TraceNorm

TraceNorm is a function that computes the trace norm of an operator (i.e., the sum of its singular values). It works with both full and sparse matrices.

Syntax

 * NRM = TraceNorm(X)

Argument descriptions

 * X: An operator to have its trace norm computed.

Trace norm of a density matrix
Density matrices all have trace norm equal to 1:

Can be used with CVX
This function can be used in the objective function or constraints of a CVX optimization problem. For example, the following code computes the minimum value of $\mathrm{Tr}(S\rho)$ over all density matrices $\rho$ with the property that the trace norm of their realignment is no larger than 1 (this set of state approximates the set of separable states), where $S$ is the swap operator: