SVD Entanglement Entropy

TL;DR

This paper introduces SVD entanglement entropy, a new measure for quantifying entanglement between two states, with applications in quantum phase transitions and holography.

Contribution

It defines the SVD entanglement entropy, explores its properties, and applies it to quantum many-body systems and holographic theories, extending traditional entanglement measures.

Findings

SVD entanglement entropy is bounded by the log of Hilbert space dimensions.

It is enhanced when states are in different quantum phases.

Calculations are performed in field theories and holographic models.

Abstract

In this paper, we introduce a new quantity called SVD entanglement entropy. This is a generalization of entanglement entropy in that it depends on two different states, as in pre- and post-selection processes. This SVD entanglement entropy takes non-negative real values and is bounded by the logarithm of the Hilbert space dimensions. The SVD entanglement entropy can be interpreted as the average number of Bell pairs distillable from intermediates states. We observe that the SVD entanglement entropy gets enhanced when the two states are in the different quantum phases in an explicit example of the transverse-field Ising model. Moreover, we calculate the R\'enyi SVD entropy in various field theories and examine holographic calculations using the AdS/CFT correspondence.