arXiv subjects

Onkar Parrikar

Publications and source records attributed to Onkar Parrikar.

At least 19 recordsLinked to original sources

arXiv2026

A semiclassical Hilbert space for random matrix theory

We study the one-sided time evolution of thermofield double (TFD) states in random matrix theory, where the Hamiltonian is taken to be a $D\times D$ random matrix drawn from a unitarily invariant emsemble of Hermitian matrices. We argue that the Krylov basis with the maximally entangled state taken as the initial vector gives a semiclassical Hilbert space description of these TFD states in random matrix theory at any $O(1)$ temperature and time in the $D\to \infty$ limit, very analogous to the ``chord Hilbert space'' construction in the double-scaled SYK (DSSYK) model. We study this semiclassical description in detail for ensembles where the spectral density in the $D\to \infty$ limit is even, compactly supported on an interval and has square root edges. With a few more conditions on the analytic structure of the spectral density, we observe that the semiclassical Hamiltonian has the same asymptotic behavior at large Krylov depth as that of DSSYK, with the corresponding parameter $\mathfrak{q}=e^{-\lambda}$ being related to the location of the nearest zero of the spectral density away from the spectral cut. Furthermore, in a large class of models corresponding to ultraviolet deformations of the DSSYK spectral density, i.e., where the spectrum in the UV is modified while leaving the near-edge behavior unchanged, we show that the semiclassical effective Hamiltonian in the Krylov basis reduces to the Liouville Hamiltonian of JT gravity in a low-energy, continuum limit. This suggests that our semiclassical Hilbert space should be interpreted as the bulk Hilbert space of a dual gravity description.

hep-th↗

arXiv2026

Stabilizer complexity and the Python's lunch

In this note, we study the stabilizer complexity of the reduced density matrix corresponding to one side of a partially entangled thermal (PET) state with fixed energy boundary conditions in a holographic CFT. In particular, we study Wigner negativity, an operationally meaningful magic monotone which can be interpreted as the complexity of classically simulating any quantum circuit preparation of the reduced state on the subregion. Using assumptions on the pseudorandomness of the CFT spectrum and the heavy operator insertion, we observe that the Wigner negativity of the PET state relative to the microcanonical density matrix at the given energy is given by $\exp\left[\frac{1}{8G_N}(A_{\text{out}} - A_{\text{min}})\right]$, where $A_{\text{out}}$ is the area of the outer extremal surface, while $A_{\text{min}}$ is the area of the minimal extremal surface. Thus, the stabilizer complexity of the reduced density matrix on the boundary subregion is $O(1)$ in the absence of a python's lunch, but gets exponentially enhanced in the presence of a python's lunch in the bulk geometry.

hep-th↗

arXiv2026

Wigner negativity in Krylov space and emergent semiclassicality

We propose that the Krylov basis gives a semiclassical representation of dynamics in general large-$N$, complex, many-body systems. As a probe of this semiclassicality, we study the growth of Wigner negativity -- a measure of the complexity of classical simulation -- under time evolution in Krylov space in several solvable models. We begin with 2d CFTs, initially in either the vacuum or the thermofield double state on a line excited by a primary operator. In both cases, Wigner negativity remains an $O(1)$ constant and does not grow at late times, indicating approximately classical dynamics in the Krylov basis. We then study random matrix theory with the maximally entangled state between two copies as the initial state. For general one-cut matrix models, we argue that Wigner negativity in the Krylov basis grows as $t^{1/2}$ at large $O(1)$ times but does not scale with the Hilbert space dimension, thus indicating semiclassical dynamics in Krylov space. Finally, in the double-scaled SYK model, we find an approximately classical phase (constant negativity) at early times and a semiclassical phase ($t^{1/2}$ growth) at late times. In all these examples, Wigner negativity either remains constant or grows slowly, demonstrating emergent semiclassicality of dynamics in Krylov space.

hep-th↗

arXiv2026

Fortuity and Complexity in a Simple Quark Model

We observe and elaborate on a structural similarity between the categorization of monotone and fortuitous BPS operators in supersymmetric theories and gauge invariant quark operators in $SU(N_c)$ QCD. Our designation of fortuity does not rely on supersymmetry and instead uses the BRST cohomology. We argue that within this designation, baryon states are fortuitous while meson states are monotone. We illustrate that in the Veneziano limit of large number of flavors and colors, this designation displays features resembling the fortuitous vs. monotone categorization of BPS operators, e.g., an exponential vs. polynomial dichotomy in the counting of operators. We explore these ideas explicitly in a toy qubit model of quarks. We further investigate the stabilizer R\'enyi entropy of meson and baryon states as a proxy for the complexity of classical simulation for these states. We show that all mesons display power law complexity and present evidence that typical baryons display super-exponential complexity in the Veneziano limit.

