Group theoretical approach to entanglement

Abstract

We present a novel, universal description of quantum entanglement using group theory and generalized characteristic functions. It leads to new reformulations of the separability problem, and the positivity of partial transpose (PPT) criterion. The latter turns out to be intimately related to a certain reality condition for group representations. Within our formalism, we also show a connection between existence of entanglement and group non-commutativity.

Final version, REVTeX4 9 pages

References in corpus (3)

• Characterizing quantum theory in terms of information-theoretic constraints
• Nonclassical Moments and their Measurement
• Hilbert's 17th problem and the quantumness of states

Cited by in corpus (16)

• Quantum entanglement
• Entanglement detection
• The theory of manipulations of pure state asymmetry: basic tools and equivalence classes of states under symmetric operations
• Testing nonclassicality in multimode fields: a unified derivation of classical inequalities
• Iterations of nonlinear entanglement witnesses
• Separability, entanglement and full families of commuting normal matrices
• Unextendible Product Basis for Fermionic Systems
• Truncated su(2) moment problem for spin and polarization states
• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Entanglement of positive definite functions on compact groups
• Entanglement and Quantum Groups
• Remark on a Group-Theoretical Formalism for Quantum Mechanics and the Quantum-to-Classical Transition
• Balanced Tripartite Entanglement, the Alternating Group A4 and the Lie Algebra $sl(3,C)\oplus u(1)$
• Entanglement of Spatial Regions vs. Entanglement of Particles
• Study of the spectral properties of spin ladders in different representations via a renormalization procedure
• On the tensor convolution and the quantum separability problem