Quantum Chaos in Time Series of Single Photons as a Superposition of Wave and Particle States

Abstract

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.

Determining Single Photon Quantum States through Robust Waveguides on Chip

“…Now, if the transmission (T) and reflection (R) parameters of the BS are controlled, the randomness of the output statistics can be controlled too, so the Fano factor should change, based on those statistics. Additionally, two interesting cases exist: those that are between F = 0.5 (random 1 s and 0 s) and the extreme case with only 1 s or 0 s (F = 0 or F = 1, respectively) because they can produce 1/f or f noises [8]. These opposed noises 1/ f and f come through the beam splitter with a probability of P T = 0.25 and P T = 0.75, respectively.…”

“…Quantum cryptography protocols may require different quantum state statistics to be analyzed so that information can be transmitted [1][2][3][4] or to protect the information [5]. For example, Poissonian statistics are the most commonly used statistics to analyze these states [6,7], but subpoissonian and chaotic statistics can also be used [8]. Even protocols that include different simultaneous statistics have been proposed [9,10].…”