local Hamiltonian on a graph with degree \(\varnothing\), the Gibbs state at inverse temperature \(\beta\) is separable (i.e., a classical distribution over product states) for all \(\beta < 1 / (c \varnothing)\), where \(c\) is a constant. This resolves the question of whether many-body systems can exhibit entanglement at high temperatures.
2. **Efficient State Preparation**: They show that the Gibbs state can be efficiently sampled from. Specifically, for \(\beta < 1 / (c \varnothing^2)\), a state \(\epsilon\)-close to the Gibbs state can be prepared using a depth-one quantum circuit and \(\text{poly}(n, 1 / \epsilon)\) classical overhead.
The paper provides a detailed technical overview of the proof, including the use of cluster expansion and sampling-to-counting reductions. The authors also discuss related work and highlight the significance of their results in understanding the behavior of entanglement in quantum many-body systems.The paper "High-Temperature Gibbs States are Unentangled and Efficiently Preparable" by Ainesh Bakshi, Allen Liu, Ankur Moitra, and Ewin Tang from MIT and UC Berkeley, respectively, explores the properties of thermal states in quantum many-body systems. The main findings are:
1. **Sudden Death of Thermal Entanglement**: The authors prove that for a local Hamiltonian on a graph with degree \(\varnothing\), the Gibbs state at inverse temperature \(\beta\) is separable (i.e., a classical distribution over product states) for all \(\beta < 1 / (c \varnothing)\), where \(c\) is a constant. This resolves the question of whether many-body systems can exhibit entanglement at high temperatures.
2. **Efficient State Preparation**: They show that the Gibbs state can be efficiently sampled from. Specifically, for \(\beta < 1 / (c \varnothing^2)\), a state \(\epsilon\)-close to the Gibbs state can be prepared using a depth-one quantum circuit and \(\text{poly}(n, 1 / \epsilon)\) classical overhead.
The paper provides a detailed technical overview of the proof, including the use of cluster expansion and sampling-to-counting reductions. The authors also discuss related work and highlight the significance of their results in understanding the behavior of entanglement in quantum many-body systems.