hep-th↗

arXiv2025

Modular Witten Diagrams and Quantum Extremality

We study entanglement entropy for ball-shaped regions in excited states of holographic conformal field theories. The excited states are prepared by the Euclidean path integral in the CFT with a source turned on for some double-trace operator, with a small, $O(1)$ amplitude $\lambda$. On the gravity side, the double-trace operator deforms the bulk geometry as well as the entanglement structure of the state of bulk matter fields. By the quantum extremal surface formula, this leads to a deformation of the shape of the entanglement wedge, an effect which becomes manifest in the entanglement entropy at $O(\lambda^2 G_N)$. On the CFT side, we explicitly calculate the entanglement entropy perturbatively in the source amplitude to $O(\lambda^2)$, in terms of modular-flowed correlation functions of double-trace operators. We then evaluate these modular-flowed correlation functions using Witten diagrams. This calculation involves a Schwinger-Keldysh contour ordering prescription in the bulk, which we motivate using analytic continuation from Euclidean replica correlators. Focusing on a particular graviton-exchange diagram, we rewrite it in a form where it manifestly reproduces the canonical energy term present in the quantum Ryu-Takayanagi formula, including the shape deformation of the entanglement wedge due to backreaction and quantum effects.

hep-th↗

arXiv2025

Covariant phase space and the semi-classical Einstein equation

The covariant phase space formalism in general relativity is a covariant method for constructing the symplectic two-form, Hamiltonian and other conserved charges on the phase space of solutions to the Einstein equation with classical matter. In this note, we consider a generalization of this formalism to the semi-classical Einstein equation coupled to quantum matter. Given a family of solutions in semi-classical gravity, we define the semi-classical symplectic two-form -- a natural generalization of the classical sympelctic two-form -- as the sum of the gravitational symplectic form and the Berry curvature associated to the quantum state of matter. We show that the semi-classical symplectic two-form is independent of the Cauchy slice, and satisfies the quantum generalization of the classical Hollands-Iyer-Wald identity. For small perturbations, we also extend our discussion to gauge-invariantly defined subregions of spacetime, where the quantum contribution is replaced by the Berry curvature of certain special purifications involving the Connes cocycle. In the AdS/CFT context, the semi-classical symplectic form defined here is naturally dual to the Berry curvature in the boundary CFT.

hep-th↗

arXiv2025

On the stabilizer complexity of Hawking radiation

We study the complexity of Hawking radiation for an evaporating black hole from the perspective of the stabilizer theory of quantum computation. Specifically, we calculate Wigner negativity -- a magic monotone which can be interpreted as a measure of the stabilizer complexity, or equivalently, the complexity of classical simulation -- in various toy models for evaporating black holes. We first calculate the Wigner negativity of Hawking radiation in the PSSY model directly using the gravitational path integral, and show that the negativity is $O(1)$ before the Page transition, but becomes exponentially large past the Page transition. We also derive a universal, information theoretic formula for the negativity which interpolates between the two extremes. We then study the Wigner negativity of radiation in a dynamical model of black hole evaporation. In this case, the negativity shows a sharp spike at early times resulting from the coupling between the black hole and the radiation system, but at late times when the system settles down, we find that the negativity satisfies the same universal formula as in the PSSY model. Finally, we also propose a geometric formula for Wigner negativity in general holographic states using intuition from fixed area states and random tensor networks, and argue that a python's lunch in the entanglement wedge implies a stabilizer complexity which is exponentially large in $\frac{1}{8G_N}$ times the difference between the areas corresponding to the outermost and minimal extremal surfaces.

