Majorana representation for mixed states

Abstract

We generalize the Majorana stellar representation of spin-$s$ pure states to mixed states, and in general to any hermitian operator, defining a bijective correspondence between three spaces: the spin density-matrices, a projective space of homogeneous polynomials of four variables, and a set of equivalence classes of points (constellations) on spheres of different radii. The representation behaves well under rotations by construction, and also under partial traces where the reduced density matrices inherit their constellation classes from the original state $\rho$. We express several concepts and operations related to density matrices in terms of the corresponding polynomials, such as the anticoherence criterion and the tensor representation of spin-$s$ states described in [1].

References in corpus (29)

• Three qubits can be entangled in two inequivalent ways
• Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• The Thermodynamical Limit of the Lipkin-Meshkov-Glick Model
• Classifying Novel Phases of Spinor Atoms
• Classicality of spin states
• Quantifying Quantumness and the Quest for Queens of Quantum
• Optimal state for keeping reference frames aligned and the Platonic solids
• Tensor Representation of Spin States
• Classifying Vortices in S=3 Bose-Einstein Condensates
• Quantum metrology at the limit with extremal Majorana constellations
• Quantum-limited Euler angle measurements using anticoherent states
• Parametrizations of density matrices
• Inert states of spin-S systems
• N-qubit states as points on the Bloch sphere
• The Extended Bloch Representation of Quantum Mechanics. Explaining Superposition, Interference and Entanglement
• Multipolar hierarchy of efficient quantum polarization measures
• Geometry of spin coherent states
• Anticoherence of spin states with point group symmetries
• Quantumness of spin-1 states
• Partial transpose criteria for symmetric states
• Anticoherence measures for pure spin states
• Absolutely classical spin states
• Polynomial method to study the entanglement of pure N-qubit states
• Four remarks on spin coherent states
• Parametrization of spin-1 classical states
• Optimal measurement strategies for fast entanglement detection
• Genuinely entangled symmetric states with no $N$-partite correlations
• Geometric Multiaxial Representation of N-qubit Mixed Symmetric Separable States

Cited by in corpus (15)

• The shape of higher-dimensional state space: Bloch-ball analog for a qutrit
• Entanglement in highly symmetric multipartite quantum states
• Majorana representation of adiabatic and superadiabatic processes in three-level systems
• Symmetric Multiqudit States: Stars, Entanglement, Rotosensors
• Three-Tangle of a General Three-Qubit State in the Representation of Majorana Stars
• Quantum Polarimetry
• Absolute separability witnesses for symmetric multiqubit states
• Platonic dynamical decoupling sequences for interacting spin systems
• Metastable spin-phase diagrams in antiferromagnetic Bose-Einstein condensates
• A Floquet analysis perspective of driven light-matter interaction models
• Phase characterization of spinor Bose-Einstein condensates: a Majorana stellar representation approach
• Dynamical decoupling of interacting spins through group factorization
• Thermal effects on the spin domain phases of high spin-f Bose-Einstein condensates with rotational symmetries
• Entangling power of symmetric multiqubit systems: a geometrical approach
• Coherent Generation and Protection of Anticoherent Spin States