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| related topics |
| {let, theorem, proof} |
| {entanglement, phys, rev} |
| {states, state, optimal} |
| {operator, operators, space} |
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| {alice, bob, state} |
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Operator-Schmidt decomposition of the quantum Fourier transform on C^N1
tensor C^N2
Jon Tyson
abstract: Operator-Schmidt decompositions of the quantum Fourier transform on C^N1
tensor C^N2 are computed for all N1, N2 > 1. 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^n, was computed by Nielsen in his study of the
communication cost of computing the quantum Fourier transform of a collection
of qubits equally distributed between two parties. [M. A. Nielsen, PhD Thesis,
University of New Mexico (1998), Chapter 6, arXiv:quant-ph/0011036.] More
generally, the special case N1=2^n1<2^n2=N2 was computed by Nielsen et. al. in
their study of strength measures of quantum operations. [M.A. Nielsen et. al,
(accepted for publication in Phys Rev A); arXiv:quant-ph/0208077.] Given the
Schmidt decompositions presented here, it follows that in all cases the
communication cost of exact computation of the quantum Fourier transform is
maximal.
- oai_identifier:
- oai:arXiv.org:quant-ph/0210100
- categories:
- quant-ph
- comments:
- 9 pages, LaTeX 2e; No changes in results. References and
acknowledgments added. Changes in presentation added to satisfy referees:
expanded introduction, inclusion of ommitted algebraic steps in the appendix,
addition of clarifying footnotes
- arxiv_id:
- quant-ph/0210100
- journal_ref:
- J. Phys. A: Math. Gen. 36 (2003) 6485-6491
- created:
- 2002-10-13
- updated:
- 2003-04-25
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