hep-th↗

arXiv2025

Entanglement spreading and emergent locality in Brownian SYK chains

The Ryu-Takayanagi (RT) formula and its interpretation in terms of quantum error correction (QEC) implies an emergent locality for the spread of quantum information in holographic CFTs, where information injected at a point in the boundary theory spreads within a sharp light-cone corresponding to the butterfly velocity. This emergent locality is a necessary condition for the existence of a geometric bulk dual with an RT-like formula for entanglement entropy. In this paper, we use tools from QEC to study the spread of quantum information and the emergence of a sharp light-cone in an analytically tractable model of chaotic dynamics, namely a one-dimensional Brownian SYK chain. We start with an infinite temperature state in this model and inject a qudit at time $t=0$ at some point $p$ on the chain. We then explicitly calculate the amount of information of the qudit contained in an interval of length $2\ell$ (centered around $p$) at some later time $t=T$. We find that at strong coupling, this quantity shows a sharp transition as a function of $\ell$ from near zero to near maximal correlation. The transition occurs at $\ell \sim v_B T$, with $v_B$ being the butterfly velocity. Underlying the emergence of this sharp light-cone is a non-linear generalization of the diffusion equation called the FKPP equation, which admits sharp domain wall solutions at late times and strong coupling. These domain wall solutions can be understood on physical grounds from properties of operator growth in chaotic systems.

hep-th↗

arXiv2025

Wigner negativity, random matrices and gravity

Given a choice of an ordered, orthonormal basis for a $D$-dimensional Hilbert space, one can define a discrete version of the Wigner function -- a quasi-probability distribution which represents any quantum state as a real, normalized function on a discrete phase space. The Wigner function, in general, takes on negative values, and the amount of negativity in the Wigner function gives an operationally meaningful measure of the complexity of simulating the quantum state on a classical computer. Further, Wigner negativity also gives a lower bound on an entropic measure of spread complexity. In this paper, we study the growth of Wigner negativity for a generic initial state under time evolution with chaotic Hamiltonians. In arXiv:2402.13694, a perturbative argument was given to show that the Krylov basis minimizes the early time growth of Wigner negativity in the large-$D$ limit. Using tools from random matrix theory, here we show that for a generic choice of basis, the Wigner negativity for a classical initial state becomes exponentially large in an $O(1)$ amount of time evolution. On the other hand, we show that in the Krylov basis the negativity grows at most as a power law, and becomes exponentially large only at exponential times. We take this as evidence that the Krylov basis is ideally suited for a dual, semi-classical effective description of chaotic quantum dynamics for large-$D$ at sub-exponential times. For the Gaussian unitary ensemble, this effective description is the $q\to 0$ limit of $q$-deformed JT gravity.

hep-th↗

arXiv2025

York time in JT gravity

The notion of time in general relativity must arise from an internal clock, i.e., a degree of freedom in the gravitational theory internal to the system that can serve the role of a physical clock. One such internal notion of time is the York time, corresponding to constant extrinsic curvature slicing of spacetime. We study the Hartle-Hawking wavefunction of asymptotically $AdS_2$ JT gravity as a function of York time. Using both canonical quantization and the JT gravity path integral, we explicitly calculate this wavefunction and show that it satisfies a Schrodinger equation with respect to York time. We find the corresponding York Hamiltonian, which turns out to be manifestly Hermitian. Our analysis cleanly avoids operator ordering ambiguities. The dependence of the wavefunction on York time should be thought of as emerging from a unitary transformation of the gravitational length basis states, and not from a physical time evolution of the state in the dual boundary theory.

hep-th↗

arXiv2024

Relational bulk reconstruction from modular flow

The entanglement wedge reconstruction paradigm in AdS/CFT states that for a bulk qudit within the entanglement wedge of a boundary subregion $\bar{A}$, operators acting on the bulk qudit can be reconstructed as CFT operators on $\bar{A}$. This naturally fits within the framework of quantum error correction, with the CFT states containing the bulk qudit forming a code protected against the erasure of the boundary subregion $A$. In this paper, we set up and study a framework for relational bulk reconstruction in holography: given two code subspaces both protected against erasure of the boundary region $A$, the goal is to relate the operator reconstructions between the two spaces. To accomplish this, we assume that the two code subspaces are smoothly connected by a one-parameter family of codes all protected against the erasure of $A$, and that the maximally-entangled states on these codes are all full-rank. We argue that such code subspaces can naturally be constructed in holography in a "measurement-based" setting. In this setting, we derive a flow equation for the operator reconstruction of a fixed code subspace operator using modular theory which can, in principle, be integrated to relate the reconstructed operators all along the flow. We observe a striking resemblance between our formulas for relational bulk reconstruction and the infinite-time limit of Connes cocycle flow, and take some steps towards making this connection more rigorous. We also provide alternative derivations of our reconstruction formulas in terms of a canonical reconstruction map we call the modular reflection operator.

