# Negativity in the generalized Valence Bond Solid state

Negativity in the generalized Valence Bond Solid state Using a graphical presentation of the spin S one-dimensional Valence Bond Solid (VBS) state, based on the representation theory of the $${\textit{SU}}(2)$$ SU ( 2 ) Lie algebra of spins, we compute the spectrum of a mixed-state reduced density matrix. This mixed state of two blocks of spins A and B is obtained by tracing out the spins outside A and B, in the pure VBS state density matrix. We find in particular that the negativity of the mixed state is nonzero only for adjacent subsystems. The method introduced here can be generalized to the computation of entanglement properties in Levin–Wen models, that possess a similar algebraic structure to the VBS state in the ground state. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Negativity in the generalized Valence Bond Solid state

Quantum Information Processing, Volume 15 (11) – Aug 11, 2016
18 pages

/lp/springer-journals/negativity-in-the-generalized-valence-bond-solid-state-ajq2uamGcr
Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-016-1415-8
Publisher site
See Article on Publisher Site

### Abstract

Using a graphical presentation of the spin S one-dimensional Valence Bond Solid (VBS) state, based on the representation theory of the $${\textit{SU}}(2)$$ SU ( 2 ) Lie algebra of spins, we compute the spectrum of a mixed-state reduced density matrix. This mixed state of two blocks of spins A and B is obtained by tracing out the spins outside A and B, in the pure VBS state density matrix. We find in particular that the negativity of the mixed state is nonzero only for adjacent subsystems. The method introduced here can be generalized to the computation of entanglement properties in Levin–Wen models, that possess a similar algebraic structure to the VBS state in the ground state.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Aug 11, 2016

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