When photons are in a state of quantum entanglement, their interactions are characterized by non-classical correlations that go beyond what can be explained by classical physics. The specific nature of photon interactions in entangled states depends on the type of entanglement involved.
For example, in the case of polarization entanglement, two photons can be prepared in a state where their polarization properties are entangled. Polarization refers to the orientation of the electric field of a photon. When two entangled photons are measured for their polarizations, the outcomes of the measurements are found to be correlated. If one photon is measured to have a certain polarization, the other photon's polarization becomes instantaneously determined, regardless of the spatial separation between them. This correlation persists even if the measurements are made far apart and appears to violate classical notions of locality and causality.
In other types of entanglement, such as frequency entanglement or spatial entanglement, the interactions between photons are also characterized by non-local correlations. For example, in frequency entanglement, photons can be entangled in their frequencies (or colors). When one photon's frequency is measured, the frequency of the entangled partner is immediately known, even if they are physically separated.
It's important to note that entangled photons do not interact with each other in the conventional sense of particle collisions or direct exchange of forces. Instead, their interactions manifest through the correlations observed in measurements performed on them. These correlations can be explained by the mathematical formalism of quantum mechanics, which allows for the description of entangled states and their measurement outcomes.
Overall, when photons are in a state of quantum entanglement, their interactions exhibit non-local correlations that defy classical explanations and play a vital role in various quantum information processing tasks and experiments.