In the era of quantum 2.0, a key technological challenge lies in preserving coherence within quantum systems. Quantum coherence is susceptible to decoherence because of the interactions with the environment. Dephasing is a process that destroys the coherence of quantum states, leading to a loss of quantum information. In this work, we explore the dynamics of the relative entropy of coherence for tripartite pure and mixed states in the presence of structured dephasing environments at finite temperatures. Our findings demonstrate that the system's resilience to decoherence depends on the bath configuration. Specifically, when each qubit interacts with an independent environment, the dynamics differ from those observed with a shared bath. In a Markov, memoryless environment, coherence in both pure and mixed states decays, whereas coherence is preserved in the presence of reservoir memory.

The dynamical behavior of quantum coherence of a displaced squeezed thermal state in contact with an external bath is discussed in the present work. We use a Fano-Anderson type of Hamiltonian to model the environment and solve the quantum Langevin equation. From the solution of the quantum Langevin equation we obtain the Green's functions which are used to calculate the expectation value of the quadrature operators which are in turn used to construct the covariance matrix. We use a relative entropy based measure to calculate the quantum coherence of the mode. The single mode squeezed thermal state is studied in the Ohmic, sub-Ohmic and the super-Ohmic limits for different values of the mean photon number. In all these limits, we find that when the coupling between the system and the environment is weak, the coherence decays monotonically and exhibit a Markovian nature. When the system and the environment are strongly coupled, we observe that the evolution is initially Markovian and after some time it becomes non-Markovian. The non-Markovian effect is due to the environmental back action on the system. Finally, we also present the steady state dynamics of the coherence in the long time limit in both low and high temperature regime. We find that the qualitative behavior remains the same in both the low and high temperature limits. But quantitative values differ because the coherence in the system is lower due to thermal decoherence.

We explore the charging advantages of a many-body quantum battery driven by a Landau-Zener field. Such a system may be modeled as a Heisenberg XY spin chain with $\textit{N}$ interacting spin-$\frac{1}{2}$ particles under an external magnetic field. Here we consider both nearest-neighbor and long-range spin interactions. The charging performance of this many-body quantum battery is evaluated by comparing Landau-Zener and periodic driving protocols within these interaction regimes. Our findings show that the Landau-Zener driving can offer superior energy deposition and storage efficiency compared to periodic driving. Notably, the Landau-Zener protocol may deliver optimal performance when combined with long-range interactions. The efficiency of a Landau-Zener quantum battery can be significantly enhanced by optimizing key parameters, such as XY anisotropy, the magnitude of the driving field, and interaction strength.

The Petz recovery map is a fundamental protocol in quantum information theory, enabling the retrieval of quantum information lost due to noisy processes. Here, we experimentally implement the Petz recovery map on a nuclear magnetic resonance (NMR) quantum processor using the duality quantum computing (DQC) algorithm. Focusing on two paradigmatic single-qubit channels, namely phase damping and amplitude damping, we demonstrate that the recovered states closely match theoretical predictions. Our results validate the feasibility of the Petz-based recovery map in current quantum platforms and highlight its relevance for near-term error mitigation strategies.

Hidden attractors are present in many nonlinear dynamical systems and are not associated with equilibria, making them difficult to locate. Recent studies have demonstrated methods of locating hidden attractors, but the route to these attractors is still not fully understood. In this letter, we present the route to hidden attractors in systems with stable equilibrium points and in systems without any equilibrium points. We show that hidden attractors emerge as a result of the saddle-node bifurcation of stable and unstable periodic orbits. Real-time hardware experiments were performed to demonstrate the existence of hidden attractors in these systems. Despite the difficulties in identifying the suitable initial conditions from the appropriate basin of attraction, we performed experiments to detect hidden attractors in nonlinear electronic circuits. Our results provide new insights into the generation of hidden attractors in nonlinear dynamical systems.

