TY - JOUR

T1 - Quantum Teleportation and Super-Dense Coding in Operator Algebras

AU - Gao, Li

AU - Harris, Samuel J.

AU - Junge, Marius

N1 - Funding Information:
This work was partially supported by the Illinois University Fellowship [to L.G.]; Trjitzinsky Fellowship [to L.G.]; and NSF (National Science Foundation) [DMS-1501103 to M.J., DMS-1700168 to L.G. and M.J.].
Publisher Copyright:
© 2019 The Author(s).

PY - 2021/6/1

Y1 - 2021/6/1

N2 - We show 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. Our argument uses a reformulation of super-dense coding and teleportation in terms of C∗-algebra isomorphisms. Namely, we prove that for certain actions of cyclic group {Zd, 'Equation Presented' where Bd is the universal unital C∗-algebra generated by the elements ujk, 0 ≤ i, j ≤ d-1, satisfying the relations that [uj,k] is a unitary operator, and C∗(Fd2) is the universal C∗-algebra of d2 unitaries. These isomorphisms provide a nice connection between the embezzlement of entanglement and the non-closedness of quantum correlation sets.

AB - We show 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. Our argument uses a reformulation of super-dense coding and teleportation in terms of C∗-algebra isomorphisms. Namely, we prove that for certain actions of cyclic group {Zd, 'Equation Presented' where Bd is the universal unital C∗-algebra generated by the elements ujk, 0 ≤ i, j ≤ d-1, satisfying the relations that [uj,k] is a unitary operator, and C∗(Fd2) is the universal C∗-algebra of d2 unitaries. These isomorphisms provide a nice connection between the embezzlement of entanglement and the non-closedness of quantum correlation sets.

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U2 - 10.1093/imrn/rnz095

DO - 10.1093/imrn/rnz095

M3 - Article

AN - SCOPUS:85143597126

SN - 1073-7928

VL - 2021

SP - 9146

EP - 9179

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 12

ER -