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Parrondo's paradox refers to an unexpected effect when some combination of biased quantum walks shows a counterintuitive inversion of the bias direction. To date this effect was studied in the case of one-dimensional discrete-time quantum walks with deterministic sequences of two or more quantum coins and one shift operator. In the present work, we show that Parrondo's paradox may also occur for one coin and two different shift operators which create deterministic periodic or aperiodic sequences. Moreover, we demonstrate how Parrondo's paradox affects the time evolution of the walker-coin quantum entanglement for this kind of quantum walks. [ABSTRACT FROM AUTHOR]

Understanding the flow, loss, and recovery of the information between a system and its environment is essential for advancing quantum technologies. The central spin system serves as a useful model for a single qubit, offering valuable insights into how quantum systems can be manipulated and protected from decoherence. This work uses the stimulated echo experiment to track the information flow between the central spin and its environment, providing a direct measure of the sensitivity of system/environment correlations to environmental dynamics. The extent of mixing and the growth of correlations are quantified through autocorrelation functions of the noise and environmental dynamics, which also enable the estimation of nested commutators between the system/environment and environmental Hamiltonians. Complementary decoupling experiments offer a straightforward measure of the strength of the system Hamiltonians. The approach is experimentally demonstrated on a spin system. [ABSTRACT FROM AUTHOR]

We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of predictive state analysis of stochastic and complex systems theory but is intrinsically quantum. Predictive states of a subsystem are formed by equivalence classes of state vectors in the exterior Hilbert space that effectively predict the same future behavior of that subsystem for some time. As an illustrative example, we present calculations in the dynamics of an isotropic Heisenberg model spin chain and show that, in comparison to the entanglement entropy, the predictive complexity better signifies dynamically important events, such as magnon collisions. It can also serve as a local order parameter that can distinguish long and short range entanglement. [ABSTRACT FROM AUTHOR]

The notion of su(2)$su(2)$ spin‐s$s$ Dicke states is introduced, which are higher‐spin generalizations of usual (spin‐1/2) Dicke states. These multi‐qudit states can be expressed as superpositions of su(2s+1)$su(2s+1)$ qudit Dicke states. They satisfy a recursion formula, which is used to formulate an efficient quantum circuit for their preparation, whose size scales as sk(2sn−k)$sk(2sn-k)$, where n$n$ is the number of qudits and k$k$ is the number of times the total spin‐lowering operator is applied to the highest‐weight state. The algorithm is deterministic and does not require ancillary qudits. [ABSTRACT FROM AUTHOR]

The formalism of generalized quantum histories allows a symmetrical treatment of space and time correlations, by taking different traces of the same history density matrix. In this framework, the characterization of spatial and temporal entanglement is revisited. An operative protocol is presented, to map a history state into the ket of a static composite system. It is demonstrated, by examples, how the Leggett–Garg and the temporal Clauser‐Horne‐Shimony‐Holt (CHSH) inequalities can be violated in this approach. [ABSTRACT FROM AUTHOR]

The quantum entanglement between the coin state and the position in nonlinear quantum walks is investigated. This study reveals that the nonlinearity of the quantum walk has a significant impact on the enhancement of quantum entanglement in an initially separable bipartite system. It is demonstrated that by selecting appropriate nonlinear parameters the initial separable states may turn to be entangled, and even approach to maximal entangled states. [ABSTRACT FROM AUTHOR]

In this short review, we present the key definitions, ideas and techniques involved in the study of symmetry resolved entanglement measures, with a focus on the symmetry resolved entanglement entropy. In order to be able to define such entanglement measures, it is essential that the theory under study possess an internal symmetry. Then, symmetry-resolved entanglement measures quantify the contribution to a particular entanglement measure that can be associated to a chosen symmetry sector. Our review focuses on conformal (gapless/massless/critical) and integrable (gapped/massive) quantum field theories, where the leading computational technique employs symmetry fields known as (composite) branch point twist fields. [ABSTRACT FROM AUTHOR]

In this paper, we investigated the sign-of-coupling dependence of the von Neumann Entanglement Entropy (EE) between system and environment in the ground state of networks of N coupled quantum oscillators. We find that whether the EE increases or decreases with the amplitude of coupling strengths between particles depends on the repulsive or attractive nature of the couplings, and it also depends on whether the coupling is between system-environment or particles both in the environment. In particular, the EE decreases with the amplitude of an attractive coupling between particles both in the environment. We also find that the EE varies nonmonotonically with number of particles directly interacting with the system with attractive couplings; besides, the position-momentum uncertainty of the particle in the system and the EE vary contrarily when the particle-number is small. [ABSTRACT FROM AUTHOR]

