General perturbation theory for local quantum uncertainty and its formulation in the linear-response regime

• URL: http://arxiv.org/abs/2605.03248v1
• Date: Tue, 05 May 2026 00:40:43 GMT
• Title: General perturbation theory for local quantum uncertainty and its formulation in the linear-response regime
• Abstract summary: We develop a general perturbation theory for the local quantum uncertainty (LQU)<n>LQU is a discord-type quantifier of nonclassicality based on the Wigner-Yanase information.<n>We apply formalism to the isotropic Heisenberg model of two coupled spins driven by a local periodic magnetic field.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a general perturbation theory for the local quantum uncertainty (LQU), a discord-type quantifier of nonclassicality based on the Wigner-Yanase skew information. Starting from a perturbed density matrix $ρ= ρ_0 + ερ_1$,we derive an explicit first-order expansion of $ρ^{1/2}$ using an integral representation based on the gamma function, and reduce the LQU optimization to the diagonalization of a $(d_1^2-1) \times (d_1^2-1)$ matrix $w = w^0 + w^1$ defined in terms of the $\mathrm{SU}(d_1)$ generators. The framework is valid for composite systems of arbitrary dimension $d_1 \times d_2$ and provides a direct computational route to the LQU from the spectral decomposition of the unperturbed state. We further specialize the theory to the quantum linear response regime, where the perturbation is generated by a time-dependent external field, and $w^1$ acquires explicit dependence on the driving frequency $ω$, the eigenstates and occupation probabilities of the equilibrium Hamiltonian $H_0$, and the matrix elements of the coupling operator $\hat{A}$. As an illustration, we apply the formalism to the isotropic Heisenberg model of two coupled spins driven by a local periodic magnetic field, obtaining closed-form expressions for the LQU as a function of temperature $T$ and frequency $ω$. Comparison with the concurrence shows that above the entanglement critical temperature $T_c$, the external field induces a resonantly enhanced quantum discord without generating entanglement, demonstrating that frequency acts as a tunable modulator of nonclassicality -- an effect of purely quantum-discord type inaccessible to entanglement-based quantifiers.

Related papers

• Discrete power-law decay of subsystem distance after a quantum quench [1.2326452468513227]
  We present a numerical study of subsystem distance decay following a global quantum quench in the infinite one-dimensional transverse-field Ising chain.<n>We show that the late-time decay follows a discrete power law $B_A(t) sim t-$, with the exponent $$ confined to discrete values.<n>Our results reveal a universal discrete structure governing local equilibration dynamics in integrable quantum systems.
  arXiv  Detail & Related papers  (2026-07-28T12:47:28Z)
• Effective Dimension Governs Generalization in Quantum Kernel Vision Models [31.082191748525137]
  We show that entanglement structure and quantum noise are two knobs that move $d_rm eff$.<n>Amplitude damping contracts $d_rm eff$ and lifts test accuracy by up to $+13%$ along an inverted-U sweet spot.
  arXiv  Detail & Related papers  (2026-06-18T12:55:59Z)
• Typical entanglement in anyon chains: Page curves beyond Lie group symmetries [41.99844472131922]
  We study bipartite entanglement statistics in one-dimensional anyon chains constrained by fusion rules of unitary pre-modular categories.<n>Surprisingly, despite the constrained Hilbert space structure, the large $L$ expansion has no universal $O(sqrtL)$ or $O(1)$ symmetry-type corrections.<n> Numerical simulations of the integrable and quantum-chaotic golden chain Hamiltonian show that chaotic mid-spectrum eigenstates match the Haar-random predictions.
  arXiv  Detail & Related papers  (2026-03-26T18:00:03Z)
• Quantum simulation of lattice gauge theories coupled to fermionic matter via anyonic regularization [0.0]
  The optimal regularization of infinite-dimensional degrees of freedom is a central open problem in the tractable simulation of lattice gauge theories on quantum computers.<n>We consider regularizing the gauge field by replacing the gauge group $G$ with a braided fusion category whose objects correspond to Wilson lines of the associated Chern-Simons theory $G_k$.<n>We demonstrate how to couple these regularized $U(1)$ and $SU(2)$ gauge groups to fermionic matter using the framework of fusion surface models.
  arXiv  Detail & Related papers  (2026-03-16T18:51:41Z)
• Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors [40.72140849821964]
  We consider the massive Thirring and Gross-Neveu models with arbitrary number of fermion flavors, $N_f$, discretized on a spatial one-dimensional lattice of size $L$.<n>We prepare the ground states of both models with excellent fidelity for system sizes up to 20 qubits with $N_f = 1,2,3,4$.<n>Our work is a concrete step towards the quantum simulation of real-time dynamics of large $N_f$ fermionic quantum field theories models.
  arXiv  Detail & Related papers  (2026-02-25T19:00:01Z)
• Transmutation based Quantum Simulation for Non-unitary Dynamics [35.35971148847751]
  We present a quantum algorithm for simulating dissipative diffusion dynamics generated by positive semidefinite operators of the form $A=Ldagger L$.<n>Our main tool is the Kannai transform, which represents the diffusion semigroup $e-TA$ as a Gaussian-weighted superposition of unitary wave propagators.
  arXiv  Detail & Related papers  (2026-01-07T05:47:22Z)
• Conformal quantum mechanics of causal diamonds: Time evolution, thermality, and instability via path integral functionals [0.0]
  An observer with a finite lifetime perceives the Minkowski vacuum as a thermal state at temperature $T_D = 2 hbar/(pi mathcalT)$.<n>In this paper, we explore the emergence of thermality in causal diamonds due to the role played by the symmetries of conformal quantum mechanics.
  arXiv  Detail & Related papers  (2024-07-25T16:36:52Z)
• Quantum tomography of helicity states for general scattering processes [55.2480439325792]
  Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics. We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
  arXiv  Detail & Related papers  (2023-10-16T21:23:42Z)
• Geometric relative entropies and barycentric Rényi divergences [16.385815610837167]
  monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure. We show that monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure.
  arXiv  Detail & Related papers  (2022-07-28T17:58:59Z)
• Analyticity constraints bound the decay of the spectral form factor [0.0]
  Quantum chaos cannot develop faster than $lambda leq 2 pi/(hbar beta)$ for systems in thermal equilibrium. We show that similar constraints also bound the decay of the spectral form factor (SFF) The relation of the derived bound with other known bounds, including quantum speed limits, is discussed.
  arXiv  Detail & Related papers  (2022-02-23T19:00:00Z)
• Complete entropic inequalities for quantum Markov chains [17.21921346541951]
  We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional algebra satisfies a modified log-Sobolev inequality. We also establish the first general approximateization property of relative entropy.
  arXiv  Detail & Related papers  (2021-02-08T11:47:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.