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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]

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]

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]

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]

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]

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.

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.

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.

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]

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]

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.

Generally speaking, entanglement entropy (EE) between two subregions of a gapped quantum many-body state is proportional to the area/length of their interface due to the short-range quantum correlation. However, the so-called area law is violated logarithmically in a quantum critical phase. Moreover, the subleading correction exists in long-range entangled topological phases. It is referred to as topological EE which is related to the quantum dimension of the collective excitation in the bulk. Furthermore, if a non-smooth sharp angle is in the presence of the subsystem boundary, a universal angle dependent geometric contribution is expected to appear in the subleading correction. In this work, we simultaneously explore the geometric and edge contributions in the integer quantum Hall (IQH) state and its edge reconstruction in a unified bipartite method. Their scaling is found to be consistent with conformal field theory (CFT) predictions and recent results of particle number fluctuation calculations.

Using the fact that we only observe those modes that exit the Hubble horizon during inflation, one can calculate the entanglement entropy of such long-wavelength perturbations by tracing out the unobservable sub-Hubble fluctuations they are coupled with. On requiring that this perturbative entanglement entropy, which increases with time, obey the covariant entropy bound for an accelerating background, we find an upper bound on the duration of inflation. This presents a new perspective on the (meta-)stability of de Sitter spacetime and an associated lifetime for it. [ABSTRACT FROM AUTHOR]

The conservation of information of evaporating black holes is a very natural consequence of unitarity, which is the fundamental symmetry of quantum mechanics. In order to study the conservation of information, we need to understand the nature of the entanglement entropy. The entropy of Hawking radiation is approximately equal to the maximum of entanglement entropy if a black hole is in a state before the Page time, i.e., when the entropy of Hawking radiation is smaller than the entropy of the black hole. However, if there exists a process generating smaller entanglements rather than maximal entanglements, the entropy of Hawking radiation will become smaller than the maximum of the entanglement entropy before the Page time. If this process accumulates, even though the probability is small, the emitted radiation can eventually be distinguished from the exactly thermal state. In this paper, we provide several interpretations of this phenomenon: (1) information of the collapsed matter emitted before the Page time, (2) there exists a firewall or a non-local effect before the Page time, or (3) the statistical entropy is greater than the areal entropy; a monster is formed. Our conclusion will help resolve the information loss paradox by providing groundwork for further research. [ABSTRACT FROM AUTHOR]

We compute the holographic entanglement entropy of a thermalized CFT on a time-dependent background in four dimensions. We consider a slab configuration extending beyond the cosmological horizon of a Friedmann-Lemaitre-Robertson-Walker metric. We identify a volume term that corresponds to the thermal entropy of the CFT, as well as terms proportional to the proper area of the entangling surface which are associated with strongly entangled degrees of freedom in the vicinity of this surface or with the expansion.

We investigated the scaling behaviors of entanglements on the two-leg ladder lattice structure implemented with Affleck–Kennedy–Lieb–Tasaki (AKLT) model on six types of topological surfaces, namely, torus, sphere, real projective plane, Klein bottle, cylinder and Möbius strip. All six topological surfaces on which our lattices were embedded are classified according to whether their boundaries are closed or open. Lattice structures on these topological surfaces are formed either by a trivalent or four-valent site to fulfill a complete spin-32or spin-2 system, respectively. Their ground states, which are the valence-bond-solid states, are derived by the tensor-product method. The von Neumann entropies for entanglement of the bipartite region on all six topological surfaces are calculated and all results show that the entanglement entropies per area are bounded from above or below when approaching the thermodynamic limit. For the spin-2 and the spin-32systems on all surfaces, except on the sphere, numerical results between even and odd cases of the number of lattice sites should be considered separately for scrutinizing their scaling behaviors. However, their entanglement entropies still satisfy the area law, but with a correction term.

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.

In this paper we compute the entanglement entropy for linearized gravitons (as helicity 2 particles) on a sphere defined over a Minkowski background. Previously, we analyse the cases of the solar and vector fields by decomposition in spherical harmonics. Then we generalise this method for the tensor field. We obtain the universal logarithmic coefficient and we analyse its relation to the conformal anomaly

Stern-Gerlach and/or matter-wave interferometry has garnered significant interest amongst members of the scientific community over the past few decades. Early theoretical results by Schwinger et al. demonstrate the fantastic precision capabilities required to realize a full-loop Stern-Gerlach interferometer, i.e., a Stern-Gerlach setup that houses the capability of recombining the split wave-packets in both, position and momentum space over a certain characteristic interferometric time. Over the years, several proposals have been put forward that seek to use Stern-Gerlach and/or matter-wave interferometry as a tool for a myriad of applications of general interest, some of which include tests for fundamental physics (viz., quantum wave-function collapse, stringent tests for the Einstein equivalence principle at the quantum scale, breaking the Standard Quantum Limit (SQL) barrier, and so forth), precision sensing, quantum metrology, gravitational wave detection and inertial navigation. In addition, a large volume of work in the existing literature has been dedicated to the possibility of using matter-wave interferometry for tests of quantum gravity. Inspired by the developments in this timely research field, this Perspective attempts to provide a general overview of the theory involved, the challenges that are yet to be addressed and a brief outlook on what lays ahead.

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 FROM AUTHOR]

We analyze the 1+1 CFT states dual to hot (time-symmetric) 2+1 multiboundary AdS wormholes. These are black hole geometries with high local temperature, -rfnet≥1 asymptotically-AdS3 regions, and arbitrary internal topology. The dual state at t = 0 is defined on n circles. We show these to be well-described by sewing together tensor networks corresponding to thermofield double states. As a result, the entanglement is spatially localized and bipartite: away from particular boundary points (vertices) any small connected region A of the boundary CFT is entangled only with another small connected region B, where B may lie on a different circle or may be a different part of the same circle. We focus on the pair-of-pants case, from which more general cases may be constructed. We also discuss finite-temperature corrections, where we note that the states involve a code subspace in each circle.

