Structure formation of entanglement entropy in a system of two superconducting qubits coupled with an LC-resonator

This paper investigates theoretically the evolutions of the entanglement entropy of a system of two coupled-charge- qubits interacting with an LC-resonator. It is found that when the initial states of the two qubits are prepared in a given superposition excited state, the evolution of the von Neumann entropy of the system depends significantly on the coupling strength between the two Josephson charge qubits. With the variation of the coupling strength, the evolution of the entanglement entropy of the system forms some structures, especially the periodically bistable properties, which are the first discovered for such a system to our knowledge. It is found that the relative entropy entanglement of the system is also sensitive to the variation of the coupling strength between the two charge qubits, some novel ＇collective oscillations＇ of the relative entropy are found for the system.

The Scaling of Entanglement Entropy for One Spatial XXZ Spin Chain

We investigate the scaling of entanglement entropy for one spatial XXZ spin chain by using matrix product states to approximate ground states. The entanglement entropy scales logarithmically with a coefficient that is determined by the associated conformal field theory, the quantum phase transitions occurred between Large-D and Halde phase, Halde phase and Neel phase. The scaling relationship is given in this paper.

A note on the entanglement entropy of primary fermion fields in JT gravity

In this paper we analyze and discuss 2D Jackiw-Teitelboim(JT)gravity coupled to primary fermion fields in asymptotically anti-de Sitter(AdS)spacetimes.We obtain a particular solution of the massless Dirac field outside the extremal black hole horizon and find the solution for the dilaton in JT gravity.As two dimensional JT gravity spacetime is conformally flat,we calculate the two point correlators of primary fermion fields under the Weyl transformations.The primary goal of this work is to present a standard technique,called resolvent,rather than using CFT methods.We redefine the fields in terms of the conformal factor as fermion fields and use the resolvent technique to derive the renormalized entanglement entropy for massless Dirac fields in JT gravity.

Holographic entanglement entropy with Power-Maxwell electrodynamics in higher dimensional AdS black hole spacetime

We investigate the behaviors of the scalar operator and holographic entanglement entropy in the metal/superconductor phase transition with Power-Maxwell electrodynamics in a higher dimensional background away from the probe limit.We observe that the larger parameters b and q make the condensation of the scalar operator more difficult,and the critical temperature decreases more slowly as the factors increase.In the belt geometry,the value of the entanglement entropy in the metal and superconductor phases is not only related to the the strength of the Power-Maxwell field but also to the width of the strip geometry.At the phase transition point,the discontinuous slope of entanglement entropy is universal for different model factors.It turns out that holographic entanglement entropy is a powerful tool to probe the properties of the phase transition in this holographic superconductor model.

Entanglement entropy of an annulus in holographic thermalization

The thermalization process of the holographic entanglement entropy(HEE)of an annular domain is investigated in the Vaidya-AdS geometry.We determine numerically the Hubeny-Rangamani-Takayanagi(HRT)surface,which may be a hemi-torus or two disks,depending on the ratio of the inner radius to the outer radius of the annulus.More importantly,for some fixed ratio of the two radii,the annulus undergoes a phase transition,or a double phase transition,during thermalization from a hemi-torus to a two-disk configuration,or vice versa.The occurrence of various phase transitions is determined by the ratio of the two radii of the annulus.The rate of entanglement growth is also investigated during the thermal quench.The local maximal rate of entanglement growth occurs in the region with a double phase transition.Finally,if the quench process is sufficiently slow,which may be controlled by the thickness of the null shell,the region with a double phase transition vanishes.

Scalar field in massive BTZ black hole and entanglement entropy

In this paper,we investigate the quantum scalar fields in a massive BTZ black hole background.We study the entropy of the system by evaluating the entanglement entropy using a discretized approach.Specifically,we fit the results with a log-modified formula of the black hole entropy,which is introduced by quantum correction.The coefficients of leading and sub-leading terms affected by the mass of graviton are numerically analyzed.

Relative entropy of entanglement of two-qubit 'X' states

Two closest single-qubit states could be diagonalised by the same unitary matrix, which helps to find the relative entropy of entanglement of a two-qubit ＇X＇ state. We formulate two binary equations for the relative entropy of entanglement and the corresponding closest separable state of a given two-qubit ＇X＇ state. This approach can be applied to get the relative entropy of entanglement of many widely-discussed two-qubit states, such as pure states, Werner states, and so on.