Unruh effect entropy is estimated for a spherically symmetric source with an exponential energy distribution; angular degrees of freedom are suggested to be equally likely to contribute. Calculations are performed with an assumption about finite energy and multiplicity ranges. The result is represented in the units of Schwarzschild black hole entropy, with the analytical ratio being expressed analytically and generalized to homogeneous distribution over other degrees of freedom. [ABSTRACT FROM AUTHOR]

In this study, we explore the ground state phase diagram of the spin-1/2 XX chain model, which features X Z Y - Y Z X -type three-spin interactions (TSIs). This model, while seemingly simple, reveals a rich tapestry of quantum behaviors. Our analysis relies on several key metrics. The ' l 1 -norm of coherence' helps us identify coherent states within the phase diagram, which represent states capable of superposition and interference. We employ the 'spin squeezing parameter' to pinpoint unique coherent states characterized by isotropic noise in all directions, making them invaluable for quantum metrology. Additionally, we utilize the 'entanglement entropy' to determine which of these coherent states exhibit entanglement, indicating states that cannot be fully described by local variables. Our research unveils diverse regions within the phase diagram, each characterized by coherent, squeezed, or entangled states, offering insights into the quantum phenomena underling these systems. We also study the critical scaling versus the system size for the mentioned quantities. [ABSTRACT FROM AUTHOR]

If an asymmetry in time does not arise from the fundamental dynamical laws of physics, it may be found in special boundary conditions. The argument normally goes that since thermodynamic entropy in the past is lower than in the future according to the Second Law of Thermodynamics, then tracing this back to the time around the Big Bang means the universe must have started off in a state of very low thermodynamic entropy: the Thermodynamic Past Hypothesis. In this paper, we consider another boundary condition that plays a similar role, but for the decoherent arrow of time, i.e. the subsystems of the universe are more mixed in the future than in the past. According to what we call the Entanglement Past Hypothesis, the initial quantum state of the universe had very low entanglement entropy. We clarify the content of the Entanglement Past Hypothesis, compare it with the Thermodynamic Past Hypothesis, and identify some challenges and open questions for future research. [ABSTRACT FROM AUTHOR]

Unruh effect entropy is estimated for a spherically symmetric source with an exponential energy distribution; angular degrees of freedom are suggested to be equally likely to contribute. Calculations are performed with an assumption about finite energy and multiplicity ranges. The result is represented in the units of Schwarzschild black hole entropy, with the analytical ratio being expressed analytically and generalized to homogeneous distribution over other degrees of freedom.

We consider a quantum system of large size N and its subsystem of size L, assuming that N is much larger than L, which can also be sufficiently large, i.e., 1 ≪ L ≲ N . A widely accepted mathematical version of this inequality is the asymptotic regime of successive limits: first the macroscopic limit N → ∞ , then an asymptotic analysis of the entanglement entropy as L → ∞ . In this paper, we consider another version of the above inequality: the regime of asymptotically proportional L and N, i.e., the simultaneous limits L → ∞ , N → ∞ , L / N → λ > 0 . Specifically, we consider a system of free fermions that is in its ground state, and such that its one-body Hamiltonian is a large random matrix, which is often used to model long-range hopping. By using random matrix theory, we show that in this case, the entanglement entropy obeys the volume law known for systems with short-range hopping but described either by a mixed state or a pure strongly excited state of the Hamiltonian. We also give streamlined proof of Page's formula for the entanglement entropy of black hole radiation for a wide class of typical ground states, thereby proving the universality and the typicality of the formula. [ABSTRACT FROM AUTHOR]

In this paper, we compute the black hole entropy and the entanglement entropy of Hawking radiations due to photons during the evaporation of a 4D asymptotically flat Kerr black hole. The Page curve for the Kerr black hole is obtained in the original way à la Page, and it qualitatively mimics the curve for the Schwarzschild black hole but has some new features. [ABSTRACT FROM AUTHOR]