We study and construct spacetimes, dubbed planar AdS-dS-wormholes, satisfying the null energy condition and having two asymptotically AdS boundaries connected through a (non-traversable) inflating wormhole. As for other wormholes, it is natural to expect dual descriptions in terms of two disconnected conformal field theories (CFTs) in appropriate entangled states. But for our cases, certain expected bulk entangling surfaces used by the Hubeny-Rangamani-Takayanagi (HRT) prescription to compute CFT entropy do not exist. In particular, no real codimension-2 extremal surface can run from one end of the wormhole to the other. According to HRT, the mutual information between any two finite-sized subregions (one in each CFT) must then vanish at leading order in large N - though the leading-order mutual information per unit area between the two CFTs taken as wholes may be nonzero. Some planar AdS-dS-wormholes also fail to have plane-symmetric surfaces that would compute the total entropy of either CFT. We suggest this to remain true of less-symmetric surfaces so that the HRT entropy is ill-defined and some modified prescription is required. It may be possible to simply extend HRT or the closely-related maximin construction by a limiting procedure, though complex extremal surfaces could also play an important role.

In this paper, we further elaborate on the Bose-Einstein condensate (BEC) dark matter model extended in our previous work [Phys. Rev. D 2020,102, 083510] by the inclusion of sixth-order (or three-particle) repulsive self-interaction term. Herein, our goal is to complete the picture through adding to the model the fourth-order repulsive self-interaction. The results of our analysis confirm the following: while in the previous work the two-phase structure and the possibility of first-order phase transition was established, here we demonstrate that with the two self-interactions involved, the nontrivial phase structure of the enriched model remains intact. For this to hold, we study the conditions which the parameters of the model, including the interaction parameters, should satisfy. As a by-product and in order to provide some illustration, we obtain the rotation curves and the (bipartite) entanglement entropy for the case of a particular dwarf galaxy. [ABSTRACT FROM AUTHOR]

We discuss the possible relevance of complex codimension-two extremal surfaces to the Ryu-Takayanagi holographic entanglement proposal and its covariant Hubeny-Rangamani-Takayanagi generalization. Such surfaces live in a complexified bulk spacetime defined by analytic continuation. We identify surfaces of this type for BTZ, Schwarzschild-AdS, and Schwarzschild-Lifshitz planar black holes. Since the dual CFT interpretation for the imaginary part of their areas is unclear, we focus on a straw man proposal relating CFT entropy to the real part of the area alone. For Schwarzschild-AdS and Schwarzschild-Lifshitz, we identify families where the real part of the area agrees with qualitative physical expectations for the time-dependence of the appropriate CFT entropy and, in addition, where it is smaller than the area of corresponding real extremal surfaces. It is thus plausible that the CFT entropy is controlled by these complex extremal surfaces.

The renormalization of entanglement entropy of quantum field theories is investigated in the simplest setting with a λϕ4 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. [ABSTRACT FROM AUTHOR]

In this work we consider two complex scalar fields distinguished by their masses coupled to constant background electric and magnetic fields in the (3+1)-dimensional Minkowski spacetime and subsequently investigate a few measures quantifying the quantum correlations between the created particle-antiparticle Schwinger pairs. Since the background magnetic field itself cannot cause the decay of the Minkowski vacuum, our chief motivation here is to investigate the interplay between the effects due to the electric and magnetic fields. We start by computing the entanglement entropy for the vacuum state of a single scalar field. Second, we consider some maximally entangled states for the two-scalar field system and compute the logarithmic negativity and the mutual information. Qualitative differences of these results pertaining to the charge content of the states are emphasised. Based upon these results, we suggest some possible effects of a background magnetic field on the degradation of entanglement between states in an accelerated frame, for charged quantum fields.

We show that quantum entanglement between causally separated regions of a nucleon in antineutrino-nucleon scattering manifests itself as a thermal component in the resulting pion momentum distribution. For antineutrino scattering coherently from the (carbon) nucleus as a whole, this thermal component is absent, as expected by our quantum entanglement thermalization proposition. These phenomena, which have been observed in proton-proton collisions at the Large Hadron Collider, and in electromagnetic deep inelastic scattering, are now for the first time shown to exist in electroweak interactions as well.

We calculate the expectation value of the Wilson line in the pure AdS3 Einstein gravity theory and also the entanglement entropy in the boundary theory. Our one-loop calculation of entanglement entropy shows a shift of the central charge 26. Finally, we show that the Wilson line provides the equivalent description to the boundary entanglement entropy. This equivalence leads to a concrete example of the building of “minimum surface=entanglement entropy”.

Recent theoretical progress shows that (2+1) black hole solution manifests long-range topological quantum entanglement similar to exotic non-Abelian excitations with fractional quantum statistics. In topologically ordered systems, there is a deep connection between physics of the bulk and that at the boundaries. Boundary terms play an important role in explaining the black hole entropy in general. We find several common properties between BTZ black holes and the Quantum Hall effect in (2+1)-dimensional bulk/boundary theories. We calculate the topological entanglement entropy of a (2+1) black hole and recover the Bekenstein–Hawking entropy, showing that black hole entropy and topological entanglement entropy are related. Using Chern–Simons and Liouville theories, we find that long-range entanglement describes the interior geometry of a black hole and identify it with the boundary entropy as the bond required by the connectivity of spacetime, gluing the short-range entanglement described by the area law. The IR bulk–UV boundary correspondence can be realized as a UV low-excitation theory on the bulk matching the IR long-range excitations on the boundary theory. Several aspects of the current findings are discussed.