Inter-qubit correlation dynamics driven by mutual interactions

Abstract

A particularly useful tool for characterizing multi-qubit systems is the correlation tensor, providing an experimentally friendly and theoretically concise representation of quantum states. In this work, we analyze the evolution of the correlation tensor elements of quantum systems composed of $\frac{1}{2}$-spins, generated by mutual interactions and the influence of the external field. We focus on two-body interactions in the form of anisotropic Heisenberg as well as antisymmetric exchange interaction models. The evolution of the system is visualized in the form of a trajectory in a suitable correlation space, which, depending on the system's frequencies, exhibits periodic or nonperiodic behavior. In the case of two $\frac{1}{2}$-spins we study the stationary correlations for several classes of Hamiltonians, which allows a full characterization of the families of density matrices invariant under the evolution generated by the Hamiltonians. We discuss some common properties shared by the 2- and 3-qubit systems and show how a strong external field can play a stabilizing factor with respect to certain correlation characteristics.

arXiv comment14 pages, 6 figures

References in corpus (29)

• Bell nonlocality
• Non-locality and Communication Complexity
• Probing entanglement entropy via randomized measurements
• A geometric theory of non-local two-qubit operations
• The randomized measurement toolbox
• Multipartite entanglement measures
• Multipartite entanglement detection from correlation tensors
• Entangled Bloch Spheres: Bloch Matrix and Two Qubit State Space
• On nonlocality as a resource theory and nonlocality measures
• Experimentally friendly geometrical criteria for entanglement
• Postulates for measures of genuine multipartite correlations
• Characterizing multipartite entanglement with moments of random correlations
• Characterizing multipartite entanglement without shared reference frames
• Quantum entanglement from random measurements
• Monogamy equalities for qubit entanglement from Lorentz invariance
• Correlation tensor criteria for genuine multiqubit entanglement
• A family of multipartite separability criteria based on correlation tensor
• Analysing quantum systems with randomised measurements
• Universal two-qubit interactions, measurement and cooling for quantum simulation and computing
• Multipartite entanglement measures: a review
• Characterizing quantum states via sector lengths
• Entanglement in a two-qubit Heisenberg XXX chain with x-components of Dzyaloshinskii-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions
• Quantum entanglement in the anisotropic Heisenberg model with multicomponent DM and KSEA interactions
• Geometry of a two-spin quantum state in evolution
• A Moment for Random Measurements
• The fastest generation of multipartite entanglement with natural interactions
• Correlation constraints and the Bloch geometry of two qubits
• Probing the geometry of two-qubit state space by evolution
• Geometry of two-body correlations in three-qubit states