Symmetry and size effects on energy and entanglement of an exciton in coupled quantum dots

We study theoretically the essential properties of an exciton in vertically coupled Gaussian quantum dots in the presence of an external magnetic field. The ground state energy of a heavy-hole exciton is split into four energy levels due to the Zeeman effect. For the symmetrical system, the entanglement entropy of the exciton state can reach a value of 1. However, for a system with broken symmetry, it is close to zero. Our results are in good agreement with previous studies.

Amplifying and freezing of quantum coherence using weak measurement and quantum measurement reversal

We analyze universal conditions where the l_1 norm and relative entropy of coherence are amplified and frozen under identical bit-flip channels;that is,using pre-measurements（quantum weak measurements or quantum measurement reversals） on the systems before undergoing local bit-flip channels.With the option of quantum weak measurements or quantum measurement reversals,the measurement strength and the success probability are all determined by the initial state of the quantum system.

Entanglement wedge cross-section with Gauss-Bonnet corrections and thermal quench

The entanglement wedge cross section(EWCS) is numerically investigated statically and dynamically in a five-dimension Ad SVaidya spacetime with Gauss-Bonnet(GB) corrections, focusing on two identical rectangular strips on the boundary. In the static case, EWCS increases as the GB coupling constant α increases and disentangles at small separation between two strips for smaller α. For the dynamic case, such a monotonic relationship between EWCS and α holds but the two strips no longer disentangle monotonically as in the static case. In the early thermal quenching stage, the disentanglement occurs at smaller αwith larger separations. Two strips then disentangle at larger separation with larger α as time evolves. Our results indicate that the higher-order derivative corrections, like the entanglement measure in the dual boundary theory, also have nontrivial effects on the EWCS evolution.

Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT

We calculate the contributions of a general non-vacuum conformal family to R′enyi entropy in twodimensional conformal field theory（CFT）. The primary operator of the conformal family can be either non-chiral or chiral, and we denote its scaling dimension by ？. For the case of two short intervals on a complex plane, we expand the R′enyi mutual information by the cross ratio x to order x^（2△＋2）. For the case of one interval on a torus with low temperature, we expand the R′enyi entropy by q = exp（-2πβ/L）, with β being the inverse temperature and L being the spatial period, to order q^（△＋2）. To make the result meaningful, we require that the scaling dimension ？ cannot be too small. For two intervals on a complex plane we need △ 〉 1, and for one interval on a torus we need △ 〉 2.We work in the small Newton constant limit on the gravity side and so a large central charge limit on the CFT side,and find matches of gravity and CFT results.

Quantum entanglement in the Sachdev–Ye–Kitaev model and its generalizations

Entanglement is one of the most important concepts in quantum physics.We review recent progress in understanding the quantum entanglement in many-body systems using large-N solvable models:the Sachdev–Ye–Kitaev(SYK)model and its generalizations.We present the study of entanglement entropy in the original SYK model using three different approaches:the exact diagonalization,the eigenstate thermalization hypothesis,and the pathintegral representation.For coupled SYK models,the entanglement entropy shows linear growth and saturation at the thermal value.The saturation is related to replica wormholes in gravity.Finally,we consider the steady-state entanglement entropy of quantum many-body systems under repeated measurements.The traditional symmetry breaking in the enlarged replica space leads to the measurement-induced entanglement phase transition.

Entanglement for a two-parameter class of states in a high-dimension bipartite quantum system

The entanglement for a two-parameter class of states in a high-dimension (m n,n≥m≥3) bipartite quantum system is discussed.The negativity (N) and the relative entropy of entanglement (Er) are calculated,and the analytic expressions are obtained.Finally the relation between the negativity and the relative entropy of entanglement is discussed.The result demonstrates that all PPT states of the two-parameter class of states are separable,and all entangled states are NPT states.Different from the 2 ? n quantum system,the negativity for a two-parameter class of states in high dimension is not always greater than or equal to the relative entropy of entanglement.The more general relation expression is mN/2≥Er.