The intricate interplay between unitary evolution and projective measurements could induce entanglement phase transitions in the nonequilibrium dynamics of quantum many-particle systems. In this work, we uncover loss-induced entanglement transitions in non-Hermitian topological superconductors. In prototypical Kitaev chains with onsite particle losses and varying hopping and pairing ranges, the bipartite entanglement entropy of steady states is found to scale logarithmically versus the system size in topologically nontrivial phases and become independent of the system size in the trivial phase. Notably, the scaling coefficients of log-law entangled phases are distinguishable when the underlying system resides in different topological phases. Log-law to log-law and log-law to area-law entanglement phase transitions are further identified when the system switches between different topological phases and goes from a topologically nontrivial to a trivial phase, respectively. These findings not only establish the relationships among spectral, topological and entanglement properties in a class of non-Hermitian topological superconductors but also provide an efficient means to dynamically reveal their distinctive topological features. [ABSTRACT FROM AUTHOR]

Genuine multipartite entanglement is crucial for quantum information and related technologies, but quantifying it has been a long-standing challenge. Most proposed measures do not meet the "genuine" requirement, making them unsuitable for many applications. In this work, we propose a journey toward addressing this issue by introducing an unexpected relation between multipartite entanglement and hypervolume of geometric simplices, leading to a tetrahedron measure of quadripartite entanglement. By comparing the entanglement ranking of two highly entangled four-qubit states, we show that the tetrahedron measure relies on the degree of permutation invariance among parties within the quantum system. We demonstrate potential future applications of our measure in the context of quantum information scrambling within many-body systems. [ABSTRACT FROM AUTHOR]

This study investigates the entanglement properties of disordered free fermion systems undergoing an Anderson phase transition from a delocalized to a localized phase. The entanglement entropy is employed to quantify the degree of entanglement, with the system randomly divided into two subsystems. To explore this phenomenon, one-dimensional tight-binding fermion models and Anderson models in one, two, and three dimensions are utilized. Comprehensive numerical calculations reveal that the entanglement entropy, determined using random bi-partitioning, follows a volume-law scaling in both the delocalized and localized phases, expressed as EE ∝ L D , where D represents the dimension of the system. Furthermore, the role of short and long-range correlations in the entanglement entropy and the impact of the distribution of subsystem sites are analyzed. [ABSTRACT FROM AUTHOR]

In this work, the entanglement entropy is examined within the context of deep inelastic scattering in ep$$ ep $$ collisions. The calculation is based on a formalism where the partonic state at small‐x$$ x $$ is maximally entangled, consisting of a large number of micro‐states occurring with equal probabilities. Analytical expressions for the number of gluons, Ngluon$$ {N}_{\mathrm{gluon}} $$, are considered, derived from gluon saturation models for dipole‐target amplitudes within the framework of the Quantum Chromodynamics (QCD) color dipole picture. A comparison of the entanglement entropy with thermodynamic entropy measured in pp$$ pp $$ and ep$$ ep $$ collisions at high energies is done. [ABSTRACT FROM AUTHOR]

We develop a mathematical formalism that allows to study decoherence with a great level generality, so as to make it appear as a geometrical phenomenon between reservoirs of dimensions. It enables us to give quantitative estimates of the level of decoherence induced by a purely random environment on a system according to their respectives sizes, and to exhibit some links with entanglement entropy. [ABSTRACT FROM AUTHOR]

One-dimensional (1D) magnetic systems offer rich phenomena in the quantum limit, proving more chemically accessible than zero-dimensional or higher-dimensional frameworks. Single-walled carbon nanotubes (SWCNT) have recently been used to encapsulate trimetric nickel(II) acetylacetonate [Nanoscale, 2019, 11, 10615–10621]. Here, we investigate the magnetization on spin chains based on nickel trimers by Matrix Product State (MPS) simulations. Our findings reveal plateaus in the exchange/magnetic-field phase diagram for three coupling configurations, showcasing effective dimeric and trimeric spin-ordering with similar or staggered entanglement across chains. These ordered states allow the qubit-like tuning of specific local magnetic moments, exhibiting disengagement or uniform coupling in entanglement plateaus. This behavior is consistent with the experimental transition from frustrated (3D) to non-frustrated (1D) molecules, corresponding to large and smaller SWCNT diameters. Our study offers insights into the potential of 1D-confined trimers for quantum computation, extending beyond the confinement of trimetric nickel-based molecules in one dimension. [ABSTRACT FROM AUTHOR]

The entropy produced by Unruh radiation is estimated and compared to the entropy of a Schwarzschild black hole. We simulate a spherical system of mass M by a set of Unruh horizons and estimate the total entropy of the outgoing radiation. Dependence on the mass and spin of the emitted particles is taken into account. The obtained results can be easily extended to any other intrinsic degrees of freedom of outgoing particles. The ratio of Unruh entropy to the Schwarzschild black hole entropy is derived in exact analytical form. For large black holes, this ratio exhibits high susceptibility to quantum numbers, e.g., spin s, of emitted quanta and varies from 0% for s=0 to 19.0% for s=5/2.

