Entanglement witnesses and geometry of entanglement of two--qutrit states

Abstract

We construct entanglement witnesses with regard to the geometric structure of the Hilbert--Schmidt space and investigate the geometry of entanglement. In particular, for a two--parameter family of two--qutrit states that are part of the magic simplex we calculate the Hilbert--Schmidt measure of entanglement. We present a method to detect bound entanglement which is illustrated for a three--parameter family of states. In this way we discover new regions of bound entangled states. Furthermore we outline how to use our method to distinguish entangled from separable states.

arXiv comment23 pages, 8 figures

References in corpus (27)

• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Separability criterion and inseparable mixed states with positive partial transposition
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Bell Inequalities and the Separability Criterion
• Information-theoretic aspects of quantum inseparability of mixed states
• Entanglement Measures under Symmetry
• Bound entanglement can be activated
• Bloch vectors for qudits
• An improved bound on distillable entanglement
• All Teleportation and Dense Coding Schemes
• Some Properties of the Computable Cross Norm Criterion for Separability
• Entanglement measures and the Hilbert-Schmidt distance
• A Geometric Picture of Entanglement and Bell Inequalities
• The state space for two qutrits has a phase space structure in its core
• A new entanglement measure induced by the Hilbert-Schmidt norm
• A special simplex in the state space for entangled qudits
• The geometry of bipartite qutrits including bound entanglement
• Optimal Entanglement Witnesses for Qubits and Qutrits
• A separability criterion for density operators
• On the geometry of entangled states
• Geometric entanglement witnesses and bound entanglement
• Bound entanglement in the magic simplex of two--qutrits
• Why Two Qubits Are Special
• Dynamical transition for a particle in a squared Gaussian potential
• Robustness of entangled states that are positive under partial transposition
• Characterizing entanglement with geometric entanglement witnesses

Cited by in corpus (23)

• Entanglement detection
• Entanglement witnesses: construction, analysis and classification
• Geometry of the generalized Bloch sphere for qutrits
• Entanglement or separability: The choice of how to factorize the algebra of a density matrix
• Quantum simulation of quantum channels in nuclear magnetic resonance
• Free versus Bound Entanglement: Machine learning tackling a NP-hard problem
• Complementarity Reveals Bound Entanglement of Two Twisted Photons
• Entanglement witnesses from mutually unbiased bases
• Quantumness of spin-1 states
• Bound entangled states fit for robust experimental verification
• Witnessing Negative Conditional Entropy
• A geometric comparison of entanglement and quantum nonlocality in discrete systems
• How many mutually unbiased bases are needed to detect bound entangled states?
• Restricted numerical shadow and geometry of quantum entanglement
• A class of symmetric Bell diagonal entanglement witnesses - a geometric perspective
• Quantitative bound entanglement in two-qutrit states
• A class of Bell diagonal entanglement witnesses in ${\mathbb{C}}^4\otimes {\mathbb{C}}^4$: optimization and the spanning property
• John Bell and the Nature of the Quantum World
• A general dichotomization procedure to provide qudits entanglement criteria
• Characterizing generalized axisymmetric quantum states in $d\times d$ systems
• Bures and Hilbert-Schmidt 2 x 2 Determinantal Moments
• Quantum Entanglement and Geometry
• Weyl's Relations, Integrable Matrix Models and Quantum Computation