Von Neumann Entropy Research Articles

A glimpse into Quantum Gravity : A Noncommutative Spacetime results in Quantization of Area, Mass and Entropy

A glimpse into Quantum Gravity : A Noncommutative Spacetime results in Quantization of Area, Mass and Entropy

Entanglement fractalization

We numerically explore the interplay of fractal geometry and quantum entanglement by analyzing the von Neumann entropy (known as entanglement entropy) and the entanglement contour in the scaling limit. Adopting quadratic fermionic models on Sierpinski carpet, we uncover intriguing findings. For gapless ground states exhibiting a finite density of states at the chemical potential, we reveal a super-area law characterized by the presence of a logarithmic correction for area law in the scaling of entanglement entropy. This extends the well-established super-area law observed on translationally invariant Euclidean lattices where the Gioev-Klich-Widom conjecture regarding the asymptotic behavior of Toeplitz matrices holds significant influence. Furthermore, different from the fractal structure of the lattice, we observe the emergence of a self-similar and universal pattern termed an “entanglement fractal” in the entanglement contour data as we approach the scaling limit. Remarkably, this pattern bears resemblance to intricate Chinese paper-cutting designs. We provide general rules to artificially generate this fractal, offering insights into the universal scaling of entanglement entropy. Meanwhile, as the direct consequence of the entanglement fractal and beyond a single scaling behavior of entanglement contour in translation-invariant systems, we identify two distinct scaling behaviors in the entanglement contour of fractal systems. For gapped ground states, we observe that the entanglement entropy adheres to a generalized area law, with its dependence on the Hausdorff dimension of the boundary between complementary subsystems. Published by the American Physical Society 2024

Relative State Counting for Semiclassical Black Holes

It has been shown that entropy differences between certain states of perturbative quantum gravity can be computed without specifying an ultraviolet completion. This is analogous to the situation in classical statistical mechanics, where entropy differences are defined but absolute entropy is not. Unlike in classical statistical mechanics, however, the entropy differences computed in perturbative quantum gravity do not have a clear physical interpretation. Here we construct a family of perturbative black hole states for which the entropy difference can be interpreted as a relative counting of states. Conceptually, this Letter begins with the algebra of mass fluctuations around a fixed black hole background, and points out that while this is a type I algebra, it is not a factor and therefore has no canonical definition of entropy. As in previous work, coupling the mass fluctuations to quantum matter embeds the mass algebra within a type II factor, in which entropy differences (but not absolute entropies) are well defined. It is then shown that for microcanonical wave functions of mass fluctuation, the type II entropy difference equals the logarithm of the dimension of the extra Hilbert space that is needed to map one microcanonical window to another using gauge-invariant unitaries. The Letter closes with comments on type II entropy difference in a more general class of states, where the von Neumann entropy difference does not have a physical interpretation, but “one-shot” entropy differences do. Published by the American Physical Society 2024

QCD evolution of entanglement entropy.

Entanglement entropy has emerged as a novel tool for probing nonperturbative quantum chromodynamics (QCD) phenomena, such as color confinement in protons. While recent studies have demonstrated its significant capability in describing hadron production in deep inelastic scatterings, the QCD evolution of entanglement entropy remains unexplored. In this work, we investigate the differential rapidity-dependent entanglement entropy within the proton and its connection to final-state hadrons, aiming to elucidate its QCD evolution. Our analysis reveals a strong agreement between the rapidity dependence of von Neumann entropy, obtained from QCD evolution equations, and the corresponding experimental data on hadron entropy. These findings provide compelling evidence for the emergence of a maximally entangled state, offering new insights into the nonperturbative structure of protons.