We discuss some general properties of the symmetry-resolved entanglement entropy in systems with particle number conservation. Using these general results, we describe how to obtain bounds on the entanglement components from correlation functions in Gaussian systems. We introduce majorization as an important tool to derive entanglement bounds. As an application, we derive lower bounds both for the number and the configurational entropy for chiral and Cn -symmetric topological phases. In some cases, our considerations also lead to an improvement of the previously known lower bounds for the entanglement entropy in such systems. [ABSTRACT FROM AUTHOR]

Unitarity and the optical theorem are used to derive the reduced density matrices of Compton scattering in the presence of a witness particle. Two photons are initially entangled wherein one photon participates in Compton scattering, while the other is a witness, i.e., does not interact with the electron. Unitarity is shown to require that the entanglement entropy of the witness photon does not change after its entangled partner undergoes scattering. The final mutual information of the electron's and witness particle's polarizations is shown to be nonzero for low-energy Compton scattering. This indicates that the two particles became correlated in spite of no direct interaction. Assuming an initial maximally entangled state, the change in entanglement entropy of the scattered photon's polarization is calculated in terms of Stokes parameters. A common ratio of areas occurs in the final reduced density matrix elements, von Neumann entropies, Stokes parameter, and mutual information. This common ratio consists of the Thomson scattering cross-section and an accessible regularized scattering area. [ABSTRACT FROM AUTHOR]

The information loss paradox associated with black hole Hawking evaporation is an unresolved problem in modern theoretical physics. In a recent brief essay, we revisited the evolution of the black hole entanglement entropy via the Euclidean path integral (EPI) of the quantum state and allow for the branching of semi-classical histories along the Lorentzian evolution. We posited that there exist at least two histories that contribute to EPI, where one is an information-losing history, while the other is an information-preserving one. At early times, the former dominates EPI, while at the late times, the latter becomes dominant. By doing so, we recovered the essence of the Page curve, and thus, the unitarity, albeit with the turning point, i.e., the Page time, much shifted toward the late time. In this full-length paper, we fill in the details of our arguments and calculations to strengthen our notion. One implication of this modified Page curve is that the entropy bound may thus be violated. We comment on the similarity and difference between our approach and that of the replica wormholes and the islands' conjectures. [ABSTRACT FROM AUTHOR]

The entropy produced by Unruh radiation is estimated and compared to the entropy of a Schwarzschild black hole. We simulate a spherical system of mass M by a set of Unruh horizons and estimate the total entropy of the outgoing radiation. Dependence on the mass and spin of the emitted particles is taken into account. The obtained results can be easily extended to any other intrinsic degrees of freedom of outgoing particles. The ratio of Unruh entropy to the Schwarzschild black hole entropy is derived in exact analytical form. For large black holes, this ratio exhibits high susceptibility to quantum numbers, e.g., spin s, of emitted quanta and varies from 0% for s = 0 to 19.0% for s = 5 / 2 . [ABSTRACT FROM AUTHOR]

Entanglement is a property of interacting particles in a quantum system. The measure of the interaction can be known by looking for the entanglement entropy value in the system. The quantum system used in this study is the Dicke model quantum system which consists of a single-mode electromagnetic radiation field and a two-level N-atom. This study aims to determine the influence of the coupling constant on entanglement entropy and system dynamics. Simulation of system dynamics is carried out with the Quantum Toolbox in Python (QuTiP) module. The simulation results show that the coupling constant has a significant effect on the entanglement entropy value. The greater the value of the coupling constant used, the entanglement entropy value increases. In addition, there is a maximum entanglement entropy value for N greater than one. The coupling constant also affects the dynamics of the system, that is, the greater the value of the coupling constant, the more quantum states can be accessed by atoms.

