Entanglement of positive definite functions on compact groups

Abstract

We define and study entanglement of continuous positive definite functions on products of compact groups. We formulate and prove an infinite-dimensional analog of Horodecki Theorem, giving a necessary and sufficient criterion for separability of such functions. The resulting characterisation is given in terms of mappings of the space of continuous functions, preserving positive definiteness. The relation between the developed group-theoretical formalism and the conventional one, given in terms of density matrices, is established through the non-commutative Fourier analysis.

published version

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Cited by in corpus (5)

• The theory of manipulations of pure state asymmetry: basic tools and equivalence classes of states under symmetric operations
• Structural approximations to positive maps and entanglement breaking channels
• Entanglement and Quantum Groups
• Tuning the separability in noncommutative space
• On the tensor convolution and the quantum separability problem