**Noiseless quantum circuits for measuring entanglement**

I will show how to construct a family of simple circuits that can determine the spectrum of the partial transpose of a density matrix, without modifying the partial transpose map to impose complete positivity. Previous proposed methods for measuring entanglement relied on full state tomography (very inefficient) or the Structural Physical Approximation, which adds large amounts of noise to shift the spectrum of the partially transposed density matrix to be positive, thus incurring a corresponding loss of sensitivity.
My networks depend only on the dimension of the density matrix and do not need any circuit components that are not already required to determine the eigenspectrum of the original density matrix by interferometry. They measure the minimum amount of information required to determine the partial-transpose-spectrum completely and they are exact, up to experimental errors.