The time evolution of a quantum particle's product of uncertainties in position and momentum is calculated when it is coupled with an external source. We have used a simple toy model where the particle is subject to a harmonic potential and coupled with an equivalent harmonic oscillator via a linear term. It is found that the long-time-averaged product is an increasing function of the coupling strength. It diverges when one of the eigenmodes of the coupled system goes soft, with the singular term twice of that for the stationary state. Generally, there is a jump of finite size for this quantity when a small coupling is turned on, compared to the uncoupled case. Similar behaviors have also been found for the von Neumann entanglement entropy, which is calculated exactly using a covariance matrix formalism. We find that the mode-interference plays an important role in the main features of this work. [ABSTRACT FROM AUTHOR]

If we interpret the Bekenstein–Hawking entropy of the Hubble horizon as thermodynamic entropy, then the entanglement entropy of the superhorizon modes of curvature perturbation entangled with the subhorizon modes will exceed the Bekenstein–Hawking bound at some point; we call this the unitary paradox of cosmological perturbations by analogy with black hole. In order to avoid a fine-tuned problem, the paradox must occur during the inflationary era at the critical time t c = ln (3 π / 2 H H inf ) / 2 H inf (in Planck units), where H = − Ḣ / H 2 is the first Hubble slow-roll parameter and H inf is the Hubble rate during inflation. If we instead accept the fine-tuned problem, then the paradox will occur during the dark energy era at the critical time t c ′ = ln (3 π H inf / 2 f e 2 N H Λ 2) / 2 H Λ , where H Λ is the Hubble rate dominated by dark energy, N is the total number of e-folds of inflation and f is a purification factor that takes the range 0 < f < 3 π H inf / 2 e 2 N H Λ 2 . [ABSTRACT FROM AUTHOR]

We show that, for a class of planar determinantal point processes (DPP) X , the growth of the entanglement entropy S (X (Ω)) of X on a compact region Ω ⊂ R 2 d , is related to the variance V X (Ω) as follows: V X (Ω) ≲ S X (Ω) ≲ V X (Ω). Therefore, such DPPs satisfy an area law S X g (Ω) ≲ ∂ Ω , where ∂ Ω is the boundary of Ω if they are of Class I hyperuniformity ( V X (Ω) ≲ ∂ Ω ), while the area law is violated if they are of Class II hyperuniformity (as L → ∞ , V X (L Ω) ∼ C Ω L d - 1 log L ). As a result, the entanglement entropy of Weyl–Heisenberg ensembles (a family of DPPs containing the Ginibre ensemble and Ginibre-type ensembles in higher Landau levels), satisfies an area law, as a consequence of its hyperuniformity. [ABSTRACT FROM AUTHOR]

We studied signatures of quantum chaos in dynamics of Rydberg-dressed bosonic atoms held in a one-dimensional triple-well potential. Long-range nearest-neighbor and next-nearest-neighbor interactions, induced by laser dressing atoms to strongly interacting Rydberg states, drastically affect mean-field and quantum many-body dynamics. By analyzing the mean-field dynamics, classical chaos regions with positive and large Lyapunov exponents were identified as a function of the potential well tilting and dressed interactions. In the quantum regime, it was found that level statistics of the eigen-energies gain a Wigner–Dyson distribution when the Lyapunov exponents are large, giving rise to signatures of strong quantum chaos. We found that both the time-averaged entanglement entropy and survival probability of the initial state have distinctively large values in the quantum chaos regime. We further showed that population variances could be used as an indicator of the emergence of quantum chaos. This might provide a way to directly probe quantum chaotic dynamics through analyzing population dynamics in individual potential wells. [ABSTRACT FROM AUTHOR]

Herein, aspects of entanglement and fidelity and their use in condensed matter systems are briefly reviewed. Both static and time-dependent situations are considered. Different signatures of phases and phase transitions are discussed, including the dynamic aspects of the evolution across a critical point. Some emphasis is placed on the use of entanglement in phase transitions with no clear order parameters and no symmetry breaking. [ABSTRACT FROM AUTHOR]

In this paper, we construct the metric tensor and volume for the manifold of purifications associated with an arbitrary reduced density operator ρ S . We also define a quantum coarse-graining (CG) to study the volume where macrostates are the manifolds of purifications, which we call surfaces of ignorance (SOI), and microstates are the purifications of ρ S . In this context, the volume functions as a multiplicity of the macrostates that quantifies the amount of information missing from ρ S . Using examples where the SOI are generated using representations of S U (2) , S O (3) , and S O (N) , we show two features of the CG: (1) A system beginning in an atypical macrostate of smaller volume evolves to macrostates of greater volume until it reaches the equilibrium macrostate in a process in which the system and environment become strictly more entangled, and (2) the equilibrium macrostate takes up the vast majority of the coarse-grained space especially as the dimension of the total system becomes large. Here, the equilibrium macrostate corresponds to a maximum entanglement between the system and the environment. To demonstrate feature (1) for the examples considered, we show that the volume behaves like the von Neumann entropy in that it is zero for pure states, maximal for maximally mixed states, and is a concave function with respect to the purity of ρ S . These two features are essential to typicality arguments regarding thermalization and Boltzmann's original CG. [ABSTRACT FROM AUTHOR]

