In 2006, Ryu and Takayanagi (RT) pointed out that (with a suitable cutoff) the entanglement entropy between two complementary regions of an equal-time surface of a d+1-dimensional conformal field theory on the conformal boundary of AdS{d+2} is, when the AdS radius is appropriately related to the parameters of the CFT, equal to 1/4G times the area of the $d$-dimensional minimal surface in the AdS bulk which has the junction of those complementary regions as its boundary, where $G$ is the bulk Newton constant. (More precisely, RT showed this for d=1 and adduced evidence that it also holds in many examples in d>1. ) We point out here that the RT-equality implies that, in the quantum theory on the bulk AdS background which is related to the boundary CFT according to Rehren's 1999 algebraic holography theorem, the entanglement entropy between two complementary bulk Rehren wedges is equal to one 1/4G times the (suitably cut off) area of their shared ridge. (This follows because of the geometrical fact that, for complementary ball-shaped regions, the RT minimal surface is precisely the shared ridge of the complementary bulk Rehren wedges which correspond, under Rehren's bulk-wedge to boundary double-cone bijection, to the complementary boundary double-cones whose bases are the RT complementary balls. ) This is consistent with the Bianchi-Meyers conjecture--that, in a theory of quantum gravity, the entanglement entropy, S between the degrees of freedom of a given region with those of its complement takes the form S = A/4G (plus lower order terms)--but only if the phrase `degrees of freedom' is replaced by `matter degrees of freedom'. It also supports related previous arguments of the author--consistent with the author's `matter-gravity entanglement hypothesis'--that the AdS/CFT correspondence is actually only a bijection between just the matter (i. e. non-gravity) sector operators of the bulk and the boundary CFT operators.

In this work, we explore the holographic entanglement entropy with an infinite strip region of the boundary in Horndeski gravity. In our prescription we consider the spherically and planar topologies black holes in the AdS4/CFT3 scenario. In such framework, we show the behavior of the entanglement entropy in function of the Horndeski parameters. Such parameters modify the information store of subsystem A, especially when the parameter $gamma$ increases the information about the subsystem will also increase or decrease when it decreases. Thus, with this scheme we compute the “first law of entanglement thermodynamics” in Horndeski gravity and we show that a very small subsystem obeys the analogous property of the first law of thermodynamics if we excite the system.

In this work‎, ‎we explore the entanglement entropy equipped with the $\kappa$-algebra‎. ‎This entanglement entropy is computed through the geometric setup as performed by Hartman-Maldacena‎, ‎which‎, ‎in their prescription‎, ‎finds that the entropy grows linearly in time‎. ‎In our case‎, ‎we show that the $\kappa$-algebra embedding provides a richer scenario where the third-order corrections in time added from $\kappa$-algebra to entanglement entropy imply that the growth of quantum correlations between subsystems is more intricate than a simple linear increase into the dynamics of black hole thermalization and quantum information flow‎. ‎In the context of holography‎, ‎such corrections suggest that the thermalization process is not instantaneous but involves higher-order interactions between subsystems‎.

In this work, we investigate a non-linear differential equation relevant to the computation of entanglement entropy in interacting quantum systems. We do this, inspired by field-theoretic and holographic models, we introduce a simplified equation to describe the entropy as a function of subsystem size and coupling strength. By comparing analytical approximations with numerical solutions, we uncover a crossover behavior between area-law and volume-law regimes, which are key features of entanglement dynamics in quantum systems. This minimal model captures the essential non-linear structure underlying entanglement growth, offering insights into the interplay between subsystem size and interaction strength. Our findings provide a framework for understanding the transition between distinct entanglement scaling laws, bridging theoretical predictions and numerical observations. This work highlights the utility of simplified models in exploring complex quantum phenomena and contributes to the broader understanding of entanglement dynamics in interacting systems, with potential applications in quantum information and condensed matter physics.

In this paper, quantum phase transitions and nuclear structure were investigated based on quantum entanglement. One of the measures for entanglement between two bodies is the von Neumann entropy, which is considered a suitable criterion for examining entanglement. The entanglement entropy of s-d bosons within the framework of the Interacting Boson Model (IBM) is investigated using the consistent-Q formalism and semiclassical approximation. This research presents a method for deriving the entanglement entropy in the dynamical symmetry limits of the IBM, including transition regions between different shapes. By utilizing the entanglement effect, the quantum phase transition was described, and the entanglement behavior of s and d bosons was investigated in various regions of the Castan triangle. A method for determining entropy in the IBM model using the semiclassical approximation was presented. The results showed that entanglement entropy values are sensitive to phase changes and can be a powerful tool for detecting quantum phase transitions in nuclei.

Construction of the reduced spin and helicity density matrix for systems of two and three particles are described by a wave packet with sharp and Gaussian momentum distribution. The entropy for the spin and helicity part of the systems is calculated from the viewpoint of moving observers.

The traditional method for studying non-stationary signals is spectrogram based on the short-time Fourier transform (STFT). The well known limitation of the STFT is the inherent trade-off between time and frequency resolution. The Wigner-Ville (WV) distribution has the best time-frequency resolution, but its draw back is generating cross-terms. The matching pursuit (MP) distribution based on using the Gaussian atom is always positive, does not include crossterm, and has convenient resolution. In this paper, we have shown in addition to the known properties, the MP distribution can also remove the additive noise inherently. On the other words, we are able to remove the noise just by limiting the algorithm iterations and without paying any additional cost. Although the MP distribution based on using the Gaussian atoms is always positive and it has convenient resolution, according to the MP the time marginal and the frequency marginal will not be obtained accurately. In this paper, it has been shown that by implementing the minimum cross entropy (MCE) technique according to the MP distribution as a priory positive distribution, the new extracted distribution has the most similarity to the MP distribution and it also satisfies the correct time and frequency marginal.

One of the most critical aspects of studying entanglement states is quantifying the degree of entanglement. One of the entanglement measures for pure states is Van-Neumann entropy, which is why Van-Neumann entropy is also called entanglement entropy. In this work, to calculate the entanglement of a three-particle atom called the Moshinsky atom,first, the reduced density matrix was calculated and then using the coordinates of the three particles in the lithium atom, the entropy entanglement was calculated. We obtained the entropy of entanglement in terms of the frequency parameter related to the external coordinate field.

The entanglement between a-type three-level atom and its spontaneous emission fields is investigated. The effect of spontaneously generated coherence (SGC) on entanglement between the atom and its spontaneous emission fields is then discussed. We find that in the presence of SGC the entanglement between the atom and its spontaneous emission fields is completely phase dependent, while in absence of this coherence the phase dependence of the entanglement disappears. Moreover, the degree of entanglement dramatically changes by the coherent superposition of the atomic states.