Information-Entropy and Purity of Decoherence Functions

Ayoub Taoussi

Description This work proposes an information-theoretic framework for describing the quantum–classical transition during cosmological inflation through open quantum system dynamics and entanglement evolution. The study introduces a normalized Quantum Persistence Function (QPF) as a scale-invariant diagnostic measure of residual quantum coherence, formulated in representation-independent form using reduced density matrix purity and entropy growth. The framework connects microscopic decoherence processes with macroscopic cosmological observables by applying spin–boson open-system dynamics to inflationary perturbations. Classical emergence is interpreted as a dynamical suppression of quantum coherence driven by entanglement entropy growth between cosmological modes rather than by simple interference cancellation. Observational constraints from primordial Gaussianity bounds are used to derive an efficiency condition for decoherence during reheating, expressed as a lower bound on the decoherence functional. The results show that classicalization occurs well below holographic entropy saturation limits, suggesting that cosmological classical emergence is governed primarily by dynamical information redistribution rather than fundamental information capacity thresholds. This work is deposited on Zenodo as an open scientific preprint to encourage constructive discussion and feedback from the scientific community. KEYWORDS: Quantum classical transition; decoherence theory; inflationary cosmology; open quantum systems; entanglement entropy; cosmological perturbations; quantum persistence function; information theory in physics; primordial fluctuations; classical emergence dynamics

Hans-Thomas Elze

Subhash C. Kak

Seyed Mohammad Hosseiny, Milad Norouzi, Jamileh Seyed‐Yazdi +1 more

Abstract In this paper, we analyze the purity and decoherence effects in quantum two-mode squeezed (QTMS) radar as a function of the squeezing parameter and temperature, using quantum information processing tools. The squeezing parameter is an important key to improving the performance of the QTMS radar. We investigate the response to the squeezing parameter controlling to system state of the QTMS radar. In this work, we deal with the QTMS radar with two cases of the transmitted signal, the presence or the absence of the target. The squeezing parameter controls the power of the generated signal and idler, the correlation between signal and idler, as well as the coherence and state of the system. We show that the decoherence effects are low at low temperatures, low squeezing parameters, and low power. In addition, we demonstrate that the purity and, consequently, the coherence of the QTMS radar are better when the target is absent than when it is present. However, the coherence and purity are maintained at high temperatures in both cases. In addition, by calculating the entropy of formation as a tool to investigate the qualitative behavior of entanglement in QTMS radar, we show that the behaviors of purity and entropy are similar. Finally, we show that the proportion of received photons in the QTMS radar is an important factor in improving the radar performance.

Adolfo del Campo, Tadashi Takayanagi

Abstract Noise sources are ubiquitous in Nature and give rise to a description of quantum systems in terms of stochastic Hamiltonians. Decoherence dominates the noise-averaged dynamics and leads to dephasing and the decay of coherences in the eigenbasis of the fluctuating operator. For energy-diffusion processes stemming from fluctuations of the system Hamiltonian the characteristic decoherence time is shown to be proportional to the heat capacity. We analyze the decoherence dynamics of entangled CFTs and characterize the dynamics of the purity, and logarithmic negativity, that are shown to decay monotonically as a function of time. The converse is true for the quantum Renyi entropies. From the short-time asymptotics of the purity, the decoherence rate is identified and shown to be proportional to the central charge. The fixed point characterizing long times of evolution depends on the presence degeneracies in the energy spectrum. We show how information loss associated with decoherence can be attributed to its leakage to an auxiliary environment and discuss how gravity duals of decoherence dynamics in holographic CFTs looks like in AdS/CFT. We find that the inner horizon region of eternal AdS black hole is highly squeezed due to decoherence.

Nilanjana Datta