One-dimensional (1D) magnetic systems offer rich phenomena in the quantum limit, proving more chemically accessible than zero-dimensional or higher-dimensional frameworks. Single-walled carbon nanotubes (SWCNT) have recently been used to encapsulate trimetric nickel(II) acetylacetonate [Nanoscale, 2019, 11, 10615–10621]. Here, we investigate the magnetization on spin chains based on nickel trimers by Matrix Product State (MPS) simulations. Our findings reveal plateaus in the exchange/magnetic-field phase diagram for three coupling configurations, showcasing effective dimeric and trimeric spin-ordering with similar or staggered entanglement across chains. These ordered states allow the qubit-like tuning of specific local magnetic moments, exhibiting disengagement or uniform coupling in entanglement plateaus. This behavior is consistent with the experimental transition from frustrated (3D) to non-frustrated (1D) molecules, corresponding to large and smaller SWCNT diameters. Our study offers insights into the potential of 1D-confined trimers for quantum computation, extending beyond the confinement of trimetric nickel-based molecules in one dimension.

The study of entanglement propagation in the dynamics of quantum multibody systems is an important problem in non-equilibrium physics. This paper optimizes the magnetic field to maximize the entanglement entropy and studies its influence on the entanglement propagation properties of quantum states. On the quantum Ising chain with the nearest neighbor coupling, the magnetic field obtained by variational optimization is applied to maximize the entanglement entropy of the final state and improve the entanglement growth rate in the ballistic transport region. At the same time, the entanglement entropy of the short chain can reach the entanglement saturation value of the long chain under a fixed magnetic field. When the chain length is increased, the saturation value of entanglement entropy increases, but the growth rate is almost the same. Specifically, by controlling the magnetic field, the entanglement growth rate of Heisenberg antiferromagnetic chain with only the nearest neighbor interaction can be increased to the same rate as that of the system with long-range interaction. The research in this paper reveals the ability of magnetic field to control entanglement propagation in non-equilibrium process, which can be applied to quantum control and information processing in the future. [ABSTRACT FROM AUTHOR]

In this article, we investigate the various physical implications of quantum circuit complexity using the squeezed state formalism of Primordial Gravitational Waves (PGW). Recently, quantum information-theoretic concepts, such as entanglement entropy and complexity, have played a pivotal role in understanding the dynamics of quantum systems, even in diverse fields such as high-energy physics and cosmology. This paper is devoted to studying the quantum circuit complexity of PGW for various cosmological models, such as de Sitter, inflation, radiation, reheating, matter, bouncing, cyclic and black hole gas models, etc. We compute complexity measures using both Covariance and Nielsen's wave function method for three different choices of quantum initial vacua: Motta-Allen, α and Bunch–Davies. Besides computing circuit complexity, we also compute the Von Neumann entanglement entropy. By making the comparison between complexity and entanglement entropy, we are able to probe various features regarding the dynamics of evolution for different cosmological models. Because entanglement entropy is independent of the squeezing angle, we are able to understand more details of the system using Nielsen's measure of complexity, which is dependent on both squeezing parameter and angle. This implies that quantum complexity could indeed be a useful probe to study quantum features on a cosmological scale. Quantum complexity is also becoming a powerful technique to understand the chaotic behaviour and random fluctuations of quantum fields. Using the growth of complexity, we are able to compute the quantum Lyapunov exponent for various cosmological models and comment on its chaotic nature. [ABSTRACT FROM AUTHOR]

We consider evaporation of the Schwarzschild black hole and note that island configurations do not provide a bounded entanglement entropy. The same remark is also valid for some other static black holes. A proposal for improving the situation is discussed. [ABSTRACT FROM AUTHOR]

A recently proposed history formalism is used to define temporal entanglement in quantum systems, and compute its entropy. The procedure is based on the time-reduction of the history density operator, and allows a symmetrical treatment of space and time correlations. Temporal entanglement entropy is explicitly calculated in two simple quantum computation circuits. [ABSTRACT FROM AUTHOR]

