We propose a holographic entanglement negativity conjecture involving the bulk geometry, for mixed states of adjacent intervals in $(1+1)$-dimensional dual conformal field theories through the $AdS/CFT$ correspondence. The holographic entanglement negativity is obtained from a specific algebraic sum of the geodesics anchored on respective intervals on the boundary which reduces to the holographic mutual information between them. Utilizing our conjecture we obtain the entanglement negativity of adjacent intervals in zero and finite temperature ($1+1$)-dimensional holographic conformal field theories dual to the bulk $AdS_3$ vacuum and the Euclidean BTZ black hole respectively. Our holographic conjecture exactly reproduces the conformal field theory results obtained through the replica technique, in the large central charge limit. We briefly elucidate the corresponding issue for the $AdS_{d+1}/CFT_d$ scenario.
We advance a holographic construction for the entanglement negativity of bipartite mixed state configurations of two disjoint intervals in $(1+1)$ dimensional conformal field theories ($CFT_{1+1}$) through the $AdS_3/CFT_2$ correspondence. Our construction constitutes the large central charge analysis of the entanglement negativity for mixed states under consideration and involves a specific algebraic sum of bulk space like geodesics anchored on appropriate intervals in the dual $CFT_{1+1}$. The construction is utilized to compute the holographic entanglement negativity for such mixed states i…
We advance a construction for the covariant holographic entanglement negativity for time dependent mixed states of disjoint intervals in $(1+1)$ dimensional conformal field theories ($CFT_{1+1}$) dual to bulk non static $AdS_3$ geometries. Application of our proposal to such mixed states in a $CFT_{1+1}$ dual to bulk non extremal and extremal rotating BTZ black holes exactly reproduces the replica technique results in the large central charge limit. We also investigate the time dependent holographic entanglement negativity for such mixed states in a $CFT_{1+1}$ dual to a bulk Vaidya-$AdS_3$ ge…
We establish our recently proposed holographic entanglement negativity conjecture for mixed states of adjacent subsystems in conformal field theories with concrete higher dimensional examples. In this context we compute the holographic entanglement negativity for mixed states of adjacent subsystems in $d$-dimensional conformal field theories dual to bulk $AdS_{d+1}$ vacuum and $AdS_{d+1}$-Schwarzschild black holes. These representative examples provide strong indication for the universality of our conjecture which affirms significant implications for diverse applications.
We propose a covariant holographic entanglement negativity constructionfor time-dependent mixed states of adjacent intervals in $(1+1)$-dimensional conformal field theories dual to non-static bulk $\mathrm{AdS_3}$ configurations. Our construction applied to $(1+1)$-dimensional conformal field theories with a conserved charge dual to non-extremal and extremal rotating BTZ black holes exactly reproduces the corresponding replica technique results, in the large central charge limit. We also utilize our conjecture to obtain the time-dependent holographic entanglement negativity for the mixed state…
We investigate the time evolution of entanglement negativity following a global quench for mixed state configurations of two disjoint and adjacent intervals in a ($1+1$)-dimensional conformal field theory ($CFT_{1+1}$) dual to the eternal black hole sliced in half by an end of the world brane, through the $AdS_3/CFT_2$ correspondence. To this end we obtain the time evolution of the holographic entanglement negativity for such mixed states from a dual bulk eternal black hole geometry and elucidate the relevant geodesic structures. The holographic entanglement negativity for such mixed states, f…
We advance a holographic conjecture for the entanglement negativity of bipartite quantum states in $(1+1)$-dimensional conformal field theories in the $AdS_3/CFT_2$ framework. Our conjecture exactly reproduces the replica technique results in the large central charge limit, for both the pure state described by the $CFT_{1+1}$ vacuum dual to bulk the pure $AdS_3$ geometry and the finite temperature mixed state dual to a Euclidean BTZ black hole respectively. The holographic entanglement negativity characterizes the distillable entanglement and reduces to a specific sum of holographic mutual inf…
We establish the large central charge behaviour of the entanglement negativity for a mixed state configuration of a single interval enclosed between two intervals in a holographic $CFT_{1+1}$. To this end we utilize the monodromy technique to elucidate the large central charge limit of a four point twist correlator which characterizes the negativity of the mixed state configuration. Subsequently we analyze the large central charge limit of the six point twist correlator which reduces to the above four point correlator in a specific limit. The results provide a strong consistency check for our …
We present a derivation of the holographic dual of logarithmic negativity in AdS$_3$/CFT$_2$ that was recently conjectured in [Phys. Rev. D 99, 106014 (2019)]. This is given by the area of an extremal cosmic brane that terminates on the boundary of the entanglement wedge. The derivation consists of relating the recently introduced Rényi reflected entropy to the logarithmic negativity in holographic conformal field theories. Furthermore, we clarify previously mysterious aspects of negativity at large central charge seen in conformal blocks and comment on generalizations to generic dimensions, d…
