Formulas for partial entanglement entropy.pdf
Recently Qiang Wen, currently an associate professor in Shing-Tung Yau center, made progress on the study of the uniqueness of the partial entanglement entropy (PEE).
The PEE characterizes how much the subset Ai of a region A contribute to the entanglement entropy of the region. It is a new measurement for quantum entanglement and has already been applied in condensed matter physics finding novel properties of entanglement spreading. So far, the PEE is defined following the above physical meaning without a strict mathematical definition. Following the physical meaning it should satisfied a set of physical requirements. We find one additional physical requirement for PEE, which is the invariance under a permutation. The partial entanglement entropy proposal satisfies all the physical requirements. We show that for Poincare invariant theories the physical requirements are enough to uniquely determine the PEE (or the entanglement contour) to satisfy a general formula. This is the first time we find the PEE can be uniquely determined. Since the solution of the requirements is unique and the PEE proposal is a solution, the PEE proposal is justified for Poincare invariant theories.
This paper was recently published on Physical Review Research: