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 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.
We investigate bipartite two-qutrit pure states and analyze their entanglement properties using eigenvalue-based quantities of the reduced density matrix. In addition to the I-concurrence, we show that the determinant of the two-qutrit coefficient matrix defines a rank-sensitive geometric invariant proportional to √ λ1λ2λ3, where λi are the eigenvalues of the reduced density matrix. Unlike the I-concurrence, this invariant vanishes identically for all rank-2 states and is nonzero only for rank-3 states, thereby providing a direct characterization of genuine three-level correlations. Furthermore, we establish an operational interpretation of the invariant in terms of triple-path interference visibility in three-path optical interferometry. These results provide a compact geometric framework for identifying rank-structured entanglement in bipartite two-qutrit systems and reveal a direct connection between high-dimensional quantum correlations and multipath interference phenomena.
Ankit Jana· Women in Optics and Photonic...· 0 citations
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.
Whether negative-partial-transpose entanglement can remain undistillable is a longstanding problem in quantum information theory. We analyze the first unresolved three-copy Werner endpoint using a sharp dimension-free inequality for complementary partial traces and an optimal exterior-square inequality for orthonormal tripartite vectors. The latter identifies local SWAP- parity statistics with metric data of a decomposable Plucker bivector. Together these inequalities prove endpoint nonnegativity for every positive semidefinite rank-two coefficient operator and for the complete normal rank-two sector in arbitrary finite local dimensions. For genuinely nonnormal operators, an exact crossed-Gram criterion proves nonnegativity when one local outpu-input support overlap is at most two, including every system with a qubit-sized factor, and when either support plane contains a product ray. Explicit anti-state and rank-boundary families establish optimality of the constants and the rank restriction.
The modular Hamiltonian plays an important role in quantum information theory, quantum field theory, and the AdS/CFT correspondence. In this paper, we study a specific dynamical setup: starting from the tensor product of the reduced density matrices of a reference state, we evolve this product state under the modular flow generated by the reference state itself. We then investigate the resulting change in the entanglement entropy of a given region, which we call the modular entanglement shift (MES). Unlike evolution under a fixed quantum channel, this modular evolution obeys no general principle requiring the MES to have a definite sign. For a bipartition into subsystems A and B, we establish an exact entropy balance: the sum of the MESs for A and B equals the mutual information generated along the orbit. Consequently, their sum is nonnegative, even though either individual shift may be negative. For two disjoint intervals in the vacuum of a two-dimensional conformal field theory, however, we prove that a global conformal involution exchanging the intervals forces the two MESs to be equal. It follows that each MES is nonnegative along the modular flow. We establish this result both using a conformally transported regulator and intrinsically in terms of Araki relative entropy. Finally, we identify the modular-flow orbit with a Connes cocycle orbit and discuss possible applications to the AdS/CFT correspondence.
Quantum resource theories characterize distinct forms of nonclassicality in many-body quantum states, raising the question of whether these resources evolve independently under generic ergodic dynamics. Considering diagnostics quadratic in the state, we show that the dynamics of different resource measures become mutually interdependent and are governed by a few common degrees of freedom. For Haar-random circuits, the purity together with a single resource witness suffices to reconstruct the remaining resource measures, as we demonstrate for coherence, various asymmetries, and number entropies. The same relations hold, to a good approximation, under chaotic Floquet and continuous-time Hamiltonian dynamics, establishing that this dynamical resource equivalence extends beyond random circuits. We further derive an exact coherence--imaginarity relation, remarkably accurate also beyond Haar-random circuits. Our results reveal an emergent simplification of many-body dynamics, in which sufficiently strong scrambling reduces seemingly distinct quantum resources to a few common dynamical degrees of freedom.
Sreemayee Aditya, X. Turkeshi, P. Sierant· 1 citation
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