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Quantum
Information and Computation
ISSN: 1533-7146
published since 2001
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Vol.4 No.3 May 2004 |
Simplifying Schmidt number witnesses via higher-dimensional embeddings
(pp207-221)
F. Hulpke, D. Bruss, M.
Levenstein, and A. Sanpera
doi:
https://doi.org/10.26421/QIC4.3-6
Abstracts:
We apply the generalised concept of witness operators to
arbitrary convex sets, and review the criteria for the optimisation of
these general witnesses. We then define an embedding of state vectors
and operators into a higher-dimensional Hilbert space. This embedding
leads to a connection between any Schmidt number witness in the original
Hilbert space and a witness for Schmidt number two (i.e. the most
general entanglement witness) in the appropriate enlarged Hilbert space.
Using this relation we arrive at a conceptually simple method for the
construction of Schmidt number witnesses in bipartite systems.
Key words: witness
operators, Schmidt number, classification of entanglement |
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