We study the time evolution of entanglement and quantum discord for a pair of maximally entangled qudits of arbitrary dimension $d$ under non-Markovian pure dephasing, using the exact solution of the independent boson model. Because this solution requires no Born--Markov, Lindblad, or rotating-wave approximation, every result reported here follows directly from the exact dynamics. Exploiting the Toeplitz structure of the resulting density matrix, we obtain a closed-form expression for the negativity as a finite sum, valid for arbitrary dimension and evolution time, together with a corresponding closed-form expression for the quantum discord. For the family of dephased maximally entangled states considered here, we prove that a computational-basis measurement is globally optimal over the entire POVM space, thereby eliminating the numerical optimization otherwise required for evaluating the quantum discord. We further show that both quantities saturate, as the dimension grows, to a dimension-independent limiting value, with a convergence rate of exactly $1/d$. For negativity, this scaling law is established through a rigorous theorem, including a Gaussian-type error bound of order $e^{-\alpha d^2}$, and is confirmed across six independent parameter regimes for two distinct classes of spectral density, Lorentzian and Ohmic; for discord, the same leading-order behavior is found numerically across the six Lorentzian regimes. The analytical results are validated by independent numerical approaches, including reconstruction from the underlying definitions, arbitrary-precision arithmetic, and a complementary pseudomode cross-check.
Absolutely maximally entangled states represent a highly constrained form of multipartite entanglement and play an important role in quantum information theory. We investigate a weaker form of uniformity of entanglement for four-party systems of local dimension $d>2$ that requires the three balanced bipartitions to have equal but not necessarily maximal linear entropy. We introduce a linear map $\Xi$ that enforces exact equality of entropies under reshuffling and partial transposition. The transformation arises as the asymptotic limit of an iterative averaging procedure and admits a group-theoretic description in terms of permutations of tensor indices. For Haar-random unitary inputs, a leading-moment analysis supported by numerical simulations predicts highly entangled outputs whose common entropy approaches the maximal value as the local dimension grows. We characterize the algebraic structure, fixed points, and asymptotic behavior of this map and its relation to two-unitary matrices and orthogonal Latin squares.
We investigate the dynamics of entanglement in a generalized version of the kicked Ising chain, extending the model from the standard qubit case (local dimension $q=2$) to higher local dimensions ($q>2$). We identify the existence of''dual-unitary''points where the model's space-time duality allows for exact analytical solutions. Our analysis reveals that while a few unique dual-unitary points exist analytically for systems with local dimensions $q=3$ and $q=4$, such points do not exist for $q \ge 5$ due to the lack of a unique kicking strength that satisfies the required matrix element conditions. Utilizing the transfer matrix method and a replica trick specifically adapted for higher dimensions, we derive exact expressions for the growth of entanglement entropy in the $q=3$ (kicked Potts-type) model starting from a class of solvable initial states. Our results demonstrate that at the dual-unitary point, both R\'enyi and von Neumann entanglement entropies grow linearly with time until reaching a maximum value determined by the subsystem size.
Coherent states bridge the gap between quantum and classical physics, but their overcomplete and nonorthogonal nature makes it difficult to identify the minimal discrete set needed to reconstruct quantum information. Finite spin-coherent tomography and discrete coherent-state operator bases are known, but here we address the more specific rank-resolved problem of preserving the canonical contravariant-symbol representation. We show that the canonical finite coherent-state formula reconstructs every operator in the rank-$S$ sector exactly if and only if the sampling points form a spherical $(2J+S)$-design. We call the associated configurations spin-coherent quantum designs. We further give a fully explicit positive-weight Gauss-Legendre construction that avoids the need for an equal-weight spherical design. Together, these results establish a unified framework for reading out physical observables from a handful of measurement samples, playing for spin systems the role that the so-called von Neumann lattice plays for canonical coherent states. Finally, we derive practical protocols for estimating moments of spin operators from these constructions, with direct applications to polarimetry, magnetometry, and quantum state tomography.
Marcin Rudzinski, A. Goldberg, A. B. Klimov et al.· 0 citations
We investigate how irreducible multipartite entanglement, a long-range correlation by nature, can emerge from short-range dynamics far from equilibrium. Focusing on the Markov gap as a probe of irreducible tripartite entanglement (IrTE) in free-fermion chains, we uncover qualitatively distinct dynamical behaviors: the Markov gap grows either quasi-linearly or in staircase-like jumps depending on the initial state. We also propose attainable upper and lower bounds for the onset time of IrTE based on the Lieb-Robinson bound. Strikingly, the Markov gap saturates to a volume-law value on a timescale $t\sim\! L^2$, much slower than the ballistic spreading of bipartite correlations. To understand what information about the wavefunctions is revealed by the Markov gap calculation, we introduce the concept of essential tripartite fermion (ETF) and an associated tripartite null matrix. The value of Markov gap closely tracks the number of small singular values of this tripartite null matrix, yielding a transparent, operational physical interpretation of the measure. We further demonstrate that several dynamical signatures persist in the interacting XXZ chain.
Simulating non-Gaussian quantum dynamics in open continuous-variable systems is notoriously challenging: exact methods scale exponentially, while approximations sacrifice non-classical features such as Wigner negativity. Here we introduce an exact finite-dimensional reduction that overcomes this curse of dimensionality. We prove that the algebra of extended Gaussian quasi-probability densities (EGQPDs) is closed under Lindblad evolution with linear jump operators, reducing the infinite-dimensional Wigner PDE to a closed system of ODEs that scales polynomially with the number of modes. A necessary and sufficient condition for closure is established: the algebra remains closed iff every jump operator is at most linear; otherwise the extended algebra with polynomial prefactors is required. We further show that the minimal number of Gaussian components defines a non-Gaussian rank—a discrete complexity measure monotonically non-increasing under the dynamics. The framework yields explicit ODEs for the component parameters, admits a rigorous density theorem and error propagation bound, and provides closed-form algebraic criteria for Gaussianity, purity, and entanglement. Seven numerical experiments validate the method across Gaussian and non-Gaussian states, entanglement decay, PT-symmetric exceptional-point dynamics, and complexity scaling, demonstrating machine-precision accuracy and exponential speedups over grid and Fock methods. The EGQPD framework provides a systematic, exact, and efficient toolbox for non-Gaussian open quantum dynamics.
Peng Guo· Quantum Science and Technolo...· 0 citations
Magic and entanglement are independent quantum resources, yet their exact relation in many-body dynamics has remained elusive. We uncover two structural principles. First, at any stabilizer state, the curvature of the second stabilizer R\'enyi entropy under an arbitrary Hermitian generator equals the quantum Fisher information up to a fixed normalization, creating a bidirectional bridge between computational and metrological resources. Second, for commuting Ising evolution on any forest graph, a Clifford pruning circuit yields the full stabilizer-R\'enyi family at arbitrary size and in any spatial embedding, thereby furnishing a graph-theoretic construction of families with finite magic density and vanishing entanglement density in the thermodynamic limit. We solve two paradigmatic one-dimensional realizations central to quantum simulation -- an Ising quench and a kicked Floquet chain -- exactly for arbitrary system size and directly in the thermodynamic limit, revealing finite magic density with vanishing entanglement density, distinct magic and entanglement revival periods, and Clifford points with zero magic but finite bipartite entanglement. The same tangent geometry fixes initial growth, perturbative revival lifting, and stability of thermodynamic magic minima. Large-scale Pauli-basis matrix-product-state calculations verify all predictions, and the tangent bridge yields a concrete protocol for detecting magic through established quantum-Fisher-information measurements.
R. Jha, Karun Gadge· 1 citation
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