hep-th↗

arXiv2024

Complexity Growth and the Krylov-Wigner function

For any state in a $D$-dimensional Hilbert space with a choice of basis, one can define a discrete version of the Wigner function -- a quasi-probability distribution which represents the state on a discrete phase space. The Wigner function can, in general, take on negative values, and the amount of negativity in the Wigner function has an operational meaning as a resource for quantum computation. In this note, we study the growth of Wigner negativity for a generic initial state under time evolution with chaotic Hamiltonians. We introduce the Krylov-Wigner function, i.e., the Wigner function defined with respect to the Krylov basis (with appropriate phases), and show that this choice of basis minimizes the early time growth of Wigner negativity in the large $D$ limit. We take this as evidence that the Krylov basis (with appropriate phases) is ideally suited for a dual, semi-classical description of chaotic quantum dynamics at large $D$. We also numerically study the time evolution of the Krylov-Wigner function and its negativity in random matrix theory for an initial pure state. We observe that the negativity rises gradually for a time of $O(D)$ and then saturates close to its upper bound of $\sqrt{D}$.

hep-th↗

arXiv2023

The S-matrix and boundary correlators in flat space

We consider the path integral of a quantum field theory in Minkowski spacetime with fixed boundary values (for the elementary fields) on asymptotic boundaries. We define and study the corresponding boundary correlation functions obtained by taking derivatives of this path integral with respect to the boundary values. The S-matrix of the QFT can be extracted directly from these boundary correlation functions after smearing. We interpret this relation in terms of coherent state quantization and derive the constraints on the path-integral as a function of boundary values that follow from the unitarity of the S-matrix. We then study the locality structure of boundary correlation functions. In the massive case, we find that the boundary correlation functions for generic locations of boundary points are dominated by a saddle point which has the interpretation of particles scattering in a small elevator in the bulk, where the location of the elevator is determined dynamically, and the S-matrix can be recovered after stripping off some dynamically determined but non-local ``renormalization'' factors. In the massless case, we find that while the boundary correlation functions are generically analytic as a function on the whole manifold of locations of boundary points, they have special singularities on a sub-manifold, points on which correspond to light-like scattering in the bulk. We completely characterize this singular scattering sub-manifold, and find that the corresponding residues of the boundary correlations at these singularities are precisely given by S-matrices. This analysis parallels the analysis of bulk-point singularities in AdS/CFT and generalizes it to the case of multi-bulk point singularities.

hep-th↗

arXiv2023

Canonical Purification and the Quantum Extremal Shock

We study the canonical purification (with respect to one of the parties) of pure, bi-partite states obtained by turning on sources in the Euclidean path integral. In holographic conformal field theories, the Lorentzian bulk dual of the canonical purification consists of the corresponding entanglement wedge glued to its CPT image at the quantum extremal surface. However, the mismatch in the classical expansions at the QES due to quantum corrections needs to be supported by a shock in the bulk matter stress tensor in order for the bulk to satisfy Einstein's equations. Working perturbatively to first order in double-trace sources around the thermofield double state, we demonstrate that the state of the bulk matter in the dual to the canonically purified boundary CFT state precisely has this quantum extremal shock in the bulk stress tensor. We interpret our results as the emergence of gravitational physics from the CFT entanglement structure in a context where bulk quantum corrections are important.

hep-th↗

arXiv2023

Quantum Error Correction from Complexity in Brownian SYK

We study the robustness of quantum error correction in a one-parameter ensemble of codes generated by the Brownian SYK model, where the parameter quantifies the encoding complexity. The robustness of error correction by a quantum code is upper bounded by the "mutual purity" of a certain entangled state between the code subspace and environment in the isometric extension of the error channel, where the mutual purity of a density matrix $ρ_{AB}$ is the difference $\mathcal{F}_ρ(A:B) \equiv \mathrm{Tr}\;ρ_{AB}^2 - \mathrm{Tr}\;ρ_A^2\;\mathrm{Tr}\;ρ_B^2$. We show that when the encoding complexity is small, the mutual purity is $O(1)$ for the erasure of a small number of qubits (i.e., the encoding is fragile). However, this quantity decays exponentially, becoming $O(1/N)$ for $O(\log N)$ encoding complexity. Further, at polynomial encoding complexity, the mutual purity saturates to a plateau of $O(e^{-N})$. We also find a hierarchy of complexity scales associated to a tower of subleading contributions to the mutual purity that quantitatively, but not qualitatively, adjust our error correction bound as encoding complexity increases. In the AdS/CFT context, our results suggest that any portion of the entanglement wedge of a general boundary subregion $A$ with sufficiently high encoding complexity is robustly protected against low-rank errors acting on $A$ with no prior access to the encoding map. From the bulk point of view, we expect such bulk degrees of freedom to be causally inaccessible from the region $A$ despite being encoded in it.

