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Schmidt Coefficients


The Schmidt coefficients of a vector in a tensor product are the nonnegative coefficients sigma_i in its Schmidt decomposition. They are the singular values of the coefficient matrix and are uniquely determined up to order. For a normalized vector,

 sum_(i)sigma_i^2=1.

The number of nonzero Schmidt coefficients is the Schmidt rank.


See also

Coefficient Matrix, Schmidt Decomposition, Schmidt Rank, Singular Value, Tensor Product, Vector

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References

Nielsen, M. and Chuang, I. Quantum Computation and Quantum Information. Cambridge, England: Cambridge University Press, 2000.

Cite this as:

Weisstein, Eric W. "Schmidt Coefficients." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SchmidtCoefficients.html

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