Hawking radiation and page curves of the black holes in thermal environment

As realistic objects in the Universe,the black holes are surrounded by complex environment.By taking the effect of thermal environment into account,we investigate the evaporation process and the time evolutions(page curves)of the entanglement entropies of Hawking radiation of various types of black holes.It is found that the black holes with the thermal environments evaporate slower than those without the environments due to the environmental contribution of the energy flux in addition to Hawking radiation.For Schwarzschild black hole and Reissner-Nordstr?m black hole in flat spaces,when the initial temperature of the black hole is higher than the environment temperature,the black holes evaporate completely and the Hawking radiation is eventually purified.For Schwarzschild-Ad S black hole,it will evaporate completely and the Hawking radiation is purified when the environment temperature is lower than the critical temperature.Otherwise,it will reach an equilibrium state with the environment and the radiation is maximally entangled with the black hole.Our results indicate that the final state of the black hole is determined by the environmental temperature and the temporal evolution and the speed of the information purification process characterized by the page curve of the Hawking radiation is also influenced by the thermal environment significantly.

Quantum phase transitions about parity breaking in matrix product systems

According to our scheme to construct quantum phase transitions （QPTs） in spin chain systems with matrix product ground states, we first successfully combine matrix product state （MPS） QPTs with spontaneous symmetry breaking. For a concrete model, we take into account a kind of MPS QPTs accompanied by spontaneous parity breaking, though for either side of the critical point the GS is typically unique, and show that the kind of MPS QPTs occur only in the thermodynamic limit and are accompanied by the appearance of singularities, diverging correlation length, vanishing energy gap and the entanglement entropy of a half-infinite chain not only staying finite but also whose first derivative discontinuous.

Quantum phase transitions in matrix product states of one-dimensional spin-(1/2) chains

For the matrix product system of a one-dimensional spin-1/2 chain, we present a new model of quantum2 phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases ｜Ψa 〉=｜1··· 1 representing all particles spin up and ｜Ψb 〉=｜0··· 0 representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where√ the two phases coexist equally, which is2 described by the so-called N-qubit maximally entangled GHZ state ｜Ψpt =√2/2（｜1··· 1 ＋｜0··· 0）. At the critical point,2the physical quantities including the entanglement are not discontinuous and the matrix product system has longrange correlation and N-qubit maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-qubit maximal entanglement.

Quantum phase transitions in matrix product states of one-dimensional spin-1 chains

We present a new model of quantum phase transitions in matrix product systems of one-dimensional spin-1 chains and study the phases coexistence phenomenon. We find that in the thermodynamic limit the proposed system has three different quantum phases and by adjusting the control parameters we are able to realize any phase, any two phases equal coexistence and the three phases equM coexistence. At every critical point the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N-spin maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of certain directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N-spin maximal entanglement.

Re-visiting supersymmetric Janus solutions: a perturbative construction

We construct holographic Janus solutions,which describe a conformal interface in the theory of M2-branes,in four-dimensional gauged supergravities using a perturbative method.In particular,we study three Einsteinscalar systems and their BPS equations,which are derived by Bobev,Pilch,and Warner(2014).The actions of our interest are all consistent truncations of D=11 supergravity,chosen to be invariant under SO(4)×SO(4),SU(3)×U(1)×U(1),and G2 symmetry subgroups of SO(8).The utility of our semi-analytic result is illustrated by the calculation of minimal area surface and the associated holographic entanglement entropy.

Quantum bit threads of MERA tensor network in large c limit

The Ryu-Takayanagi(RT)formula plays a large role in the current theory of gauge-gravity duality and emergent geometry phenomena.The recent reinterpretation of this formula in terms of a set of"bit threads"is an interesting effort in understanding holography.In this study,we investigate a quantum generalization of the"bit threads"based on a tensor network,with particular focus on the multi-scale entanglement renormalization ansatz(MERA).We demonstrate that,in the large c limit,isometries of the MERA can be regarded as"sources"(or"sinks")of the information flow,which extensively modifies the original picture of bit threads by introducing a new variableρ:density of the isometries.In this modified picture of information flow,the isometries can be viewed as generators of the flow.The strong subadditivity and related properties of the entanglement entropy are also obtained in this new picture.The large c limit implies that classical gravity can emerge from the information flow.