arXiv subjects

Gábor Homa

Publications and source records attributed to Gábor Homa.

7 recordsLinked to original sources

arXiv2026

Quantitative comparison of quantum pseudo-telepathy games and Bell inequalities

Quantum pseudo-telepathy games, such as the Mermin-Peres magic square and the doily game, theoretically allow players to win with unit probability when using entangled quantum strategies. We quantitatively characterize the quantum advantage in these games and compare it with violations of two Bell inequalities: the Clauser-Horne-Shimony-Holt and the Collins-Gisin inequalities. The analysis is restricted to two families of two-qubit states: modified Werner states and Bell-diagonal states. For each case, we identify and quantify the regions of quantum state space that exhibit either a quantum advantage or a Bell inequality violation, relative to the set of all entangled states. Within these families, the doily game captures a larger fraction of entangled states than the Mermin-Peres magic square game, though both are significantly more limited than the regions associated with Bell inequality violations. Although both approaches are fundamentally linked to quantum contextuality, our analysis of the examined two-qubit state families indicates that Bell inequalities are more effective at revealing entanglement, even if pseudo-telepathy games offer a more intuitive and conceptually appealing perspective.

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arXiv2026

An exact Markovian decoherence dynamics of two interacting harmonic oscillators coupled to a bosonic heat bath

We present an exact analytical solution of the Hu-Paz-Zhang master equation in a precise Markovian limit for a system of two harmonically coupled harmonic oscillators interacting with a common thermal bath of harmonic oscillators. The thermal bath is initially considered to be at arbitrary temperatures and characterized by an Ohmic Lorentz-Drude spectral density. In the examined system, couplings between the two harmonic oscillators and the environment ensure a complete decoupling of the center-of-mass and relative degrees of freedom, resulting in undamped dynamics in the relative coordinate. The exact time evolution is used to analyze the system's entanglement dynamics, quantified through logarithmic negativity and quantum mutual information, while ensuring the positivity of the density operator to confirm the physical validity of the results. We demonstrate that, under certain parameter regimes and initial conditions, the asymptotic dynamics can give rise to periodic entanglement-disentanglement behavior. Furthermore, numerical simulations reveal that for negative values of the direct coupling between the oscillators, which are sufficiently close to a critical lower bound beyond which the system becomes unstable, the system can maintain entanglement across a broad temperature range and for arbitrarily long durations.

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arXiv2025

Effective eigenvalue approximation from moments for self-adjoint trace-class operators

Spectral properties of bounded linear operators play a crucial role in several areas of mathematics and physics. For each self-adjoint, trace-class operator $O$ we define a set $Λ_n\subset \mathbb{R}$, and we show that it converges to the spectrum of $O$ in the Hausdorff metric under mild conditions. Our set $Λ_n$ only depends on the first $n$ moments of $O$. We show that it can be effectively calculated for physically relevant operators, and it approximates the spectrum well without diagonalization. We prove that using the above method we can converge to the minimal and maximal eigenvalues with super-exponential speed. We also construct monotone increasing lower bounds $q_n$ for the minimal eigenvalue (or decreasing upper bounds for the maximal eigenvalue). This sequence only depends on the moments of $O$ and a concrete upper estimate of its $1$-norm; we also demonstrate that $q_n$ can be effectively calculated for a large class of physically relevant operators. This rigorous lower bound $q_n$ tends to the minimal eigenvalue with super-exponential speed provided that $O$ is not positive semidefinite. As a by-product, we obtain computable upper bounds for the $1$-norm of $O$, too. Numerical examples demonstrate the relevance of our approximation in estimating entropy and negativity, which is useful, among others, in quantum optical and in open quantum system models. The results can be directly applicable to problems in quantum information, statistical mechanics, and quantum thermodynamics, where using traditional techniques based on diagonalization is impractical.

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arXiv2024

Positivity and entanglement of polynomial Gaussian integral operators

Positivity preservation is an important issue in the dynamics of open quantum systems: positivity violations always mark the border of validity of the model. We investigate the positivity of self-adjoint polynomial Gaussian integral operators $\widehatκ_{PG}$, that is, the multivariable kernel $κ_{PG}$ is a product of a polynomial $P$ and a Gaussian kernel $κ_G$. These operators frequently appear in open quantum systems. We show that $\widehatκ_{PG}$ can be only positive if the Gaussian part is positive, which yields a strong and quite easy test for positivity. This has an important corollary for the bipartite entanglement of the density operators $\widehatκ_{PG}$: if the Gaussian density operator $\widehatκ_G$ fails the Peres-Horodecki criterion, then the corresponding polynomial Gaussian density operators $\widehatκ_{PG}$ also fail the criterion for all $P$, hence they are all entangled. We prove that polynomial Gaussian operators with polynomials of odd degree cannot be positive semidefinite. We introduce a new preorder $\preceq$ on Gaussian kernels such that if $κ_{G_0}\preceq κ_{G_1}$ then $\widehatκ_{PG_0}\geq 0$ implies $\widehatκ_{PG_1}\geq 0$ for all polynomials $P$. Therefore, deciding the positivity of a polynomial Gaussian operator determines the positivity of a lot of another polynomial Gaussian operators having the same polynomial factor, which might improve any given positivity test by carrying it out on a much larger set of operators. We will show an example that this really can make positivity tests much more sensitive and efficient. This preorder has implication for the entanglement problem, too.

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arXiv2024

Photon number states via iterated photon addition in a loop

We consider the probabilistic generation of time-bin photon number states from a train of single photon pulses. We propose a simple interferometric feedback loop setup having a beam splitter and a possibly non-idel detector. This Hong-Ou-Mandel type scheme implements iterated photon additions. Our detailed study shows that up to 4 photons this simple setup can provide reasonable success probabilities and fidelities.

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arXiv2019

Short time behavior of continuous time quantum walks on graphs

Dynamical evolution of systems with sparse Hamiltonians can always be recognized as continuous time quantum walks (CTQWs) on graphs. In this paper, we analyze the short time asymptotics of CTQWs. In recent studies, it was shown that for the classical diffusion process the short time asymptotics of the transition probabilities follows power laws whose exponents are given by the usual combinatorial distances of the nodes. Inspired by this result, we perform a similar analysis for CTQWs both in closed and open systems, including time-dependent couplings. For time-reversal symmetric coherent quantum evolutions, the short time asymptotics of the transition probabilities is completely determined by the topology of the underlying graph analogously to the classical case, but with a doubled power-law exponent. Moreover, this result is robust against the introduction of on-site potential terms. However, we show that time-reversal symmetry breaking terms and non-coherent effects can significantly alter the short time asymptotics. The analytical formulas are checked against numerics, and excellent agreement is found. Furthermore, we discuss in detail the relevance of our results for quantum evolutions on particular network topologies.

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arXiv2017

Notes on oldest jump unravelling of spatial decoherence master equation

Solution of free particle quantum master equation with spatial decoherence can be unravelled into stochastic quantum trajectories in many ways. The first example, published in 1985, proposed a piecewise deterministic jump process for the wave function. While alternative unravellings, diffusive ones in particular, proved to be tractable analytically, the jump process 1985, also called orthojump, allows for few analytic results, it needs numeric methods as well. Here we prove that, similarly to diffusive unravellings, it is localizing the quantum state.

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