Tensor representation of spin States.

@article{Giraud2015TensorRO,
  title={Tensor representation of spin States.},
  author={Olivier Giraud and Daniel Braun and Dorian Baguette and T Bastin and J. Mart{\'i}n},
  journal={Physical review letters},
  year={2015},
  volume={114 8},
  pages={
          080401
        }
}
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… 
Majorana representation for mixed states
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
Coherent-State Approach for Majorana representation
By representing a quantum state and its evolution with the majorana stars on the Bloch sphere, the Majorana representation (MR) provide us an intuitive way to study a physical system with SU(2)
Geometry of spin coherent states
Spin states of maximal projection along some direction in space are called (spin) coherent, and are, in many aspects, the "most classical" available. For any spin $s$, the spin coherent states form a
Extremal quantum states and their Majorana constellations
The characterization of quantum polarization of light requires knowledge of all the moments of the Stokes variables, which are appropriately encoded in the multipole expansion of the density matrix.
Stars of the quantum Universe : extremal constellations on the Poincare sphere
The characterization of the polarization properties of a quantum state requires the knowledge of the joint probability distribution of the Stokes variables. This amounts to assessing all the moments
All possible permutational symmetries of a quantum system
We investigate the intermediate permutational symmetries of a system of qubits, that lie in between the perfect symmetric and antisymmetric cases. We prove that, on average, pure states of qubits
Geometric representation of spin correlations and applications to ultracold systems
We provide a one-to-one map between the spin correlations and certain three-dimensional shapes, analogous to the map between single spins and Bloch vectors, and demonstrate its utility. Much as one
Majorana decomposition for two-qubit pure states
The Majorana representation (MR), which represents a quantum state and its evolution with the Majorana stars (MSs) on the Bloch sphere, provides us an intuitive way to study symmetric multiqubit pure
Berry phases of higher spins due to internal geometry of Majorana constellation and relation to quantum entanglement
Majorana stars, the antipodal directions associated with the coherent states that are orthogonal to a spin state, provide a visualization and a geometric understanding of the structures of general
Optimal Detection of Rotations by Coherent and Anticoherent States.
Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are
...
...

References

SHOWING 1-10 OF 81 REFERENCES
Positivity of the N × N density matrix expressed in terms of polarization operators
We use polarization operators known from the quantum theory of angular momentum to expand the (N × N)-dimensional density operators. Thereby we construct generalized Bloch vectors representing
Parametrization of spin-1 classical states
We give an explicit parametrization of the set of mixed quantum states and of the set of mixed classical states for a spin-1 Hilbert space. The boundary of the set of mixed classical states is
FEYNMAN RULES FOR ANY SPIN
The explicit Feynman rules are given for massive particles of any spin j, in both a 2j+1-component and a 2(2j+l)-component formalism. The propagators involve matrices which transform like symmetric
Geometry of entangled states, Bloch spheres and Hopf fibrations
We discuss a generalization of the standard Bloch sphere representation for a single qubit to two qubits, in the framework of Hopf fibrations of highdimensional spheres by lower dimensional spheres.
Central-moment description of polarization for quantum states of light
We present a moment expansion for the systematic characterization of the polarization properties of quantum states of light. Specifically, we link the method to the measurements of the Stokes
The Bloch-Vector Space for N-Level Systems: the Spherical-Coordinate Point of View
TLDR
A dual property of the space is found which provides an overall picture of thespace and three classes of quantum-state representations based on actual measurements and discuss their state-spaces are provided.
Entanglement and symmetry in permutation-symmetric states
We investigate the relationship between multipartite entanglement and symmetry, focusing on permutation symmetric states. We give a highly intuitive geometric interpretation to entanglement via the
Bloch vectors for qudits
TLDR
A new method to decompose density matrices via so-called standard matrices is presented, and a representation of an entanglement witness in terms of expectation values of spin-1 measurements is shown, appropriate for an experimental realization.
Spherical designs and anticoherent spin states
Anticoherent spin states are quantum states that exhibit maximally nonclassical behaviour in a certain sense. Any spin state whose Majorana representation is a Platonic solid is called a perfect
Quantum versus classical polarization states: when multipoles count
We advocate a simple multipole expansion of the polarization density matrix. The resulting multipoles are used to construct bona fide quasiprobability distributions that appear as a sum of successive
...
...