Separation of measurement uncertainty into quantum and classical parts based on Kirkwood–Dirac quasiprobability and generalized entropy

Abstract Measurement in quantum mechanics is notoriously unpredictable. The uncertainty in quantum measurement can arise from the noncommutativity between the state and the measurement basis which is intrinsically quantum, but it may also be of classical origin due to the agent’s ignorance. It is of fundamental as well as practical importance to cleanly separate the two contributions which can be directly accessed using laboratory operations. Here, we propose two ways of decomposition of the total measurement uncertainty additively into quantum and classical parts. In the two decompositions, the total uncertainty of a measurement described by a positive-operator-valued measure (POVM) over a quantum state is quantified respectively by two generalized nonadditive entropies of the measurement outcomes; the quantum parts are identified, respectively, by the nonreality and the nonclassicality—which captures simultaneously both the nonreality and negativity—of the associated generalized Kirkwood–Dirac quasiprobability relative to the POVM of interest and a projection-valued measure and maximized over all possible choices of the latter; and, the remaining uncertainties are identified as the classical parts. Both decompositions are shown to satisfy a few plausible requirements. The minimum of the total measurement uncertainties in the two decompositions over all POVM measurements are given by the impurity of the quantum state quantified by certain generalized quantum entropies, and are entirely classical. We argue that nonvanishing genuine quantum uncertainty in the two decompositions are sufficient and necessary to prove quantum contextuality via weak measurement with postselection. Finally, we suggest that the genuine quantum uncertainty is a manifestation of a specific measurement disturbance.

Von Neumann Entropy and Evolution

In this paper I outline a hypothesis where quantum information in the form of von Neumann entropy provides a universal driving force for increasing complexity of systems and for evolutionary processes. Interference between quantum states of interacting systems allows storage of free energy that can be used to overcome kinetic barriers and accelerate reactions. This informational work cycle is analogous to entanglement in quantum Carnot engines where energy is stored as phase or so-called phaseonium fuel. The von Neumann entropy subadditivity and Araki-Lieb inequality properties of combined states can lower effective entropy and favour routes to increasing complexity of systems. It is proposed that observed macroscopic evolutionary processes are the emergent manifestation of this microscopic informational drive to complexity.

Functional Hypergraphs of Stock Markets.

In stock markets, nonlinear interdependencies between various companies result in nontrivial time-varying patterns in stock prices. A network representation of these interdependencies has been successful in identifying and understanding hidden signals before major events like stock market crashes. However, these studies have revolved around the assumption that correlations are mediated in a pairwise manner, whereas, in a system as intricate as this, the interactions need not be limited to pairwise only. Here, we introduce a general methodology using information-theoretic tools to construct a higher-order representation of the stock market data, which we call functional hypergraphs. This framework enables us to examine stock market events by analyzing the following functional hypergraph quantities: Forman-Ricci curvature, von Neumann entropy, and eigenvector centrality. We compare the corresponding quantities of networks and hypergraphs to analyze the evolution of both structures and observe features like robustness towards events like crashes during the course of a time period.

Exploiting Neighbor Effect: Conv-Agnostic GNN Framework for Graphs With Heterophily.

Due to the homophily assumption in graph convolution networks (GCNs), a common consensus in the graph node classification task is that graph neural networks (GNNs) perform well on homophilic graphs but may fail on heterophilic graphs with many interclass edges. However, the previous interclass edges' perspective and related homo-ratio metrics cannot well explain the GNNs' performance under some heterophilic datasets, which implies that not all the interclass edges are harmful to GNNs. In this work, we propose a new metric based on the von Neumann entropy to reexamine the heterophily problem of GNNs and investigate the feature aggregation of interclass edges from an entire neighbor identifiable perspective. Moreover, we propose a simple yet effective Conv-Agnostic GNN framework (CAGNNs) to enhance the performance of most GNNs on the heterophily datasets by learning the neighbor effect for each node. Specifically, we first decouple the feature of each node into the discriminative feature for downstream tasks and the aggregation feature for graph convolution (GC). Then, we propose a shared mixer module to adaptively evaluate the neighbor effect of each node to incorporate the neighbor information. The proposed framework can be regarded as a plug-in component and is compatible with most GNNs. The experimental results over nine well-known benchmark datasets indicate that our framework can significantly improve performance, especially for the heterophily graphs. The average performance gain is 9.81%, 25.81%, and 20.61% compared with graph isomorphism network (GIN), graph attention network (GAT), and GCN, respectively. Extensive ablation studies and robustness analysis further verify the effectiveness, robustness, and interpretability of our framework. Code is available at https://github.com/JC-202/CAGNN.

