Schmidt Decomposition of the Quantum Fourier Transform on C N 1 ⊗ C N 2
نویسنده
چکیده
Schmidt decompositions of the quantum Fourier transform on C1 ⊗C2 are computed for all N1,N2 ≥ 2. The Schmidt decomposition is shown to be completely degenerate when N1 is a factor of N2 and when N1 > N2. This generalizes previous decompositions, found for N1 = N2 = 2 n [M. A. Nielsen, PhD Thesis, University of New Mexico (1998), Chapter 6; arXiv:quant-ph/0011036], and, more generally, for N1 = 2 n1 ≤ 22 = N2 [M. A. Nielsen et. al, (to appear); arXiv:quant-ph/0208077]. PACS numbers: 03.67.-a
منابع مشابه
Operator-schmidt Decomposition of the Quantum Fourier Transform on C N 1 ⊗ C N 2
Operator-Schmidt decompositions of the quantum Fourier transform on C N1 ⊗ C N2 are computed for all N1,N2 ≥ 2. The decomposition is shown to be completely degenerate when N1 is a factor of N2 and when N1 > N2. The first known special case, N1 = N2 = 2 , was computed by Nielsen in his study of the communication cost of computing the quantum Fourier transform of a collection of qubits equally di...
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