Quantum channels arising from abstract harmonic analysis

Abstract

We present a new application of harmonic analysis to quantum information by constructing intriguing classes of quantum channels stemming from specific representations of multiplier algebras over locally compact groups $G$. Beginning with a representation of the measure algebra $M(G)$, we unify and elaborate on recent counter-examples to fixed point subalgebras in infinite dimensions, as well as present an application to the noiseless subsystems method of quantum error correction. Using a representation of the completely bounded Fourier multiplier algebra $McbA(G)$, we provide a new class of counter-examples to the recently solved asymptotic quantum Birkhoff conjecture, along with a systematic method of producing the examples using a geometric representation of Schur maps. Further properties of our channels including duality, quantum capacity, and entanglement preservation are discussed along with potential applications to additivity conjectures.

20 pages; a few typos corrected from original

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Cited by in corpus (5)

• The quantum-to-classical graph homomorphism game
• Capacity Estimates via comparison with TRO channels
• Fidelity of density operator in an operator-algebraic framework
• Capacity Bounds via Operator Space Methods
• Quantum information theory and Fourier multipliers on quantum groups