As with a Bell inequality, Hardy's paradox manifests a contradiction between the prediction given by quantum theory and local-hidden variable theories. In this work, we give two generalizations of Hardy's arguments for manifesting such a paradox to an arbitrary, but symmetric Bell scenario involving two observers. Our constructions recover that of Meng et al. [Phys. Rev. A. 98, 062103 (2018)] and that first discussed by Cabello [Phys. Rev. A 65, 032108 (2002)] as special cases. Among the two constructions, one can be naturally interpreted as a demonstration of the failure of the transitivity of implications (FTI). Moreover, a special case of which is equivalent to a ladder-proof-type argument for Hardy's paradox. Through a suitably generalized notion of success probability called degree of success, we provide evidence showing that the FTI-based formulation exhibits a higher degree of success compared with all other existing proposals. Moreover, this advantage seems to persist even if we allow imperfections in realizing the zero-probability constraints in such paradoxes. Explicit quantum strategies realizing several of these proofs of nonlocality without inequalities are provided.

Preserving multipartite entanglement amidst decoherence poses a pivotal challenge in quantum information processing. However, assessing multipartite entanglement in mixed states amid decoherence presenting a formidable task. Employing reservoir memory offers a means to attenuate the decoherence dynamics impacting multipartite entanglement, thereby slowing its degradation. One of the important measures which can be implemented to quantify entanglement is the relative entropy of entanglement. Although this measure is not monogamous \cite{horodeckirev2009}, it can universally be applied to both pure and mixed states. Based on this fundamental novelty, in this work, therefore, we introduce a quantifier which will investigate how entanglement remain distributed among the qubits of multipartite states when these states are exposed to multipartite dephasing setting. For our study we use various pure and mixed tripartite states subjected to finite temperature in both Markovian and non-Markovian local/common bath. Here, we consider situations where the three qubits interact with a common reservoir as well as a local bosonic reservoir. We also show that the robustness of a quantum system to decoherence depends on the distribution of entanglement and its interaction with various configurations of the bath. When each qubit has its own local environment, the system exhibits different distribution dynamics compared to when all three qubits share a common environment with one exception regarding a mixed state.

A generalization of the Laplace transform based on the generalized Tsallis $q$-exponential is given in the present work for a new type of kernel. We also define the inverse transform for this generalized transform based on the complex integration method. We prove identities corresponding to the Laplace transform and inverse transform like the $q$-convolution theorem, the action of generalized derivative and generalized integration on the Laplace transform. We then derive a $q$-generalization of the inverse Laplace transform based on the Post-Widder's method which bypasses the necessity for a complex contour integration. We demonstrate the usefulness of this in computing the Laplace and inverse Laplace transform of some elementary functions. Finally we use the Post-Widder's method based inverse Laplace transform to compute the density of states from the partition function for the case of a generalized classical ideal gas and linear harmonic oscillator in $D$-dimensions.

We investigate the physics informed neural network method, a deep learning approach, to approximate soliton solution of the nonlinear Schrödinger equation with parity time symmetric potentials. We consider three different parity time symmetric potentials, namely Gaussian, periodic and Rosen-Morse potentials. We use physics informed neural network to solve the considered nonlinear partial differential equation with the above three potentials. We compare the predicted result with actual result and analyze the ability of deep learning in solving the considered partial differential equation. We check the ability of deep learning in approximating the soliton solution by taking squared error between real and predicted values. {Further, we examine the factors that affect the performance of the considered deep learning method with different activation functions, namely ReLU, sigmoid and tanh. We also use a new activation function, namely sech which is not used in the field of deep learning and analyze whether this new activation function is suitable for the prediction of soliton solution of nonlinear Schrödinger equation for the aforementioned parity time symmetric potentials. In addition to the above, we present how the network's structure and the size of the training data influence the performance of the physics informed neural network. Our results show that the constructed deep learning model successfully approximates the soliton solution of the considered equation with high accuracy.

