Positivity, negativity, and entanglement

Abstract

We explore properties of the universal terms in the entanglement entropy and logarithmic negativity in 4d CFTs, aiming to clarify the ways in which they behave like the analogous entanglement measures in quantum mechanics. We show that, unlike entanglement entropy in finite-dimensional systems, the sign of the universal part of entanglement entropy is indeterminate. In particular, if and only if the central charges obey $a>c$, the entanglement across certain classes of entangling surfaces can become arbitrarily negative, depending on the geometry and topology of the surface. The negative contribution is proportional to the product of $a-c$ and the genus of the surface. Similarly, we show that in $a>c$ theories, the logarithmic negativity does not always exceed the entanglement entropy.

5 pages + refs. v2: minor change, added refs. v3: added refs

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Cited by in corpus (31)

• The entanglement negativity in random spin chains
• Negativity spectrum of one-dimensional conformal field theories
• Quantum information dynamics in multipartite integrable systems
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects
• Shape Dependence of Holographic Renyi Entropy in Conformal Field Theories
• Universal scaling of the logarithmic negativity in massive quantum field theory
• Wilson Lines and Holographic Entanglement Entropy in Galilean Conformal Field Theories
• Negativity spectrum in 1D gapped phases of matter
• Entanglement structures in qubit systems
• On shape dependence of holographic entanglement entropy in AdS4/CFT3
• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• Generalized entanglement entropy
• Entanglement and classical fluctuations at finite-temperature critical points
• Holographic Entanglement Negativity for Conformal Field Theories with a Conserved Charge
• Gravity duals of boundary cones
• Weyl, Pontryagin, Euler, Eguchi and Freund
• Time Evolution of Entanglement Negativity from Black Hole Interiors
• Entanglement entropy after selective measurements in quantum chains
• Scale vs Conformal invariance from Entanglement Entropy
• Classification of large N superconformal gauge theories with a dense spectrum
• On the Shape Dependence of Entanglement Entropy
• Entanglement and RG in the $O(N)$ vector model
• Conformal bounds in three dimensions from entanglement entropy
• Infinitely many 4d N=1 SCFTs with a=c
• Universal corner contributions to entanglement negativity
• Entanglement at the Soft-Hair Horizon
• Information Theoretic Inequalities as Bounds in Superconformal Field Theory
• Disks globally maximize the entanglement entropy in $2+1$ dimensions
• A duality theorem for a four dimensional Willmore energy
• Limitations on Dimensional Regularization in Renyi Entropy