arXiv subjects

Morteza Ahmadi

Publications and source records attributed to Morteza Ahmadi.

6 recordsLinked to original sources

arXiv2026

Deformed Convolution, Cumulant Transforms, and Semigroup Generators in Hurwitz Series Rings

Let $R$ be a commutative $\Q$-algebra and let $HR$ denote its Hurwitz series ring. We introduce a one-parameter convolution $\hconv{t}$ on $HR$ for which the specialization $t=-1$ is the intrinsic Hurwitz product. Positive integral parameters act on finite-support truncations and reproduce finite free convolution in coefficient coordinates. A logarithmic transform yields additive and homogeneous cumulants, an explicit inversion formula, binomial, Hermite, Laguerre, and hypergeometric families, and coefficientwise analogues of the law of large numbers and the central limit theorem. At $t=-1$, addition of independent random variables becomes multiplication of their moment sequences in $HR$; this gives applications to classical cumulants, beta--gamma products, and self-decomposable laws. Weighted coefficient norms turn $\hconv{t}$ into a commutative Banach algebra product. Norm-continuous convolution semigroups then have generators conjugate to multiplication operators. Explicit formulas are obtained for the Hermite and Laguerre semigroups, the finite free heat generator, and the Lévy--Khintchine generator.

math.RA↗

arXiv2026

Factorization Bounds and Irreducibility Criteria in Hurwitz Series Rings

Let R be a principal ideal domain and let $HR$ denote the Hurwitz series ring over R. We first give a recursive splitting formula for a Hurwitz series whose constant coefficient is a product of two coprime nonunits. This construction leads to irreducibility tests for prime-power constant coefficients, decompositions indexed by the distinct prime divisors of the constant coefficient, and upper and lower bounds for the length of every irreducible factorization. Over a discrete valuation domain, the valuation of any selected coefficient yields a sharper length bound. We then introduce the Hurwitz--Newton polygon and prove a product rule on ranges in which the relevant binomial coefficients are units. Primitive one-edge polygons consequently provide Dumas-type irreducibility criteria. Finally, localization is used to combine independent criteria at several prime elements. Examples over Z, localized polynomial rings, and the Gaussian integers illustrate the results.

math.AC↗

arXiv2026

Pound-Drever-Hall Feedforward for Trapped-Ion Optical Qubits

Laser phase noise is one of the limiting factors that dictate gate fidelities and coherence times in trapped-ion quantum systems. Previous studies have reported that when the Rabi frequency of an ion qubit is close to the servo-bump phase-noise frequency, the driving laser limits the fidelity and coherence time. This issue has typically been mitigated by choosing a Rabi frequency outside the servo-bump region. However, this constrains the usable range of gate speeds and can limit the achievable fidelity. To address this issue, we developed an active phase-noise stabilization system for a barium-ion optical-qubit laser at 1762 nm, employing a fiber electro-optic modulator (EOM) with an electrical feedforward servo. Our results demonstrate that this setup, based on the Pound-Drever-Hall (PDH) feedforward method, can suppress servo-bump phase noise by 15 dB near the bump peak frequency in our locking system. The laser phase noise is analyzed using delayed self-heterodyne interferometry (DSHI). We further tested the stabilized laser on an optical qubit and observed a clear improvement in coherence time based on the measured amplitude decay of Rabi oscillations, even when the Rabi frequency lies within the servo-bump bandwidth. This technique can be readily adapted to other optical qubits with minimal modifications.

quant-ph↗

arXiv2024

Graded quasi-Baer $\ast$-ring characterization of Steinberg algebras

Given a graded ample, Hausdorff groupoid $G$, and an involutive field $K$, we consider the Steinberg algebra $A_K(G)$. We obtain necessary and sufficient conditions on $G$ under which the annihilator of any graded ideal of $A_K(G)$ is generated by a homogeneous projection. This property is called graded quasi-Baer $\ast$. We use the Steinberg algebra model to characterize graded quasi-Baer $\ast$ Leavitt path algebras.

math.RA↗

arXiv2024

A scalable narrow linewidth high power laser for barium ion optical qubit

The linewidth of a laser plays a pivotal role in ensuring the high fidelity of ion trap quantum processors and optical clocks. As quantum computing endeavors scale up in qubit number, the demand for higher laser power with ultra-narrow linewidth becomes imperative, and leveraging fiber amplifiers emerges as a promising approach to meet these requirements. This study explores the effectiveness of Thulium-doped fiber amplifiers (TDFAs) as a viable solution for addressing optical qubit transitions in trapped barium ion qubits. We demonstrate that by performing high-fidelity gates on the qubit while introducing minimal intensity noise, TDFAs do not significantly broaden the linewidth of the seed lasers. We employed a Voigt fitting scheme in conjunction with a delayed self-heterodyne method to accurately measure the linewidth independently, corroborating our findings through quadrupole spectroscopy with trapped barium ions. Our results show linewidth values of $160 \pm 15$ Hz and $156 \pm 16$ Hz, respectively, using these two methods, underscoring the reliability of our measurement techniques. The slight variation between the two methods can be attributed to factors such as amplified spontaneous emission in the TDFA or the influence of 1/f noise within the heterodyne setup delay line. These contribute to advancing our understanding of laser linewidth control in the context of ion trap quantum computing as well as stretching the availability of narrow linewidth, high-power tunable lasers beyond the C-band.

quant-ph↗

arXiv2006

Is entanglement entropy proportional to area?

It is known that the entanglement entropy of a scalar field, found by tracing over its degrees of freedom inside a sphere of radius ${\cal R}$, is proportional to the area of the sphere (and not its volume). This suggests that the origin of black hole entropy, also proportional to its horizon area, may lie in the entanglement between the degrees of freedom inside and outside the horizon. We examine this proposal carefully by including excited states, to check probable deviations from the area law.

hep-th↗