The entanglement entropy of s and d bosons in the framework of Interacting Boson Model -1 (IBM-1) has been obtained using consistent-Q formalism and semiclassical approximation. This has been possible by using Schmidt decomposition and expressing s and d bosons entanglement entropy in terms of Schmidt numbers. In this research, a simple method in the framework of IBM-1 has been presented for deriving the entanglement entropy in the Casten triangle. The results indicated that the entanglement entropy is sensitive to the shape-phase transition in the various regions of the Casten triangle. It was demonstrated that the entanglement entropy of s and d bosons in the semiclassical approximation depends only on the values of the deformation parameter (β) and is independent of the angular parameter (γ). Also, the entanglement entropy between s and d bosons reaches its maximum value in the O (6) limit, while it decreases in the S U (3) limit, and reaches zero in the U (5) limit. Based on the results obtained via Schmidt decomposition, it is shown that the probability distribution functions of the number of s bosons in IBM-1 are the binomial distributions. For N B ≫ 1 , it was proved that the distribution function in the S U (3) , O (6) and S U (3) ‾ limits is the Gaussian, and in the U (5) limit is the Poissonian. [ABSTRACT FROM AUTHOR]

Semantic interaction modeling is a fundamental technology in natural language understanding that guides models to extract deep semantic information from text. Currently, the attention mechanism is one of the most effective techniques in semantic interaction modeling, which learns word-level attention representation by measuring the relevance between different words. However, the attention mechanism is limited to word-level semantic interaction, it cannot meet the needs of fine-grained interactive information for some text classification tasks. In recent years, quantum-inspired language modeling methods have successfully constructed quantized representations of language systems in Hilbert spaces, which use density matrices to achieve fine-grained semantic interaction modeling. This paper presents a Q uantum-inspired hierarchical S emantic I nteraction M odel (QSIM), which follows the sememe-word-sentence language construction principle and utilizes quantum entanglement theory to capture hierarchical semantic interaction information in Hilbert space. Our work builds on the idea of the attention mechanism and extends it. Specifically, we explore the original semantic space from a quantum theory perspective and derive the core semantic space using the Schmidt decomposition technique, where: (1) Sememe is represented as the unit vector in the two-dimensional minimum semantic space; (2) Word is represented as reduced density matrices in the core semantic space, where Schmidt coefficients quantify sememe-level semantic interaction. Compared to density matrices, reduced density matrices capture fine-grained semantic interaction information with lower computational cost; (3) Sentence is represented as quantum superposition states of words, and the degree of word-level semantic interaction is measured using entanglement entropy. To evaluate the model's performance, we conducted experiments on 15 text classification datasets. The experimental results demonstrate that our model is superior to classical neural network models and traditional quantum-inspired language models. Furthermore, the experiment also confirms two distinct advantages of QISM: (1) flexibility , as it can be integrated into various mainstream neural network text classification architectures; and (2) practicability , as it alleviates the problem of parameter growth inherent in density matrix calculation in quantum language model. [ABSTRACT FROM AUTHOR]

Semiconducting nanowires with strong Rashba spin–orbit coupling in the proximity with a superconductor and under a strong Zeeman field can potentially manifest Majorana zero modes (MZMs) at their edges and are a topical candidate for topological superconductivity. However, protocols for their detection based on the local and the non-local conductance spectroscopy have been subject to intense scrutiny. In this work, by taking current experimental setups into account, we detail mathematical ideas related to the entanglement entropy and the fermion parity fluctuations to faithfully distinguish between true MZMs and trivial quasi-MZMs. We demonstrate that the disconnected entanglement entropy, derived from the von Neumann entanglement entropy, provides a distinct and robust signature of the topological phase transition which is immune to system parameters, size and disorders. In order to understand the entanglement entropy of the Rashba nanowire system, we establish its connection to a model of interacting spinfull Kitaev chains. Moreover, we relate the entanglement entropy to the fermionic parity fluctuation, and show that it behaves concordantly with entanglement entropy, hence making it a suitable metric for the detection of MZMs. In connection with the topological gap protocol that is based on the conductance spectra, the aforesaid metrics can reliably point toward the topological transitions even in realistic setups.

From the viewpoint of the Bose–Einstein condensation (BEC) of the fermion system, the maximum geminal of the second-order reduced density matrix of the superconducting state exactly corresponds to the Cooper pair. In this paper the entanglement entropy (EE) for the maximum geminal of the BCS ground state is evaluated. The EE behaves logarithmically with respect to the number of the maximum geminal. Furthermore, the disappearance point of superconductivity is defined on the basis of the fermion BEC. In the superconducting ground state, almost all electrons in the energy width of the gap parameter near the Fermi level are condensed as a maximum geminal. They suddenly change to normal electrons with a finite gap of the EE at the disappearance point like a first-order phase transition.

