We address into a neuronal system modeled as a two-neuron system, exploring the impact of diverse factors and external perturbations on correlations and information processing capabilities. Incorporating elements such as protein aggregation, synaptic dysfunction, Hopfield coupling, neuronal loss and non-Markovian dephasing noise, the analysis reveals the system’s sensitivity to parameters like synaptic dysfunction, protein aggregation, temperature, coupling strength and non-Markovian factor. Notably, heightened synaptic dysfunction enhances both purity and nonlocality by disrupting local processing and fostering global correlations, while protein aggregation disrupts correlations and increases uncertainty. Hopfield coupling initially enhances correlations but exacerbates uncertainty over time, while neuronal loss and temperature rapidly deteriorate correlations and elevate uncertainty, underscoring the importance of structural integrity in maintaining coherent information processing. This interdisciplinary research advances understanding of neuronal dynamics from a quantum perspective, offering insights into neurodegenerative diseases and paving the way for innovative diagnostic and therapeutic approaches.
We address into a neuronal system modeled as a two-neuron system, exploring the impact of diverse factors and external perturbations on correlations and information processing capabilities. Incorporating elements such as protein aggregation, synaptic dysfunction, Hopfield coupling, neuronal loss and non-Markovian dephasing noise, the analysis reveals the system’s sensitivity to parameters like synaptic dysfunction, protein aggregation, temperature, coupling strength and non-Markovian factor. Notably, heightened synaptic dysfunction enhances both purity and nonlocality by disrupting local processing and fostering global correlations, while protein aggregation disrupts correlations and increases uncertainty. Hopfield coupling initially enhances correlations but exacerbates uncertainty over time, while neuronal loss and temperature rapidly deteriorate correlations and elevate uncertainty, underscoring the importance of structural integrity in maintaining coherent information processing. This interdisciplinary research advances understanding of neuronal dynamics from a quantum perspective, offering insights into neurodegenerative diseases and paving the way for innovative diagnostic and therapeutic approaches.
We investigate the preservation and dynamics of entanglement and Bell nonlocality in a two-photon system subject to local dephasing, particularly emphasizing environments exhibiting non-Markovian memory effects. By analyzing the interplay between entanglement, as measured by concurrence, and Bell inequality violation, we identify time regions where Bell inequality is not violated, even when concurrence remains high. This indicates that strongly entangled states do not always exhibit nonclassical correlations with certainty. Our study further explores the effects of refractive index variations, spectral width, and interaction symmetry, demonstrating how structured environments and controlled environmental interactions can mitigate decoherence and enhance the resilience of quantum correlations. We propose that these theoretical predictions can be tested using modifications of recent experimental optical setups. These findings provide valuable insights into the conditions under which quantum correlations remain irreproducible by classical local hidden-variable models, with direct implications for quantum communication, quantum information processing, and foundational studies in quantum mechanics. Furthermore, our findings highlight the crucial importance of quantum coherence in maintaining entanglement and nonlocality over extended time evolution. These results show remarkable alignment with the experimental observations, demonstrating high accuracy and consistency within the expected parameter range.
This paper proposes a novel framework for understanding neuronal information processing, moving beyond the conventional emphasis on synaptic transmission. We hypothesize that neuronal information encoding relies fundamentally on the quantum entropy extracted from correlations between neurons, mediated by quantum entanglement. While synaptic transmission undoubtedly plays a role in facilitating information transfer, it is posited as a secondary mechanism supporting the primary quantum-based encoding process. We introduce a theoretical model leveraging the concept of quantum entanglement to describe how neuronal states are measured and how this measurement yields information that can be used to build a neuronal network's information processing model. The core idea is that the inherent quantum fluctuations within neurons, when coupled through entanglement, provide a source of information that can be quantified as entropy, forming the basis for neuronal communication. This approach challenges the prevailing view of neuronal information processing and opens new avenues for exploring the potential of quantum mechanics in biological systems. Mathematical formalism is presented to illustrate key aspects of this framework, focusing on entropy calculations and entanglement correlation analysis.
