Trace Norm

The trace norm of a matrix is the sum of its singular values:

Here is the conjugate transpose and the square root is the positive semidefinite matrix square root. It is the Schatten norm with parameter 1, also called the nuclear norm. For a diagonal matrix with entries 3 and , its value is 7. The trace distance between two density matrices is half the trace norm of their difference. The diamond norm applies this norm to linear transformations with an auxiliary tensor factor.