Quantum Teleportation and Super-dense Coding in Operator Algebras

2017/09/08 by Gao, Li, Harris, Samuel J., Junge, Marius · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Operator Algebras (math.OA) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1709.02785

Abstract

Let B_d be the unital C^*-algebra generated by the elements u_jk, 0 ≤ i, j ≤ d-1, satisfying the relations that [u_j,k] is a unitary operator, and let C^*(\mathbbF_d²) be the full group C^*-algebra of free group of d² generators. Based on the idea of teleportation and super-dense coding in quantum information theory, we exhibit the two *-isomorphisms M_d(C^*(\mathbbF_d²))≅ B_d\rtimes ℤ_d\rtimes ℤ_d and M_d(B_d)≅ C^*(\mathbbF_d²)\rtimes ℤ_d\rtimes ℤ_d, for certain actions of ℤ_d. As an application, we show that for any d,m≥ 2 with (d,m)≠ (2,2), the matrix-valued generalization of the (tensor product) quantum correlation set of d inputs and m outputs is not closed.

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