Anticoherence measures for pure spin states

Abstract

The set of pure spin states with vanishing spin expectation value can be regarded as the set of the less coherent pure spin states. This set can be divided into a finite number of nested subsets on the basis of higher order moments of the spin operators. This subdivision relies on the notion of anticoherent spin state to order $t$: A spin state is said to be anticoherent to order $t$ if the moment of order $k$ of the spin components along any directions are equal for $k=1,2,\dots ,t$. Most spin states are neither coherent nor anticoherent, but can be arbitrary close to one or the other. In order to quantify the degree of anticoherence of pure spin states, we introduce the notion of anticoherence measures. By relying on the mapping between spin-$j$ states and symmetric states of $2j$ spin-$1/2$ (Majorana representation), we present a systematic way of constructing anticoherence measures to any order. We briefly discuss their connection with measures of quantum coherence. Finally, we illustrate our measures on various spin states and use them to investigate the problem of the existence of anticoherent spin states with degenerated Majorana points.

References in corpus (32)

• Quantifying Coherence
• Operational Families of Entanglement Classes for Symmetric $N$-Qubit States
• Multiqubit symmetric states with high geometric entanglement
• The maximally entangled symmetric state in terms of the geometric measure
• On the effective size of certain "Schrödinger cat'' like states
• Classicality of spin states
• Quantifying Quantumness and the Quest for Queens of Quantum
• Entanglement in the symmetric sector of $n$ qubits
• Quantum degrees of polarization
• Optimal state for keeping reference frames aligned and the Platonic solids
• Nonlocality of Symmetric States
• Quantum geometric phase in Majorana's stellar representation: Mapping onto a many-body Aharonov-Bohm phase
• Tensor Representation of Spin States
• Representation of Berry phase by the trajectories of Majorana stars
• Barycentric measure of quantum entanglement
• Inert states of spin-S systems
• Critical sets of the total variance of state detect all SLOCC entanglement classes
• Multiqubit symmetric states with maximally mixed one-qubit reductions
• Classification of Entanglement in Symmetric States
• Multipolar hierarchy of efficient quantum polarization measures
• Anticoherence of spin states with point group symmetries
• Quantumness of spin-1 states
• Quantification of entanglement via uncertainties
• Characterization of symmetry-protected topological phases in polymerized models by trajectories of Majorana stars
• Bloch sphere representation of three-vertex geometric phases
• SU(2)-invariant depolarization of quantum states of light
• Geometric description of modular and weak values in discrete quantum systems using the Majorana representation
• On entanglement in neutrino mixing and oscillations
• Entanglement, local measurements, and symmetry
• Entanglement of a Single Spin-1 Object: An Example of Ubiquitous Entanglement
• Anticoherent Subspaces
• Coherent control of phase diffusion in a Bosonic Josephson junction by scattering length modulation

Cited by in corpus (21)

• Quantum-limited Euler angle measurements using anticoherent states
• Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States
• Geometry of spin coherent states
• Majorana representation for mixed states
• Extreme depolarization for any spin
• Symmetric Multiqudit States: Stars, Entanglement, Rotosensors
• Generating a 4-photon Tetrahedron State: Towards Simultaneous Super-sensitivity to Non-commuting Rotations
• Quantum metrology of rotations with mixed spin states
• Nonclassical states that generate zero entanglement with a beam splitter
• 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
• Superselection rules and bosonic quantum computational resources
• Parity symmetry breaking of spin-$j$ coherent state superpositions in Gaussian noise channel
• Speed excess and total acceleration: a kinematical approach to entanglement
• Stellar representation of extremal Wigner-negative spin states
• Coherent Generation and Protection of Anticoherent Spin States
• Entangling power of symmetric multiqubit systems: a geometrical approach
• Thermal effects on the spin domain phases of high spin-f Bose-Einstein condensates with rotational symmetries
• Universality in fidelity-based quantum metrology
• Spin coherence scale: operator-ordering sensitivity beyond the Heisenberg-Weyl group
• Non-Gaussianity from superselection rules