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Vahagn Abgaryan

Publications and source records attributed to Vahagn Abgaryan.

8 recordsLinked to original sources
arXiv2026

Propagation of Two-Photon Zernike States in Atmospheric Turbulence

We analyze propagation and detection of two-photon states expanded in Zernike modes through atmospheric turbulence using the extended Huygens-Fresnel formalism. For SPDC states prepared with a single Zernike pump mode, we analytically reduce the 8-dimensional continuous propagation integrals to an exact, discrete modal expansion. In the absence of turbulence, Zernike addition enforces conservation of azimuthal index and a strict radial-order bound. Turbulence relaxes these constraints, driving structured azimuthal and radial crosstalk dominated by low-order aberration modes.

quant-ph↗
arXiv2025

Zernike system revisited: imaginary gauge and Higgs oscillator

We analyze that recently proposed clasical/quantum mechanical interpretation of Zernike system and establish its equivalence to the Higgs oscillator on sphere or pseudosphere (Lobachevsky plane). We show that the non-reality of the classical Zernike Hamiltonian is an insignificant artifact of imaginary gauge and can be eliminated with a canonical transformation. The quantum counterpart of this canonical transformation is a similarity transformation mapping the system to the quantum Higgs oscillator with integration measure depending on $α,β$ parameters. When $α=2 β$ it results in the Hermitian Hamiltonian describing a free particle on (pseudo)sphere, while deviation from this point leads to a pseudo-Hermitian system.

quant-ph↗
arXiv2021

Kenfack Zyczkowski indicator of nonclassicality for two non-equivalent representations of Wigner function of qutrit

The Wigner function of a finite-dimensional system can be constructed via dual pairing of a density matrix with the Stratonovich-Weyl kernel. Following Kenfack and $\dot{\text{Z}}$yczkowski, we consider the indicator of nonclassicality of a finite-dimensional quantum system which depends on the volume of the negative part of the Wigner function. This indicator is defined over the unitary non-equivalent classes of quantum states, i.e. represents an invariant, but since for a given quantum system there is no unique Wigner function it turns to be sensitive to the choice of representations for the Wigner function. Based on the explicit parameterization of the moduli space of the Wigner functions, we compute the corresponding Kenfack-$\dot{\text{Z}}$yczkowski indicators of a 3-level system for degenerate, unitary non-equivalent Stratonovich-Weyl kernels.

quant-ph↗
arXiv2021

On overall measure of non-classicality of $N$-level quantum system and its universality in the large $N$ limit

In this report we are aiming at introducing a global measure of non-classicality of the state space of $N$-level quantum systems and estimating it in the limit of large $N$. For this purpose we employ the Wigner function negativity as a non-classicality criteria. Thus, the specific volume of the support of negative values of Wigner function is treated as a measure of non-classicality of an individual state. Assuming that the states of an $N$-level quantum system are distributed by Hilbert-Schmidt measure (Hilbert-Schmidt ensemble), we define the global measure as the average non-classicality of the individual states over the Hilbert-Schmidt ensemble. We present the numerical estimate of this quantity as a result of random generation of states, and prove a proposition claiming its exact value in the limit of $N\to \infty$

quant-ph↗
arXiv2019

The global indicator of classicality of an arbitrary $N$-level quantum system

It is commonly accepted that a deviation of the Wigner quasiprobability distribution of a quantum state from a proper statistical distribution signifies its nonclassicality. Following this ideology, we introduce the global indicator $\mathcal{Q}_N$ for quantification of "classicality-quantumness" correspondence in the form of the functional on the orbit space $\mathcal{O}[\mathfrak{P}_N]$ of the $SU(N)$ group adjoint action on the state space $\mathfrak{P}_N$ of an $N$-dimensional quantum system. The indicator $\mathcal{Q}_{N}$ is defined as a relative volume of a subspace $\mathcal{O}[\mathfrak{P}^{(+)}_N] \subset \mathcal{O}[\mathfrak{P}_N]\,,$ where the Wigner quasiprobability distribution is positive. An algebraic structure of $\mathcal{O}[\mathfrak{P}^{(+)}_N]$ is revealed and exemplified by a single qubit $(N=2)$ and single qutrit $(N=3)$. For the Hilbert-Schmidt ensemble of qutrits the dependence of the global indicator on the moduli parameter of the Wigner quasiprobability distribution has been found.

quant-ph↗
arXiv2018

On moduli space of the Wigner quasiprobability distributions for $N$-dimensional quantum systems

A mapping between operators on the Hilbert space of $N$-dimensional quantum system and the Wigner quasiprobability distributions defined on the symplectic flag manifold is discussed. The Wigner quasiprobability distribution is constructed as a dual pairing between the density matrix and the Stratonovich-Weyl kernel. It is shown that the moduli space of the Stratonovich-Weyl kernel is given by an intersection of the coadjoint orbit space of the $SU(N)$ group and a unit $(N-2)$-dimensional sphere. The general consideration is exemplified by a detailed description of the moduli space of 2, 3 and 4-dimensional systems.

quant-ph↗
arXiv2018

Two novel approaches to the hadron-quark mixed phase in compact stars

First-order phase transitions, like the liquid-gas transition, proceed via formation of structures such as bubbles and droplets. In strongly interacting compact star matter, at the crust-core transition, but also at the hadron-quark transition in the core, these structures form different shapes dubbed "pasta phases". We describe two methods to obtain one-parameter families of hybrid equations of state (EoS) which mimic the thermodynamic behavior of pasta phases in between a low-density hadron and a high-density quark matter phase, thus generalizing the Maxwell construction. The first method replaces the behavior of pressure vs. chemical potential in a finite region around the critical %chemical potential pressure of the Maxwell construction by a polynomial interpolation. The second method uses extrapolations of the hadronic and quark matter EoS beyond the Maxwell point to define a mixing of both with weight functions bounded by finite limits around the Maxwell point. We apply both methods to the case of a hybrid EoS with a strong first order transition that entails the formation of a third family of compact stars and the corresponding mass twin phenomenon. We investigate for both models the robustness of this phenomenon against variation of the single parameter, the pressure increment at the critical chemical potential which quantifies the deviation from the Maxwell construction. We also show sets of results for other compact star observables than mass and radius, namely the moment of inertia and the baryon mass.

astro-ph.HE↗