Quantumness of spin-1 states

Abstract

We investigate quantumness of spin-1 states, defined as the Hilbert-Schmidt distance to the convex hull of spin coherent states. We derive its analytic expression in the case of pure states as a function of the smallest eigenvalue of the Bloch matrix and give explicitly the closest classical state for an arbitrary pure state. Numerical evidence is provided that the exact formula for pure states provides an upper bound on the quantumness of mixed states. Due to the connection between quantumness and entanglement we obtain new insights into the geometry of symmetric entangled states.

References in corpus (6)

• The geometric measure of entanglement for symmetric states
• Multiqubit symmetric states with high geometric entanglement
• Entanglement witnesses and geometry of entanglement of two--qutrit states
• Tensor Representation of Spin States
• Unpolarized states and hidden polarization
• Detection and typicality of bound entangled states

Cited by in corpus (13)

• Geometry of spin coherent states
• Partial transpose criteria for symmetric states
• Majorana representation for mixed states
• Anticoherence measures for pure spin states
• Entanglement and the truncated moment problem
• Absolutely classical spin states
• Symmetric Multiqudit States: Stars, Entanglement, Rotosensors
• Tensor eigenvalues and entanglement of symmetric states
• Modular-value-based metrology with spin coherent pointers
• Fortran code for generating random probability vectors, unitaries, and quantum states
• Maximum entanglement of mixed symmetric states under unitary transformations
• Geometric Multiaxial Representation of N-qubit Mixed Symmetric Separable States
• Regularly Decomposable Tensors and Classical Spin States