The study of many-body quantum systems, that fail to thermalize in the presence of disorder, has recently attracted lots of interests. This is due to the appearance of the many-body localized phase and breakdown of eigenstate thermalization hypothesis in such systems which can be described by the local integrals of motion. In this paper, we consider a disordered spin chain in the many-body localized phase and try to study the dynamics of entanglement generation in this system using the local integrals of motion. To this end, we, first, solve the non-interacting system analytically to describe the mechanism of entanglement generation for different kinds of initial states, exactly. Then, we generalize this approach to the interacting system to learn the dynamics of entanglement generation. Finally, we discuss the physical meaning of different behaviors in the dynamics of entanglement generation in the presence and absence of interaction.‎

By entangling soft massless particles, one can create an arbitrarily large amount of entanglement entropy that carries an arbitrarily small amount of energy. By dropping this entropy into the black hole (b.h.), one can increase the b.h. entropy by an amount that violates the Bekenstein bound or any other reasonable bound, leading to a version of the b.h. information paradox that does not involve Hawking radiation. Among the many proposed solutions for the standard b.h. information paradox with Hawking radiation, only a few can also resolve this version without Hawking radiation. The assumption that both versions should be resolved in the same way significantly helps to reduce the number of possible resolutions. [ABSTRACT FROM AUTHOR]

The topological Haldane phase is one of the most important prototypes in the topological phases of matter. Its counterpart in quantum gases, namely the Haldane insulator in a bosonic system, has been elusive since the first proposal in 2006. A typical way to detect this phase is by measuring its nonlocal string order. Here we propose an alternative way, by breaking the Haldane insulator. By carefully considering the edge effects, we can see the half-chain entanglement entropy and its spectrum remain relatively robust during the dynamical process. Our results are hopefully to be realized in the following cold atoms experiments. [ABSTRACT FROM AUTHOR]

Geared as an invitation for undergraduates, beginning graduate students, we present a pedagogical introduction to one-dimensional topological phases—in particular, the Su-Schrieffer-Heeger model. In the process, we delve upon ideas of entanglement using the correlator method and the von-Neumann density-matrix method, geometric phase, polarization, transport signatures and the role of electron-electron interactions. Through hands-on numerical experiments, whose codes are shared, we try to drive home the message why a program of simulating quantum electronics with topological toy models is the storehouse for discovering fantastic physics ideas. [ABSTRACT FROM AUTHOR]

According to Whitehead, nature is disclosed to mind by an ensemble of events characterized by unobservable hidden intrinsic factors (e.g., mass, gravitation) and observable extrinsic factors (e.g., motion, density). Mass is not the substratum of dynamics. It implies spatial extension and temporal duration, which are both necessary conditions of observable natural phenomena. Therefore, an instant, deprived of duration, is immeasurable. Whitehead’s claims on mass, space, and time corroborate Verlinde’s alternative conception of quantum gravitation. Within the de Sitter space-time, this conception starts from the competition of the short distance degrees of freedom of the Ryn-Takanayagi tensor with long-distance thermalized excitations. This enables the creation of a baryonic mass and a decrease in de Sitter entropy. The memory effect of the original baryon creation leads to gravitation and the production of extensive thermodynamic entropy. However, the baryon production shrinks, and the dissipating space-time transforms into a space-timeless cold sink with an accompanying strong contracting memory effect. This is equivalent to the alternate motion of a giant Carnot engine, where the heat source and sink energy exchange produce the eternal periodic dynamics of the Universe. This suggests that the Universe did not start from Big Bang but oscillated eternally as a Big Bounce Universe.

Abstract The renormalization of entanglement entropy of quantum field theories is investigated in the simplest setting with a λ ϕ 4 scalar field theory. The 3+1 dimensional spacetime is separated into two regions by an infinitely flat 2-dimensional interface. The entanglement entropy of the system across the interface has an elegant geometrical interpretation using the replica trick, which requires putting the field theory on a curved spacetime background. We demonstrate that the theory, and hence the entanglement entropy, is renormalizable at order λ once all the relevant operators up to dimension 4 are included in the action. This exercise has a one-to-one correspondence to entanglement entropy interpretation of the black hole entropy which suggests that our treatment is sensible. Our study suggests that entanglement entropy is renormalizable and is a physical quantity.