Isolating causes for unphysical eigenvalues in experimental optical quantum state tomography

It is generally accepted that quantum states are described with positive semi-definite density matrices. In order to satisfy this, these states must have non-negative eigenvalues. Quantum mechanics generally forbids the existence of negative eigenvalues, as they are considered to be unphysical. However, negative eigenvalues in density matrices have been measured experimentally. These results are oftentimes attributed to statistical errors and fluctuations in the experimental apparatuses. Due to the inherently probabilistic nature of quantum mechanics, along with the noise caused by preparation and measurement settings, intrinsic noise can be introduced into a quantum mechanical system. However, some unphysical results may not solely be attributed to the experimental imperfections and expected statistical errors. We experimentally explore the root causes of unphysical eigenvalues in high fidelity single optical qubit state tomography. We determine causes of any experimental and theoretical disparities. Through this exploration, we isolate experimental factors and expected statistical fluctuations contributing to unphysical results. Our results can lead to a better understanding of noise and biases that are built into quantum states and potentially help explain incongruencies between some theoretical and experimental results.