SVD Entanglement Entropy
arXiv:2307.06531 · doi:10.1007/JHEP12(2023)123
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 Rényi SVD entropy in various field theories and examine holographic calculations using the AdS/CFT correspondence.
42 pages, 23 figures, V2: minor adjustments
References in corpus (13)
- QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
- Aspects of generic entanglement
- Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
- Entanglement of low-energy excitations in Conformal Field Theory
- Quantum Dimension as Entanglement Entropy in 2D CFTs
- Notes on Quantum Entanglement of Local Operators
- Pseudo Entropy in Free Quantum Field Theories
- Aspects of Pseudo Entropy in Field Theories
- AdS/BCFT with Brane-Localized Scalar Field
- Topological pseudo entropy
- Holographic BCFT with a Defect on the End-of-the-World Brane
- On the real-time evolution of pseudo-entropy in 2d CFTs
- Pseudo complexity of purification for free scalar field theories
Cited by in corpus (13)
- Temporal Entanglement Entropy as a probe of Renormalization Group Flow
- Entanglement Phase Transition in Holographic Pseudo Entropy
- Pseudo entropy under joining local quenches
- Probing quantum chaos through singular-value correlations in sparse non-Hermitian SYK model
- Relation between time- and spacelike entanglement entropy
- Sum rule for the pseudo-Rényi entropy
- Musings on SVD and pseudo entanglement entropies
- Complex entanglement entropy for complex conformal field theory
- Holographic timelike entanglement in AdS Vaidya
- Spacetime quantum mechanics for bosonic and fermionic systems
- The ITransverse.jl library for transverse tensor network contractions
- Non-Hermiticity induced thermal entanglement phase transition
- Generalised Entanglement Entropies from Unit-Invariant Singular Value Decomposition