Geometry of two-body correlations in three-qubit states
arXiv:2309.09549 · doi:10.1103/PhysRevA.110.062419
Abstract
We study restrictions of two-body correlations in three-qubit states, using three local-unitarily invariant coordinates based on the Bloch vector lengths of the marginal states. First, we find tight nonlinear bounds satisfied by all pure states and extend this result by including the three-body correlations. Second, we consider mixed states and conjecture a tight non-linear bound for all three-qubit states. Finally, within the created framework we give criteria to detect different types of multipartite entanglement as well as characterize the rank of the quantum state.
arXiv comment15 pages, 7 figures
References in corpus (34)
- Separability Criterion for Density Matrices
- On the volume of the set of mixed entangled states
- Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
- Probing entanglement entropy via randomized measurements
- Information-theoretic aspects of quantum inseparability of mixed states
- Multipartite entanglement and high precision metrology
- Generalized Schmidt decomposition and classification of three-quantum-bit states
- The randomized measurement toolbox
- Optimal spin squeezing inequalities detect bound entanglement in spin models
- Quantum Steering Ellipsoids
- Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information
- Multiqubit symmetric states with high geometric entanglement
- Entangled Bloch Spheres: Bloch Matrix and Two Qubit State Space
- One-qubit reduced states of a pure many-qubit state: polygon inequalities
- Parts of Quantum States
- The shape of higher-dimensional state space: Bloch-ball analog for a qutrit
- Bound entanglement from randomized measurements
- Three-party pure quantum states are determined by two two-party reduced states
- Dimensionally sharp inequalities for the linear entropy
- Anisotropic invariance and the distribution of quantum correlations
- A complete hierarchy for the pure state marginal problem in quantum mechanics
- Three-dimensional visualization of a qutrit
- Entanglement Polygon Inequality in Qubit Systems
- When is a pure state of three qubits determined by its single-particle reduced density matrices?
- Analysing quantum systems with randomised measurements
- Useful multipartite correlations from useless reduced states
- Multiparticle entanglement as an emergent phenomenon
- Characterizing quantum states via sector lengths
- Almost all four-particle pure states are determined by their two-body marginals
- Maximum -body correlations do not in general imply genuine multipartite entanglement
- A simplex of bound entangled multipartite qubit states
- Certifying Quantum Separability with Adaptive Polytopes
- Faithful geometric measures for genuine tripartite entanglement
- Correlation constraints and the Bloch geometry of two qubits