Graphical description of the action of local Clifford transformations on graph states

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 69, Issue 2, 2004, Pages 223161-223167

  Van den Nest, Maarten ^a   Dehaene, Jeroen ^a   De Moor, Bart ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; DATA PROCESSING; EIGENVALUES AND EIGENFUNCTIONS; ERROR ANALYSIS; GRAPH THEORY; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; TENSORS; THEOREM PROVING; VECTORS;

CLIFFORD TRANSFORMATIONS; GRAPH STATES;

QUANTUM THEORY;

EID: 1942443839     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (13)

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5. M. Hein, J. Eisert, and H. Briegel, e-print quant-ph/0307130.
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7. J. Dehaene and B. De Moor, Phys. Rev. A 68, 042318 (2003).
8. D. Schlingemann, e-print quant-ph/0111080.
9. R. Diestel, Graph Theory (Springer, Heidelberg, 2000).
10. I. Chuang and M. Nielsen, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
11. We will show in Sec. III that each stabilizer state is equivalent to a graph state under the local Clifford group.
12. i are equal to zero.
13. Here we have used the fact that |ψ〉 and |ψ′〉 are equivalent under the local Clifford group iff they have equivalent stabilizers S, S′, i.e., iff there exists a local Clifford operation U such that U SU† = S′.