Quantum data compression under localized features

In this paper, we first introduce the local quantum information processing task by compressing the density operator based on local quantum Bernoulli noises. Then, the local quantum compression theorem is given, that is, the local quantum entropy is the minimum achievable rate of local compression. Finally, we prove the theorem with the proof of the direct coding theorem and the inverse theorem. The direct coding theorem shows that a scheme with such a local compression rate exists, and that this local compression rate converges to the local quantum entropy. The inverse theorem shows that the compression scheme with the rate below the local entropy is unachievable. With the continuous development of quantum technology, local quantum data compression technology will have broad application prospects and development space.

Bound-state confinement after trap-expansion dynamics in integrable systems

Abstract Integrable systems possess stable families of quasiparticles, which are composite objects (bound states) of elementary excitations. Motivated by recent quantum computer experiments, we investigate bound-state transport in the spin- 1 / 2 anisotropic Heisenberg chain (XXZ chain). Specifically, we consider the sudden vacuum expansion of a finite region A prepared in a non-equilibrium state. In the hydrodynamic regime, if interactions are strong enough, bound states remain confined in the initial region. Bound-state confinement persists until the density of unbound excitations remains finite in the bulk of A. Since region A is finite, at asymptotically long times bound states are ‘liberated’ after the ‘evaporation’ of the unbound excitations. Fingerprints of confinement are visible in the space-time profiles of local spin-projection operators. To be specific, here we focus on the expansion of the p-Néel states, which are obtained by repetition of a unit cell with p up spins followed by p down spins. Upon increasing p, the bound-state content is enhanced. In the limit p → ∞ one obtains the domain-wall initial state. We show that for p < 4, only bound states with n > p are confined at large chain anisotropy. For p ≳ 4 , bound states with n = p are also confined, consistent with the absence of transport in the limit p → ∞ . The scenario of bound-state confinement leads to a hierarchy of timescales at which bound states of different sizes are liberated, which is also reflected in the dynamics of the von Neumann entropy.

On Tesla-inspired Extended Quantum-Holographic Framework for Reprogramming Macro-Quantum Correlations of Individual and Collective Consciousness

Nikola Tesla's visions and inventions realized in his controlled altered states of consciousness were considered previously as manifestations of his meditative insights within extended framework of quantum-holographic macroquantum correlations of individual & collective consciousness. This Tesla-inspired paper now focuses on some related psychosomatice aspects of quantum entropy & entanglement, and consequences on the usually observablebiological arrow of time & spiritual-informational time reversal. Finally we discuss some spiritual-informational implicationson free will & individual and collective consciousness reprogramming.

