I am working on calculating the concurrence of a two-qubit system, and I encountered an issue where my density matrix occasionally has small negative eigenvalues due to numerical errors in my computations (e.g., constructing the density matrix from Green's functions). To address this, I applied an algorithm to make the matrix positive semi-definite, such as eigenvalue clipping or spectral decomposition followed by normalization.
However, after this correction, the concurrence of the density matrix changes significantly. In some cases, it decreases, and in others, it drops to zero.
My questions are:
- How does correcting a density matrix to make it positive semi-definite impact the calculation of concurrence?
- Is there a "best practice" for handling small negative eigenvalues while preserving the entanglement properties of the system?
- Are there any specific techniques to ensure that the corrected density matrix remains as close as possible to the original physical state?
