arXiv subjects

Qi-Feng Wu

Publications and source records attributed to Qi-Feng Wu.

4 recordsLinked to original sources

arXiv2026

Filtering out Erratic Observables: Wormholes from Gauging Nonlocal Symmetries

The wormhole contribution to the gravitational path integral may be interpreted as smooth remnant of correlations among the erratic large-$N$ behaviors of dual CFTs. In this work, we investigate this idea in (2+1)-dimensional gravity. We show that one-sided boundary gravitons are intrinsically incomplete in the sense that the associated observable algebra has a nontrivial center regardless of choices of boundary conditions. Based on asymptotic symmetries, we bootstrap a general Poisson bracket to construct completions of the boundary gravitons. In the simplest completion, the commutant of the boundary graviton observable algebra is given by an observable algebra of monodromy data which we interpret as an effective description of one-sided black holes. We show that, to describe Lorentzian multi-boundary wormholes, only the monodromy data with a positivity restriction is needed. The positivity restriction results in emergent erratic large-$N$ behaviors for some observables. We filter out the erratic observables by restricting to a subspace on which they act trivially. The monodromy observables generate nonlocal symmetries lack of corresponding local currents. We show that gauging the nonlocal symmetries is equivalent to filtering out the erratic observables. For one CFT, gauging the nonlocal symmetries at the quantum level removes all black hole states. Filtering the partition function of CFTs leads to an apparent ensemble averaging. For two CFTs, a Hilbert subspace describing wormholes survives after gauging global part of the nonlocal symmetries. The filtered partition function of the two CFTs is an ensemble average over quantum gates entangling the monodromy degrees of freedom of the two CFTs. The correlation between the erratic observables of the two CFTs is preserved, which contributes to the filtered partition function as a wormhole term.

hep-th↗

arXiv2026

Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes

One approach to analyzing entanglement in a gauge theory is embedding it into a factorized theory with edge modes on the entangling boundary. For topological quantum field theories (TQFT), this naturally leads to factorizing a TQFT by adding local edge modes associated with the corresponding CFT. In this work, we instead construct a minimal set of edge modes compatible with the topological invariance of Chern-Simons theory. This leads us to propose a minimal factorization map. These minimal edge modes can be interpreted as the degrees of freedom of a particle on a quantum group. Of particular interest is three-dimensional gravity as a Chern-Simons theory with gauge group SL$(2,\mathbb{R}) \times$ SL$(2,\mathbb{R})$. Our minimal factorization proposal uniquely gives rise to quantum group edge modes factorizing the bulk state space of 3d gravity. This agrees with earlier proposals that relate the Bekenstein-Hawking entropy in 3d gravity to topological entanglement entropy.

hep-th↗

arXiv2023

Entanglement Classification via Operator Size

In this work, multipartite entanglement is classified by polynomials. I show that the operator size is closely related to the entanglement structure. Given a generic quantum state, I define a series of subspaces generated by operators of different sizes acting on it. The information about the entanglement is encoded into these subspaces. With the dimension of these subspaces as coefficients, I define a polynomial which I call the entanglement polynomial. The entanglement polynomial induces a homomorphism from quantum states to polynomials. It implies that we can characterize and find the building blocks of entanglement by polynomial factorization. Two states share the same entanglement polynomial if they are equivalent under the stochastic local operations and classical communication. To calculate the entanglement polynomial practically, I construct a series of states, called renormalized states, whose ranks are related to the coefficients of the entanglement polynomial.

quant-ph↗

arXiv2022

Sectional curvatures distribution of complexity geometry

In the geometric approach to define complexity, operator complexity is defined as the distance on the operator space. In this paper, based on the analogy with the circuit complexity, the operator size is adopted as the metric of the operator space where path length is the complexity. The typical sectional curvatures of this complexity geometry are positive. It is further proved that the typical sectional curvatures are always positive if the metric is an arbitrary function of operator size. While complexity geometry is usually expected to be defined on negatively curved manifolds. By analyzing the sectional curvatures distribution for $N$-qubit system, it is shown that surfaces generated by Hamiltonians of size smaller than the typical size can have negative curvatures. In the large $N$ limit, the form of complexity metric is uniquely constrained up to constant corrections if we require sectional curvatures are of order $1/N^2$ . With the knowledge of states, the operator size should be modified due to the redundant action of operators, thus is generalized to be state-dependent. Then we use this state-dependent operator size as the metric of the Hilbert space to define state complexity. It can also be shown that in the Hilbert space, 2-surfaces generated by operators of size much smaller than the typical size acting on typical states also have negative curvatures.

hep-th↗