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A New Generalized Schur-Weyl Duality

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Schur-Weyl duality theory has many applications in quantum information and quantum computation theory. In this paper, we first give an equivalent relationship about the subgroup of unitary group U(d) and give several examples of subgroup of U(d) which satisfy the equivalent relationship. Next, we establish a new generalized Schur-Weyl which is an improvement of the classical Schur-Weyl duality and a generalized Schur-Weyl duality proved recently.

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  1. Goodman, R., Wallach, N.R.: Representations and invariants of the classical groups. Cambridge University Press (1998)

  2. Harrow, A.: Applications of coherent classical communication and Schur transform to quantum information theory, PHD thesis, MIT (2005)

  3. Lěvy, T.: Schur-Weyl duality and the heat kernel measure on the unitary gruop. Adv. Math. 218, 537–575 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. Zhu, H.J.: Quantum State Estimation and Symmetric Informationally Complete POMs, PHD thesis. NUS (2012)

  5. Blasiak, J.: Quantum Schur-Weyl duality and projected canonical bases. J. Algebra 402, 499–532 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  6. Benson, D., Doty, S.: Schur-Weyl duality over finite fields. Arch. Math. 93, 425–435 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  7. Marvian, I., Spekkens, R.W.: A generalization of Schur-Weyl duality with applications in quantum estimation. Commu. Math. Phys. 331, 431–475 (2014)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. Beltita, D., Neeb, K.H.: Schur-Weyl theory for C -algebra. Math. Nachr. 285, 1170–1198 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  9. Wang, S.H.: New Turaev braided group categories and Group Schur-Weyl Duality. Appl. Categor. Struct. 21(21), 141–166 (2013)

    Article  MATH  Google Scholar 

  10. Tsilevich, N.V., Vershik, A.M.: Infinite-Dimensional Schur-Weyl duality and the Coxeter-Laplace operator. Commun. Math. Phys. 327, 873–885 (2014)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. Theory of quantum computation, communication, and cryptography, 141C152, Lecture Notes in Comput. Sci. 7582, Springer, Heidelberg (2013)

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This work is supported by National Natural Science Foundation of China (11101108 and 11171301 and J1210038) and the Doctoral Programs Foundation of Ministry of Education of China (J20130061).

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Correspondence to Junde Wu.

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Lei, Q., Yu, H. & Wu, J. A New Generalized Schur-Weyl Duality. Int J Theor Phys 54, 4034–4040 (2015).

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