Consciousness: a quantum optical effect in fluorescent protein pathways

This paper presents a physical mechanism of embodied consciousness based on the dynamic organicity theory. We use the entropic pilot wave theory to describe the quantum dipole oscillations from dipole-bound delocalized (quasi-free) electrons in nonpolar nanocavities of aromatic amino acid residues (benzene moiety /cyclic hydrocarbons that contain resonance structures) and their fluorescent pathways. These pathways contain cavity quasipolariton condensates composed of quantized polarization waves of entangled photons. The behavior of oscillating molecular dipoles is influenced by the quantum nature of dynamic organicity, which causes energy fluctuations necessary to move delocalized electrons and create bare polaritons (quantized polarization waves). These waves correspond to photon quasiparticles interacting with water molecules to form quasipolaritons, softened by interacting with hydroxide ions (OH-) within crystal lattices of interfacial water H30. When [H3O+]=[OH−], the solution is neutral in hydrophobic nanocavities. In such nonpolar cavities, evanescent photons (non-radiative transitions in the absence of any source) are emitted while protons (H+) diffuse due to recombination with hydroxide (OH-) ions, acting as protonic analogs of ‘holes’ or excitons. In protein pores, proton motion strongly coupled with π-electron delocalization is a conduit for exciton-photon (polariton) and its polarization wave component. Internal energy fluctuations comprise both quantum potential energy and negative quantum kinetic energy. We explore how quantum potential energy influences the negentropic effect of a 'repulsive force' guided by entropic pilot waves through pilot wave force (negentropic force), functioning as an information-based action of the polarization wave as a conduit of the cavity quasipolariton. When the rate of change of quantum entropy is zero, and momentum of the polarization wave is zero the internal energy transduction between quantum potential energy to quantum kinetic energy manifests as the negentropic force and facilitates the movement of information-based action for information encoding when negative quantum kinetic energy happens at certain times. Experiments have shown that biphoton entanglement interferes with anaesthetics. We postulate that the disruption of cavity polaritonic condensate through its polarization wave component disrupts the decoding of information, suggesting consciousness is attributed to a quantum optical effect. Therefore, we further theorize that consciousness is attributed to the negative quantum kinetic energy of the polarization wave, which provides an informational structure of multiscale redundancy when negentropic action reduces information redundancy. This has profound implications for understanding consciousness as nonmechanical action channeled through negentropic force when the rate of change of quantum entropy is zero.

Evanescent Electron Wave-Spin.

This study demonstrates the existence of an evanescent electron wave outside both finite and infinite quantum wells by solving the Dirac equation and ensuring the continuity of the spinor wavefunction at the boundaries. We show that this evanescent wave shares the spin characteristics of the wave confined within the well, as indicated by analytical expressions for the current density across all regions. Our findings suggest that the electron cannot be confined to a mathematical singularity and that quantum information, or quantum entropy, can leak through any quantum confinement. These results emphasize that the electron wave, fully characterized by Lorentz-invariant charge and current densities, should be considered the true and sole entity of the electron.

On an inequality of Lin, Kim and Hsieh and strong subadditivity

We give an elementary proof of an inequality of Lin, Kim and Hsieh that implies strong subadditivity of the von Neumann entropy.

Investigating Entropic Dynamics of Multiqubit Cavity QED System

AbstractEntropic dynamics of a multiqubit cavity quantum electrodynamics system is simulated and various aspects of entropy are explored. In the modified version of the Tavis–Cummings–Hubbard model, atoms are held in optical cavities through optical tweezers and can jump between different cavities through the tunneling effect. The interaction of atom with the cavity results in different electronic transitions and the creation and annihilation of corresponding types of photon. Electron spin and the Pauli exclusion principle are considered. Formation and break of covalent bond and creation and annihilation of phonon are also introduced into the model. The system is bipartite. The effect of all kinds of interactions on entropy is studied. And the von Neumann entropy of different subsystems is compared. The results show that the entropic dynamics can be controlled by selectively choosing system parameters, and the entropy values of different subsystems satisfy certain inequality relationships.

Optical tomography and coherence of a cavity interacting with two time-dependent position qubits

Optical tomography is a widely used method for estimating complex information. It provides a monotonic relation between the coherent field states density and their corresponding probability distributions. This approach is critical for validating any quantum information processing system’s implementation. This paper explores the optical tomography and coherence dynamics for a cavity interacting with two two-level atoms having time-dependent locations. We analyze the dynamics of the photon-field states, as two moving atoms enter a cavity filled with two superposed coherent states. The von-Neumann entropy dynamics illustrates how interaction couplings between the two atoms and cavity can give rise to entangled states under the effects of the atom-field couplings and the time-dependent atomic location parameter. Aside from coherence, the interactions between the cavity and atoms are essential for producing nonclassical proprieties in optical tomography. Furthermore, we investigate the dynamics of optical tomography densities with respect to the couplings between atoms and photons for time-dependent atomic location. Our results show that the couplings between atoms and cavity not only accelerate but also improve the processes involved in generating nonclassical optical tomography and coherence dynamics.