We study conformal twist field four-point functions on a $\mathbb Z_N$ orbifold. We examine in detail the case $N=3$ and analyze theories obtained by replicated $N$-times a minimal model with central charge $c<1$. A fastly convergent expansion of the twist field correlation function in terms of sphere conformal blocks with central charge $Nc$ is obtained by exploiting covering map techniques. We discuss extensive applications of the formalism to the entanglement of two disjoint intervals in CFT, in particular we propose a conformal block expansion for the partially transposed reduced density m…
We investigate the extension of a holographic construction for the entanglement negativity of two disjoint subsystems in proximity to $CFT_d$s with a conserved charge dual to bulk $AdS_{d+1}$ geometries. The construction involves a specific algebraic sum of the areas of bulk co-dimension two static minimal surfaces homologous to certain appropriate combinations of the subsystems in question. In this connection we compute the holographic entanglement negativity for two disjoint subsystems in proximity, with long rectangular strip geometries in $CFT_d$s dual to bulk non extremal and extremal RN-…
We study the application of our recent holographic entanglement negativity conjecture for mixed states of adjacent subsystems in conformal field theories with a conserved charge. In this context we obtain the holographic entanglement negativity for zero and finite temperature mixed state configurations in $d$-dimensional conformal field theories dual to bulk extremal and non extremal charged $AdS_{d+1}$ black holes. Our results conform to quantum information theory expectations and constitute significant consistency checks for our conjecture.
Both reflected entropy and entanglement negativity provide valid measures of entanglement between subsystems of a mixed state. For general 2D eternal black holes coupled with CFT matters in large $c$ limit, we perform the replica-trick computation and find that both effective Renyi reflected entropy and effective entanglement negativity can be expressed in terms of the combination of modified backreacting cosmic branes in $\mathrm{AdS}_3$ bulk. We then develop a holographic scheme to calculate effective reflected entropy and entanglement negativity for general 2D eternal black holes coupled wi…
We establish a construction for the entanglement wedge in asymptotically flat bulk geometries for subsystems in dual $(1+1)$-dimensional Galilean conformal field theories in the context of flat space holography. In this connection we propose a definition for the bulk entanglement wedge cross section for bipartite states of such dual non relativistic conformal field theories. Utilizing our construction for the entanglement wedge cross section we compute the entanglement negativity for such bipartite states through the generalization of an earlier proposal, in the context of the usual $AdS/CFT$ …
We investigate the time evolution of reflected entropy and entanglement negativity for mixed state configurations involving two adjacent and disjoint intervals in the radiation flux of moving mirrors by utilizing the $AdS/BCFT$ duality. These measures are computed for the required mixed state configurations by using the respective replica techniques in the large central charge limit of the $BCFT_{1+1}$. We demonstrate that the results obtained exactly agree with the corresponding holographic computations in the dual bulk $AdS_3$ geometry with an end of the world brane. In this context, the ana…
We consider the logarithmic negativity and related quantities of time evolution operators. We study free fermion, compact boson, and holographic conformal field theories (CFTs) as well as numerical simulations of random unitary circuits and integrable and chaotic spin chains. The holographic behavior strongly deviates from known non-holographic CFT results and displays clear signatures of maximal scrambling. Intriguingly, the random unitary circuits display nearly identical behavior to the holographic channels. Generically, we find the "line-tension picture" to effectively capture the entangle…
We investigate the ground state of a (1+1)-dimensional conformal field theory built with $M$ species of massless free Dirac fermions coupled at one boundary point via a conformal junction/interface. Each CFT represents a wire of finite length $L$. We develop a systematic strategy to compute the Rényi entropies for a generic bipartition between the wires and the entanglement negativity between two non-complementary sets of wires. Both these entanglement measures turn out to grow logarithmically with $L$ with an exactly calculated universal prefactor depending on the details of the junction and …
In this paper, we consider the computation of charged moments of the reduced density matrix of two disjoint intervals in the $1+1$ dimensional free compactified boson conformal field theory (CFT) by studying the four-point function of the fluxed twist fields. We obtained the exact scaling function of this four-point function and discussed its decompactification limit. This scaling function was used to obtain the charged moments of the partial transpose which we refer as charged Rényi negativity. These charged moments and the charged moments of the partial transpose are essential for the proble…
