Entanglement of Formation of Mixed Many-Body Quantum States via Tree Tensor Operators

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• Computational Physics

Background:

• Estimating quantum entanglement in large quantum systems is computationally challenging.
• Bipartite entanglement measures, like entanglement of formation, are crucial for understanding quantum correlations.
• Existing methods struggle with the scalability required for many-body systems.

Purpose of the Study:

• To present an efficient numerical strategy for estimating bipartite entanglement measures in many-body quantum systems.
• To introduce and utilize the tree tensor operator (TTO) tensor network Ansatz for this purpose.
• To extend the understanding of entanglement scaling laws to mixed states and finite temperatures.

Main Methods:

• Development of a numerical strategy leveraging the tree tensor operator (TTO) tensor network Ansatz.
• Utilizing TTO as a positive loopless representation for density matrices.
• Efficiently encoding bipartite entanglement information within the TTO Ansatz for upscaled estimation.

Main Results:

• Demonstrated the efficiency of the TTO Ansatz in encoding bipartite entanglement.
• Observed a finite-size scaling law for the entanglement of formation in 1D critical lattice models.
• Extended the known scaling law for entanglement entropy to mixed states at finite temperatures.

Conclusions:

• The TTO Ansatz provides an efficient and scalable method for estimating entanglement in quantum many-body systems.
• The study reveals a finite-size scaling law for entanglement of formation in relevant models.
• This work bridges the gap between entanglement entropy and entanglement of formation for mixed states.