arXiv subjects

Suprakash Paul

Publications and source records attributed to Suprakash Paul.

3 recordsLinked to original sources

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.

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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.

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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.

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