hep-th↗

arXiv2022

Quantum Error Correction in the Black Hole Interior

We study the quantum error correction properties of the black hole interior in a toy model for an evaporating black hole: Jackiw-Teitelboim gravity entangled with a non-gravitational bath. After the Page time, the black hole interior degrees of freedom in this system are encoded in the bath Hilbert space. We use the gravitational path integral to show that the interior density matrix is correctable against the action of quantum operations on the bath which (i) do not have prior access to details of the black hole microstates, and (ii) do not have a large, negative coherent information with respect to the maximally mixed state on the bath, with the lower bound controlled by the black hole entropy and code subspace dimension. Thus, the encoding of the black hole interior in the radiation is robust against generic, low-rank quantum operations. For erasure errors, gravity comes within an $O(1)$ distance of saturating the Singleton bound on the tolerance of error correcting codes. For typical errors in the bath to corrupt the interior, they must have a rank that is a large multiple of the bath Hilbert space dimension, with the precise coefficient set by the black hole entropy and code subspace dimension.

hep-th↗

arXiv2021

The Markov gap for geometric reflected entropy

The reflected entropy $S_R(A:B)$ of a density matrix $ρ_{AB}$ is a bipartite correlation measure lower-bounded by the quantum mutual information $I(A:B)$. In holographic states satisfying the quantum extremal surface formula, where the reflected entropy is related to the area of the entanglement wedge cross-section, there is often an order-$N^2$ gap between $S_R$ and $I$. We provide an information-theoretic interpretation of this gap by observing that $S_R - I$ is related to the fidelity of a particular Markov recovery problem that is impossible in any state whose entanglement wedge cross-section has a nonempty boundary; for this reason, we call the quantity $S_R - I$ the Markov gap. We then prove that for time-symmetric states in pure AdS$_3$ gravity, the Markov gap is universally lower bounded by $\log(2) \ell_{\text{AdS}}/2 G_N$ times the number of endpoints of the cross-section. We provide evidence that this lower bound continues to hold in the presence of bulk matter, and comment on how it might generalize above three bulk dimensions. Finally, we explore the Markov recovery problem controlling $S_R - I$ using fixed area states. This analysis involves deriving a formula for the quantum fidelity -- in fact, for all the sandwiched Rényi relative entropies -- between fixed area states with one versus two fixed areas, which may be of independent interest. We discuss, throughout the paper, connections to the general theory of multipartite entanglement in holography.

hep-th↗

arXiv2021

Islands with Gravitating Baths: Towards ER = EPR

We study the Page curve and the island rule for black holes evaporating into gravitating baths, with an eye towards establishing a connection with the ER=EPR proposal. We consider several models of two entangled 2d black holes in Jackiw-Teitelboim (JT) gravity with negative cosmological constant. The first, "doubled PSSY," model is one in which the black holes have end-of-the-world (ETW) branes with a flavour degree of freedom. We study highly entangled states of this flavour degree of freedom and find an entanglement-induced Hawking-Page-like transition from a geometry with two disconnected black holes to one with a pair of black holes connected by a wormhole, thus realising the ER = EPR proposal. The second model is a dynamical one in which the ETW branes do not have internal degrees of freedom but the JT gravity is coupled to a 2d CFT, and we entangle the black holes by coupling the two CFTs at the $AdS$ boundary and evolving for a long time. We study the entanglement entropy between the two black holes and find that the story is substantially similar to that with a non-gravitating thermal bath. In the third model, we couple the two ends of a two-sided eternal black hole and evolve for a long time. Finally, we discuss the possibility of a Hawking-Page-like transition induced by real-time evolution that realises the ER = EPR proposal in this dynamical setting.

hep-th↗