Dissecting the qutrit

Abstract

To visualize a higher dimensional object it is convenient to consider its two-dimensional cross-sections. The set of quantum states for a three level system has eight dimensions. We supplement a recent paper by Goyal et al by considering the set of all possible two-dimensional cross-sections of the qutrit. Each such cross-section is bounded by a plane cubic curve.

12 pages, 4 figures

References in corpus (6)

• The Bloch Vector for N-Level Systems
• Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation
• The structure of reversible computation determines the self-duality of quantum theory
• Restricted numerical range: a versatile tool in the theory of quantum information
• Numerical shadow and geometry of quantum states
• Quantum Convex Support

Cited by in corpus (7)

• The shape of higher-dimensional state space: Bloch-ball analog for a qutrit
• Classification of joint numerical ranges of three hermitian matrices of size three
• Exploring the geometry of qutrit state space using symmetric informationally complete probabilities
• Qutrit and Ququint Magic States
• Relative volume of separable bipartite states
• Generalized Two-Qubit Whole and Half Hilbert-Schmidt Separability Probabilities
• Correlation constraints and the Bloch geometry of two qubits