This paper investigates the potential of quantum neural networks (QNNs) enhanced by non-Markovian dynamics. Traditional Markovian QNNs suffer from limitations in capturing long-range dependencies, a crucial aspect in complex data processing. We propose a novel QNN architecture that incorporates quantum memory and entanglement to facilitate non-Markovian information processing. This approach allows the network to retain and utilize the entire past history of the input, fundamentally altering the dynamics of information flow. Through theoretical analysis and mathematical formulations, we demonstrate how this architecture can significantly improve the network's ability to learn and represent complex patterns, particularly those exhibiting long-range correlations. Specifically, we introduce a modified update rule leveraging the concept of quantum memory and entanglement, expressed as: $ \Delta w_{ij} = \alpha \cdot E[\rho(t)|x_1, x_2, ..., x_K] \cdot \langle \psi_i | \rho(t) | \psi_j \rangle - (1 - \alpha) \cdot w_{ij}$ Where: * $ \Delta w_{ij}$ is the change in the synaptic weight between neurons *i* and *j*. * α is the learning rate. * E[ρ(t)∣x1,x2,...,xK] represents the expected state of the quantum memory at time *t*, given the entire input sequence x1,x2,...,xK. * ρ(t) is the density matrix representing the quantum state at time *t*. * ⟨ψi∣ρ(t)∣ψj⟩ is the inner product between the quantum states ψi and ψj within the density matrix ρ(t). * wij is the current synaptic weight between neurons *i* and *j*. The core of our innovation lies in the utilization of quantum memory, modeled as a quantum state ρ(t), which retains information about the entire past sequence. The entanglement between neurons further enables correlated updates, bypassing the limitations of Markovian models that only consider immediate dependencies. We explore the impact of varying the strength of entanglement and the capacity of the quantum memory on the network's performance using mathematical models. The results suggest a significant improvement in accuracy and convergence speed compared to standard Markovian QNNs when dealing with datasets exhibiting long-range dependencies. Further investigation into the scalability and practical implementation of this architecture is warranted.
We investigate the dynamics of non-classical correlations and quantum coherence in open quantum systems by employing metrics like local quantum Fisher information, local quantum uncertainty, and quantum Jensen-Shannon divergence. Our focus here is on a system of two qubits in two distinct physical situations: the first one when the two qubits are coupled to a single-mode cavity, while the second consists of two qubits immersed in dephasing reservoirs. Our study places significant emphasis on how the evolution of these quantum criterion is influenced by the initial state's purity (whether pure or mixed) and the nature of the environment (whether Markovian or non-Markovian). We observe that a decrease in the initial state's purity corresponds to a reduction in both quantum correlations and quantum coherence, whereas higher purity enhances these quantumness. Furthermore, we establish a quantum teleportation strategy based on the two different physical scenarios. In this approach, the resulting state of the two qubits functions as a quantum channel integrated into a quantum teleportation protocol. We also analyze how the purity of the initial state and the Markovian or non-Markovian regimes impact the quantum teleportation process.
Abstract We investigate a hybrid qubit–qutrit system exposed to both a magnetic field and classical dephasing noise. The quantum system’s characteristics encompass diverse parameters, including spin-exchange interaction, dephasing, and the magnetic field. To incorporate thermal effects, we employ the system’s Hamiltonian to generate an initial qubit–qutrit density matrix within the framework of the Gibbs density operator. Furthermore, we model dephasing effects on the initial thermal state of the system using an Ornstein–Uhlenbeck process. We employ geometric discord, negativity, and entropic coherence functions to depict the quantum correlations across various parameter settings. Our results reveal that initially, quantum correlations attain non-maximal values, with their dynamics intricately reliant on the underlying system parameters. Specifically, when the system is primarily characterized by the magnetic field, we observe heightened levels of quantum correlations. Additionally, temperature-based characterization is found to have the most detrimental effect on the state. Geometric discord is observed to capture a higher degree of quantum correlations, albeit saturating rapidly at zero compared to entanglement and coherence. Finally, we investigated the effects of common environmental coupling and more pronounced non-Markovian dynamics in the system, revealing an enhanced preservation of quantum correlations. These modifications allow for prolonged coherence and entanglement, underscoring the potential of structured environmental interactions to mitigate decoherence effects and sustain quantum correlations over time.
Maintaining quantum coherence and entanglement in the presence of environmental noise, particularly within non-Markovian contexts, represents a significant challenge for the progression of quantum information science and technology. This study offers a substantial advancement by investigating the dynamics of a two-qubit system subjected to diverse noise conditions, encompassing relaxation, dephasing, and their cumulative effects. By employing quantum-state-diffusion equations specifically crafted for non-Markovian environments, we introduce an innovative strategy to counteract the detrimental influences of environmental noise on quantum teleportation fidelity and entanglement concurrence. Our results underscore the potential for external interventions to markedly improve the resilience of quantum information processing tasks over prolonged durations, especially in settings where dephasing noise prevails. A key revelation is the intricate relationship between dephasing noise and the initial state of entanglement, which profoundly impacts the occurrence of entanglement sudden death. This research not only deepens our comprehension of quantum system dynamics under noisy circumstances but also furnishes practical directives for engineering robust quantum systems, a necessity for the development of scalable quantum technologies.