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Condition (1) requires that the coefficients
depend upon the Hamiltonian eigenvalues
.
Resulting condition number of the Hessian of
is^{}

Instead start by imposing condition (2), making the
independent of state (so that
) e.g.

For
, the minimum occurs for

i.e. for approximately idempotent density-matrices.

Peter D. Haynes
2001-11-19