Quantum entropy couples matter with geometry

Abstract We propose a theory for coupling matter fields with discrete geometry on higher-order networks, i.e. cell complexes. The key idea of the approach is to associate to a higher-order network the quantum entropy of its metric. Specifically we propose an action having two contributions. The first contribution is proportional to the logarithm of the volume associated to the higher-order network by the metric. In the vacuum this contribution determines the entropy of the geometry. The second contribution is the quantum relative entropy between the metric of the higher-order network and the metric induced by the matter and gauge fields. The induced metric is defined in terms of the topological spinors and the discrete Dirac operators. The topological spinors, defined on nodes, edges and higher-dimensional cells, encode for the matter fields. The discrete Dirac operators act on topological spinors, and depend on the metric of the higher-order network as well as on the gauge fields via a discrete version of the minimal substitution. We derive the coupled dynamical equations for the metric, the matter and the gauge fields, providing an information theory principle to obtain the field theory equations in discrete curved space.

Device-independent lower bounds on the conditional von Neumann entropy

The rates of several device-independent (DI) protocols, including quantum key-distribution (QKD) and randomness expansion (RE), can be computed via an optimization of the conditional von Neumann entropy over a particular class of quantum states. In this work we introduce a numerical method to compute lower bounds on such rates. We derive a sequence of optimization problems that converge to the conditional von Neumann entropy of systems defined on general separable Hilbert spaces. Using the Navascués-Pironio-Acín hierarchy we can then relax these problems to semidefinite programs, giving a computationally tractable method to compute lower bounds on the rates of DI protocols. Applying our method to compute the rates of DI-RE and DI-QKD protocols we find substantial improvements over all previous numerical techniques, demonstrating significantly higher rates for both DI-RE and DI-QKD. In particular, for DI-QKD we show a minimal detection efficiency threshold which is within the realm of current capabilities. Moreover, we demonstrate that our method is capable of converging rapidly by recovering all known tight analytical bounds up to several decimal places. Finally, we note that our method is compatible with the entropy accumulation theorem and can thus be used to compute rates of finite round protocols and subsequently prove their security.

Correction to: Ruminations on matrix convexity and the strong subadditivity of quantum entropy

Correction to: Ruminations on matrix convexity and the strong subadditivity of quantum entropy

Longitudinal variability of complexities associated with equatorial electrojet and its coupling with Solar Quiet Daily variation Sq field

The large-scale solar quiet (Sq) current and the Equatorial Electrojet (EEJ) current are two structures produced by electric current in the Earth’s ionosphere. For a long time, the characteristics of these two currents, particularly whether the EEJ is an extended portion of the Sq current has been a hot topic within the community. This study examined magnetic data obtained from ground-based magnetometers at 6 representative stations for the year 2009 and for geomagnetically quiet days (Ap⩽3). The selected stations are along the magnetic equator in the South America (Huancayo), Africa (Ilorin; Addis Ababa), and the Philippines (Langkawi, dip latitude -2.32°; Davao, dip latitude -1.02°; Yap, dip latitude -1.49°). Results showed that both current systems are complex, and this complexity varies significantly from one longitudinal station to another. The strongest and weakest complexity were found in Huancayo and Ilorin, respectively. Afterwards, using four entropy quantifiers (Phase synchronization, Mutual Information, Ensemble Symbolic Coupling Traces, and S-independence), this study examined the relationship between the EEJ and Sq currents. Results revealed clearly a significant information exchange between both currents; that is, the Sq and EEJ currents are indeed coupled. As a step further, using the transfer entropy approach, a directional investigation was carried out to ascertain the direction of information flow between the Sq and EEJ stations. Observations revealed that due to the weak coupling obtained over the African sectors, only the currents over these stations exchanged information. This study further discussed the possible physical mechanisms responsible for the identified variabilities.