Computation on an error-avoiding quantum code and symmetrization

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 60, Issue 2, 1999, Pages R729-R732

  Zanardi, Paolo ^a,b  

^a INFM   (Italy)

^b ISI FOUNDATION   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000383972     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.60.R729     Document Type: Article

References (23)

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3. The set of operators over (Formula presented) is endowed with the Hilbert space topology generated by the Hilbert-Schmidt scalar product (Formula presented).
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12. Let (Formula presented) be the group generated by the (Formula presented)’s (Formula presented)’s]. (Formula presented) is an algebra isomorphism; then (Formula presented) Moreover, from continuity, (Formula presented).
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16. Let (Formula presented) be a basis of (Formula presented); then (Formula presented) is defined as the linear space of (formal) polynomials in the (Formula presented)’s. The latter satisfy the relations (Formula presented) where (Formula presented) are the structure constants of (Formula presented), and (Formula presented).
17. Given a group (Formula presented) of finite order, its group algebra (Formula presented) is the vector space generated by complex combinations of elements of (Formula presented). Multiplication is introduced by linear extension of the group operation.
18. Using this expression one can easily check that the equation (Formula presented), following immediately from Eq. (3), reproduces the correct Catalan numbers (Formula presented).
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