Tensor Representation of Spin States

Abstract

We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch vectors. Our representation, based on covariant matrices introduced by Weinberg in the context of quantum field theory, allows for a simple parametrization of coherent spin states, and a straightforward transformation of density matrices under local unitary and partial tracing operations. It enables us to provide a criterion for anticoherence, relevant in a broader context such as quantum polarization of light.

5 pages + 7 pages of supplementary information

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Cited by in corpus (35)

• Extremal quantum states and their Majorana constellations
• Quantum-limited Euler angle measurements using anticoherent states
• Extremal quantum states
• Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States
• Anticoherence of spin states with point group symmetries
• Geometry of spin coherent states
• Partial transpose criteria for symmetric states
• Quantumness of spin-1 states
• Majorana representation for mixed states
• Analysis of continuous and discrete Wigner approximations for spin dynamics
• Anticoherence measures for pure spin states
• Entanglement and the truncated moment problem
• Extreme depolarization for any spin
• Tensor eigenvalues and entanglement of symmetric states
• Three-Tangle of a General Three-Qubit State in the Representation of Majorana Stars
• Quantum metrology of rotations with mixed spin states
• Modular-value-based metrology with spin coherent pointers
• Geometric representation of spin correlations and applications to ultracold systems
• Optimal measurement strategies for fast entanglement detection
• Genuinely entangled symmetric states with no $N$-partite correlations
• Coherent-State Approach for Majorana representation
• Quantum Estimation of the Stokes Vector Rotation for a General Polarimetric Transformation
• Orthonormal bases of extreme quantumness
• Correlations for subsets of particles in symmetric states: what photons are doing within a beam of light when the rest are ignored
• All possible permutational symmetries of a quantum system
• Berry phases of higher spins due to internal geometry of Majorana constellation and relation to quantum entanglement
• Stellar representation of extremal Wigner-negative spin states
• 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
• Invariant Vector and Majorana Star Representations of Qutrit States
• Multiqubit monogamy relations beyond shadow inequalities
• Universality in fidelity-based quantum metrology
• Regularly Decomposable Tensors and Classical Spin States
• Spin coherence scale: operator-ordering sensitivity beyond the Heisenberg-Weyl group
• Entanglement in the symmetric subspace: mapping multipartite to bipartite states