We build a time series of single photons with quantum chaos statistics, using a version of the Grangier anti-correlation experiment. The criteria utilized to determine the presence of quantum chaos is the frame of the Fano factor and the power spectrum. We also show that photons with chaotic statistics are in a balanced superposition of photons with both wave-like and particle like behaviors. To support the presence of quantum chaos, we study both Shannon’s entropy, and the complexity of single photons time series.

Background: The Fano factor is used to characterize statistical noises, in quantum optics to determine correlations and anticorrelations, in transport theory to characterize the limit of quantum chaos experienced by electrons in a mesoscopic cavity. However, to our knowledge, it has not been used in nuclear physics to study the spectral fluctuations.

We carry out a theoretical investigation about quantum noise in coherent mixtures of states with different statistics. On the one hand, we investigate the dependence between the behavior wave-particle and associated noise. On the other hand, we are interested in studying the persistence of chaotic behavior in mixtures of states with quantum and classical behavior. For this, we perform mixtures of single photons with coherent states of different averages. We find that the noise associated with quantum chaos depends on the proportion of the quantum–classical mixture and that quantum wave states are more efficient than classical wave states in terms of their randomness properties.

In complex systems theory, there are different ways to describe a system in terms of information, such as emergence (Shannon entropy), self-organisation, and complexity. These measures provide information about the dynamic behaviour of a complex system. We study the differences in entropy and complexity for many-body systems undergoing a transition from a regular to a chaotic regime. To do this, we analyse the eigenvectors of the ⁴⁸Ca nucleus for different quadrupole-type two-body interactions. We obtain the eigenvectors by diagonalising the two-body Hamiltonian for ⁴⁸Ca using the Antoine code. We then calculate the entropy and complexity for the different quadrupole-type interactions. The differences found in information entropy and complexity are clear when comparing a regular system with a chaotic one. We find that the complexity of the regular and chaotic states of ⁴⁸Ca shows differences associated with its internal interactions.

In complex systems theory, there are different ways to describe a system in terms of information, such as emergence (Shannon entropy), self-organization, and complexity. These measures provide information about the dynamic behavior of a complex system. We study the differences in entropy and complexity for many-body systems undergoing a transition from a regular to a chaotic regime. To do this, we analyze the eigenvectors of the ⁴⁸Ca nucleus for different quadrupole-type two-body interactions. We obtain the eigenvectors by diagonalizing the two-body Hamiltonian for ⁴⁸Ca using the ANTOINE code. We then calculate the entropy and complexity for the different quadrupole-type interactions. The differences found in information entropy and complexity are clear when comparing a regular system with a chaotic one. We find that the complexity of the regular and chaotic states of ⁴⁸Ca shows differences associated with its internal interactions.

The wave–particle duality is the quintessence of quantum mechanics. This duality gives rise to distinct behaviors depending on the experimental setup, with the system exhibiting either wave-like or particle-like properties, depending on whether the focus is on interference (wave) or trajectory (particle). In the interaction with a beam splitter, photons with particle behavior can transform into a wave behavior and vice versa. In Wheeler’s delayed-choice gedanken experiment, this interaction is delayed so that the wave that initially travels through the interferometer can become a particle, avoiding the interaction. We show that this contradiction can be resolved using polarized entangled photon pairs. An analysis of Shannon’s entropy supports this proposal.