arXiv subjects

Rana Zibakhsh

Publications and source records attributed to Rana Zibakhsh.

5 recordsLinked to original sources

arXiv2026

Algebras for generalized entanglement wedges

In asymptotically AdS spacetimes, the mathematical structure of the set of entanglement wedges reflects the algebraic structure of the underlying holographic description. For more general spacetimes, Bousso and Penington (BP) have recently proposed a generalization of entanglement wedges sharing many of the same properties as usual entanglement wedges. In this paper, we explore the hypothesis that each generalized entanglement wedge can be associated with an algebra in the (generally unknown) fundamental description (in a semiclassical limit). We postulate features of the map from entanglement wedges to algebras that provide a natural algebraic interpretation for some of the basic mathematical properties of the set of entanglement wedges. Quantitatively, we suggest a possible generalization of the Ryu-Takayanagi formula that associates the gravitational entropy of a generalized entanglement wedge with an entropic quantity for the associated algebra. Through this assignment, inclusion monotonicity and strong-subadditivity properties shown by BP for generalized entanglement wedges would follow from various inequalities satisfied by algebraic entropies. We include a detailed appendix reviewing relevant algebraic background, including a discussion of algebraic entropies and their inequalities.

hep-th↗

arXiv2026

Factor Code Networks

For a quantum code defined by an isometry $T:H_{\rm code} \to H_{\rm phys}$, an operator map is a *-homomorphism $φ: B(H_{\rm code}) \to B(H_{\rm phys})$ from the space of operators on the logical Hilbert space to the space of operators on the physical Hilbert space satisfying $φ({\cal O}) T = T {\cal O}$ for every operator ${\cal O}$ on $H_{\rm code}$. This can additionally be taken to be unital $φ(I_{code}) = I_{phys}$ if and only if $\dim H_{\rm code}$ divides $\dim H_{\rm phys}$. In this case, $φ(B(H_{\rm code})$ is a von Neumann factor subalgebra of $B(H_{\rm phys})$ and we call the pair $(T,φ)$ a {\it factor code}. A code network is a family of Hilbert spaces $\{{\cal H}_i\}$ indexed by a partially ordered set with isometries $T_{ji}:{\cal H}_i \to {\cal H}_j$ for $i < j$ satisfying $T_{kj} T_{ji} = T_{ki}$ for $i < j < k$. In this paper, we ask when this can be promoted to a {\it factor code network} by defining unital operator maps $φ_{ji}$ so that $(T_{ji}, φ_{ji})$ is a factor code and $φ_{kj} φ_{ji} = φ_{ki}$. We show that the divisibility conditions on Hilbert space dimensions are sufficient for any code network with a tree structure but not in general. For a diamond-shaped network, we show that promotion is possible if and only if the principle angles between $T_{42} H_2$ and $T_{43} H_3$ all have multiplicity divisible by $H_1$. For incomparable $i_1,i_2 < j$, we characterize when $φ_{j i_1} (B(H_{i_1}))$ and $φ_{j i_2} (B(H_{i_2}))$ commute, when they generate all of $B(H_j)$, and when they intersect only on multiples of the identity. For $i < j_1,j_2 < k$, we characterize when $φ_{k j_1} (B(H_{j_1})) \cap φ_{k j_2} (B(H_{j_2})) = φ_{k i} (B(H_{i}))$ and when these algebras together with $B(H_k)$ form a nondegenerate commuting square.

quant-ph↗

arXiv2026

Algebraic structure in holographic tensor networks

In a previous work 2511.21852, we explored the hypothesis that in general theories of quantum gravity, spacetime regions known as generalized entanglement wedges (introduced by Bousso and Penington) have an associated subalgebra of observables in a semiclassical limit. We defined an entropy associated with these subalgebras that obeys the same monotonicity and strong subadditivity properties as the generalized gravitational entropy of generalized entanglement wedges. Here, we test aspects of these ideas making use of tensor network toy models for holography. In this context, the analog of a generalized entanglement wedge is a region for which no region containing it has a smaller number of boundary legs. In the limit of large bond dimension (analogous to the semiclassical limit), we argue that each such region has a canonically associated subalgebra of the full algebra of observables on the boundary Hilbert space, as well as a family of unitarily related von Neumann factor subalgebras. We investigate in detail how various algebraic operations on these subalgebras (e.g. their intersections, joins, and commutants) are related to corresponding geometrical operations on the tensor network regions. We study to what extent the monotonicity and strong subadditivity properties of generalized entropy for generalized entanglement wedges follow from properties of our algebraic entropy. We also introduce an alternative entropic quantity $S(ω|| ω\circ E_{\mathcal{A}'})$ associated with a subalgebra $\mathcal{A}$ that also obeys monotonicity and strong subadditivity properties with suitable conditions. Finally, we explain how to define a type $II_1$ von Neumann algebra based on an infinite family of random tensor networks with increasing bond dimension such that the regions corresponding to generalized entanglement wedges can be associated with exact subalgebras of this full algebra.

hep-th↗

arXiv2025

Cosmology with non-conformal holographic matter

We investigate the effect on cosmological evolution of a strongly coupled quantum field that undergoes renormalization group flow from a UV CFT to an IR CFT. The field theory is defined by perturbation of a holographic CFT by a relevant operator associated with a bulk scalar field that evolves from a local maximum of its potential near the boundary to a local minimum of its potential deep in the bulk. By studying the gravity solutions dual to this theory on $\mathbb{R}^3 \times S^1$, we find that the equation of state parameter $w$ for the field theory has the conformal behavior $w=1/3$ for high and low temperatures, but dips to lower values for intermediate temperatures. Thus, at scales where the field theory has significant scale-dependence, its effect on cosmological evolution is intermediate between matter and radiation. Compared to the unperturbed UV CFT (which acts as radiation), the energy density experiences less dilution during the expansion as a result of the RG flow, and the rate of expansion is greater.

hep-th↗

arXiv2020

Quantum Bell Nonlocality is Entanglement

Bell nonlocality describes a manifestation of quantum mechanics that cannot be explained by any local hidden variable model. Its origin lies in the nature of quantum entanglement, although understanding the precise relationship between nonlocality and entanglement has been a notorious open problem. In this paper, we resolve this problem by developing a dynamical framework in which quantum Bell nonlocality emerges as special form of entanglement, and both are unified as resources under local operations and classical communication (LOCC). Our framework is built on the notion of quantum processes, which are abstract quantum channels mapping elements between fixed intervals in space and time. Entanglement is then identified as a quantum process that cannot be generated by LOCC while Bell nonlocality is the subset of these processes that have an instantaneous input-output delay time. LOCC pre-processing is a natural set of free operations in this theory, thereby enabling all entangled states to activate some form of Bell nonlocality. In addition, we generalize the CHSH witnesses from the state domain to the domain of entangled quantum measurements, and provide a systematic method to quantify the Bell nonlocality of a bipartite quantum channel.

quant-ph↗