We investigate quantum entanglement in a non-relativistic critical system by calculating the logarithmic negativity of a class of mixed states in the quantum Lifshitz model in one and two spatial dimensions. In 1+1 dimensions we employ a correlator approach to obtain analytic results for both open and periodic biharmonic chains. In 2+1 dimensions we use a replica method and consider spherical and toroidal spatial manifolds. In all cases, the universal finite part of the logarithmic negativity vanishes for mixed states defined on two disjoint components. For mixed states defined on adjacent com…
In this thesis we apply techniques from quantum information theory to study quantum gravity within the framework of the anti-de Sitter / conformal field theory correspondence (AdS/CFT). Through AdS/CFT, progress has been made in understanding the structure of entanglement in quantum field theories, and in how gravitational physics can emerge from these structures. However, this understanding is far from complete and will require the development of new tools to quantify correlations in CFT. This thesis presents refinements of a duality between operator product expansion (OPE) blocks in the CFT,…
We investigate the time evolution of odd entanglement entropy (OEE) and logarithmic negativity (LN) for the thermofield double (TFD) states in free scalar quantum field theories using the covariance matrix approach. To have mixed states, we choose non-complementary subsystems, either adjacent or disjoint intervals on each side of the TFD. We find that the time evolution pattern of OEE is a linear growth followed by saturation. On a circular lattice, for longer times the finite size effect demonstrates itself as oscillatory behavior. In the limit of vanishing mass, for a subsystem containing a …
We calculate logarithmic negativity, a quantum entanglement measure for mixed quantum states, in quantum error-correcting codes and find it to equal the minimal cross sectional area of the entanglement wedge in holographic codes with a quantum correction term equal to the logarithmic negativity between the bulk degrees of freedom on either side of the entanglement wedge cross section. This leads us to conjecture a holographic dual for logarithmic negativity that is related to the area of a cosmic brane with tension in the entanglement wedge plus a quantum correction term. This is closely relat…
We investigate whether Swampland constraints on the low-energy dynamics of weakly coupled, moduli-stabilised string vacua in AdS can be related to inconsistencies of their putative holographic duals or, more generally, recast in terms of CFT data. We find that various swampland consistency constraints are equivalent to a negativity condition on the sign of certain mixed anomalous dimensions. This condition is similar to well-established CFT positivity bounds arising from causality and unitarity, but not known to hold in general. The studied scenarios include LVS, KKLT, and both perturbative an…
Defects in two-dimensional conformal field theories (CFTs) contain signatures of their characteristics. In this work, we compute the entanglement entropy (EE) and the entanglement negativity (EN) of subsystems in the presence of energy and duality defects in the Ising CFT using the density matrix renormalization group (DMRG) technique. We show that the EE for the duality defect exhibits fundamentally different characteristics compared to the energy defect due to the existence of localized and delocalized zero energy modes. Of special interest is the nontrivial `finite-size correction' in the E…
A basic diagnostic of entanglement in mixed quantum states is known as the positive partial transpose (PT) criterion. Such criterion is based on the observation that the spectrum of the partially transposed density matrix of an entangled state contains negative eigenvalues, in turn, used to define an entanglement measure called the logarithmic negativity. Despite the great success of logarithmic negativity in characterizing bosonic many-body systems, generalizing the operation of PT to fermionic systems remained a technical challenge until recently when a more natural definition of PT for ferm…
Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
我们提出了一个家庭的AdS/CFT对应的一种新的构造的量子纠错码的张量网络结构的基础上，完全可解的玩具模型。我们的构建块是一种特殊类型的张量与最大的纠缠沿任何bipartition，这引起了一个等距从散装希尔伯特空间的边界希尔伯特空间。整个张量网络是量子纠错码的编码器，其中体自由度和边界自由度可以分别被标识为逻辑自由度和物理自由度。这些模型捕捉到了AdS/CFT对应中纠缠的关键特征;特别是，Ryu-Takayanagi公式和三方信息的负性在许多情况下都完全遵守。体逻辑算子可以在多个边界区域上表示，这模拟了从体算子重构边界算子的Rindler-wedge重构，明确实现了Almheiri等人最近提出的AdS/CFT的量子纠错特性. al in arXiv：1411.7041.
Bipartite entanglement entropy of a segment with the length $l$ in $1+1$ dimensional conformal field theories (CFT) follows the formula $S=\frac{c}{3}\ln l+γ$, where $c$ is the central charge of the CFT and $γ$ is a cut-off dependent constant which diverges in the absence of an ultraviolet cutoff. According to this formula, systems with larger central charges have {\it{more}} bipartite entanglement entropy. Using quantum Fisher information (QFI), we argue that systems with bigger central charges not only have larger bipartite entanglement entropy but also have more multipartite entanglement co…