We analyse the dynamics of the improved discretised version of the well known Izhikevich neuronmodel under the action of external electromagnetic field. It is found that the three-dimensional IZHmap shows rich dynamics. With the variation of the electromagnetic field, period-doubling routeto chaos in a repeating fashion is observed from the bifurcation diagram. Even the forward andbackward continuation bifurcation diagram which do not completely overlap suggests that there is multistability in the system. The phenomenon of bistability (coexistence of periodic and chaotic attractors) is observed. The presence of periodic and chaotic attractor is aided by the maximal Lyapunov exponent diagram. The Lyapunov phase diagram of electromagnetic field and synapses current shows a large parameter region of chaotic and periodic behaviors with the presence of unbounded regions as well. The IZH map shows a plethora of spiking and bursting patterns such as mixed-mode patterns, tonic spiking, phasic spiking, steady spikes, regular spikes, spike bursting, periodic bursting, phasic bursting, chaotic firing, etc with the variation of electromagnetic coupling strength and the synapses current. We also investigate the presence of chimera states in a ring-star, ring, star network of IZH map neurons. Chimera states are found in the case of ring-star and ring network while synchronised clusters were found in the case of star network and are aided by the spatiotemporal plots, space-time plot, recurrence plots. The rich dynamics shown by the discretised IZH map makes it a promising research model to study about neurodynamics.

Bell's theorem revealed that a local hidden-variable model cannot completely reproduce the quantum mechanical predictions. Bell's inequality provides an upper bound under the locality and reality assumptions that can be violated by correlated measurement statistics of quantum mechanics. Greenberger, Horne, and Zeilinger (GHZ) gave a more compelling proof of Bell's theorem without inequalities by considering perfect correlations rather than statistical correlations. This work presents a temporal analog of the GHZ argument that establishes Bell's theorem in time without inequalities.

Dynamical systems can be coupled in a manner that is designed to drive the resulting dynamics onto a specified lower dimensional submanifold in the phase space of the combined system. On the submanifold, the variables of the two systems have a well-specified functional relationship. This process can be viewed as a control technique that ensures generalized synchronization. Depending on the nature of the dynamical systems and the specified submanifold, different coupling functions can be derived in order to achieve a desired control objective. We discuss a circuit implementation of this strategy for coupled chaotic Lorenz oscillators, as well as a demonstration of the methodology for designing coordinated motion (swarming) in a set of autonomous drones.

We aim to bridge the gap between quantum coherence, quantum correlations, and nonequilibrium quantum transport in a quantum double-dot (QDD) system interacting with fermionic reservoirs. The system-reservoir coupling is modeled using a Fano-Anderson-type Hamiltonian. The density operator elements of the QDD system are expressed in terms of expectation values involving various combinations of the fermionic creation and annihilation operators associated with the system. By utilizing the quantum Langevin equation and the Heisenberg equation of motion, we derive the precise temporal behavior of these operator averages in terms of nonequilibrium Green's functions and subsequently obtain the time evolution of the density operator elements. Our approach is valid in both the strong coupling and non-Markovian regimes. Additionally, we examine the time evolution of quantum coherence in the QDD system, quantifying it using standard measures such as the l1-norm and the relative entropy of coherence. As observed, coherence reaches a non-zero steady-state value, highlighting its significant potential for applications in quantum information processing and quantum technologies. Furthermore, we establish a connection between quantum coherence and transport current in a QDD system serially coupled to fermionic reservoirs. We then investigate the effects of coupling strength and reservoir memory by tuning the finite spectral width of the reservoir, examining their impact on both transient and steady-state properties, such as quantum coherence and particle current, which could play a crucial role in ultrafast nanodevice applications.

We analyze a system of three or more qubits collectively interacting with a zero-temperature bosonic bath characterized by a Lorentzian spectral density. Our study focuses on the emergence of decoherence-free subspaces and the genuine-entanglement dynamics. Specifically, we study the three qubit system in detail, where the genuine entanglement is quantified through the convex roof extension of negativity. By examining the transition between Markovian and non-Markovian regimes, we reveal how the entanglement in the system evolves under the influence of the environment. Notably, we observe transitions between genuinely multi-qubit entangled and bi-separable states, including a revival of entanglement even in the Markovian regime. These findings provide insights into the robustness of quantum correlations and the conditions under which decoherence-protected states can be sustained.

Quantum coherence and quantum entanglement are two different manifestations of the superposition principle. In this article we show that the right choice of basis to be used to estimate coherence is the separable basis. The quantum coherence estimated using the Bell basis does not represent the coherence in the system, since there is a coherence in the system due to the choice of the basis states. We first compute the entanglement and quantum coherence in the two qubit mixed states prepared using the Bell states and one of the states from the computational basis. The quantum coherence is estimated using the l1-norm of coherence, the entanglement is measured using the concurrence and the mixedness is measured using the linear entropy. Then we estimate these quantities in the Bell basis and establish that coherence should be measured only in separable basis, whereas entanglement and mixedness can be measured in any basis. We then calculate the teleportation fidelity of these mixed states and find the regions where the states have a fidelity greater than the classical teleportation fidelity. We also examine the violation of the Bell-CHSH inequality to verify the quantum nonlocal correlations in the system. The estimation of the above mentioned quantum correlations, teleportation fidelity and the verification of Bell-CHSH inequality is also done for bipartite states obtained from the tripartite systems by the tracing out of one of their qubits. We find that for some of these states teleportation is possible even when the Bell-CHSH inequality is not violated, signifying that nonlocality is not a necessary condition for quantum teleportation.

The quantum coherence of a multipartite system is investigated when some of the parties are moving with uniform acceleration and the analysis is carried out using the single mode approximation. Due to acceleration the quantum coherence is divided into two parts as accessible and inaccessible coherence and the entire analysis has been carried out in the single-mode approximation. First we investigate tripartite systems, considering both GHZ and W-states. We find that the quantum coherence of these states does not vanish in the limit of infinite acceleration, rather asymptoting to a non-zero value. These results hold for both single- and two-qubit acceleration. In the GHZ and W-states the coherence is distributed as correlations between the qubits and is known as global coherence. But quantum coherence can also exist due to the superposition within a qubit, the local coherence. To study the properties of local coherence we investigate separable state. The GHZ state, W-state and separable states contain only one type of coherence. Next we consider the $W \bar{W}$ and star states in which both local and global coherences coexist. We find that under uniform acceleration both local and global coherence show similar qualitative behaviour. Finally we derive analytic expressions for the quantum coherence of N-partite GHZ and W-states for n < N accelerating qubits. We find that the quantum coherence of a multipartite GHZ state falls exponentially with the number of accelerated qubits, whereas for multipartite W-states the quantum coherence decreases only polynomially. We conclude that W-states are more robust to Unruh decoherence and discuss some potential applications in satellite-based quantum communication and black hole physics.

Extreme events are unusual and rare large-amplitude fluctuations that occur can unexpectedly in nonlinear dynamical systems. Events above the extreme event threshold of the probability distribution of a nonlinear process characterize extreme events. Different mechanisms for the generation of extreme events and their prediction measures have been reported in the literature. Based on the properties of extreme events, such as rare in frequency of occurrence and extreme in amplitude, various studies have shown that extreme events are both linear and nonlinear in nature. Interestingly, in this work, we report on a special class of extreme events which are nonchaotic and nonperiodic. These nonchaotic extreme events appear in between the quasi-periodic and chaotic dynamics of the system. We report the existence of such extreme events with various statistical measures and characterization techniques.

Bell-Kochen-Specker theorem states that a non-contextual hidden-variable theory cannot completely reproduce the predictions of quantum mechanics. Asher Peres gave a remarkably simple proof of quantum contextuality in a four-dimensional Hilbert space of two spin-1/2 particles. Peres's argument is enormously simpler than that of Kochen and Specker. Peres contextuality demonstrates a logical contradiction between quantum mechanics and the noncontextual hidden variable models by showing an inconsistency when assigning noncontextual definite values to a certain set of quantum observables. In this work, we present a similar proof in time with a temporal version of the Peres-like argument. In analogy with the two-particle version of Peres's argument in the context of spin measurements at two different locations, we examine here single-particle spin measurements at two different times $t=t_1$ and $t=t_2$. We adopt three classical assumptions for time-separated measurements, which are demonstrated to conflict with quantum mechanical predictions. Consequently, we provide a non-probabilistic proof of certified quantumness in time, without relying on inequalities, demonstrating that our approach can certify the quantumness of a device through single-shot, time-separated measurements. Our results can be experimentally verified with the present quantum technology.