Quantifying Quantumness and the Quest for Queens of Quantum

Abstract

We introduce a measure of ''quantumness'' for any quantum state in a finite dimensional Hilbert space, based on the distance between the state and the convex set of classical states. The latter are defined as states that can be written as a convex sum of projectors onto coherent states. We derive general properties of this measure of non-classicality, and use it to identify for a given dimension of Hilbert space what are the "Queen of Quantum" states, i.e. the most non-classical quantum states. In three dimensions we obtain the Queen of Quantum state analytically and show that it is unique up to rotations. In up to 11-dimensional Hilbert spaces, we find the Queen of Quantum states numerically, and show that in terms of their Majorana representation they are highly symmetric bodies, which for dimensions 5 and 7 correspond to Platonic bodies.

23 pages, 4 figures

References in corpus (7)

• Entanglement and permutational symmetry
• The geometric measure of entanglement for symmetric states
• Multiqubit symmetric states with high geometric entanglement
• Classicality of spin states
• Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
• Optimal state for keeping reference frames aligned and the Platonic solids
• Quantum Channels and Representation Theory

Cited by in corpus (55)

• Fisher information and multiparticle entanglement
• Exciton dynamics and Quantumness of energy transfer in the Fenna-Matthews-Olson complex
• Multiqubit symmetric states with high geometric entanglement
• The maximally entangled symmetric state in terms of the geometric measure
• Entanglement between identical particles is a useful and consistent resource
• Extremal quantum states and their Majorana constellations
• Tensor Representation of Spin States
• Quantum metrology at the limit with extremal Majorana constellations
• Quantum-limited Euler angle measurements using anticoherent states
• Two quantum walkers sharing coins
• Optimal and Variational Multi-Parameter Quantum Metrology and Vector Field Sensing
• Barycentric measure of quantum entanglement
• Improving the dynamics of quantum sensors with reinforcement learning
• Quantumness of noisy quantum walks: a comparison between measurement-induced disturbance and quantum discord
• Extremal quantum states
• Modal Majorana sphere and hidden symmetries of structured-Gaussian beams
• Classification of Entanglement in Symmetric States
• Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States
• Geometry of spin coherent states
• Anticoherence of spin states with point group symmetries
• Quantumness of spin-1 states
• Partial transpose criteria for symmetric states
• Majorana representation for mixed states
• Entanglement in highly symmetric multipartite quantum states
• Anticoherence measures for pure spin states
• Sub-Planck structures: Analogies between the Heisenberg-Weyl and SU(2) groups
• Nonclassicality of coherent states: Entanglement of joint statistics
• Unpolarized states and hidden polarization
• Absolutely classical spin states
• Symmetric Multiqudit States: Stars, Entanglement, Rotosensors
• Quantumness Beyond Entanglement: The Case of Symmetric States
• Tensor eigenvalues and entanglement of symmetric states
• Generating a 4-photon Tetrahedron State: Towards Simultaneous Super-sensitivity to Non-commuting Rotations
• Entangling power of symmetric two-qubit quantum gates
• Nonclassical states from the joint statistics of simultaneous measurements
• Four remarks on spin coherent states
• Quantum Polarimetry
• Parametrization of spin-1 classical states
• Optimal measurement strategies for fast entanglement detection
• Maximum entanglement of mixed symmetric states under unitary transformations
• Dynamics and quantumness of excitation energy transfer through a complex quantum network
• Symmetric quantum states: a review of recent progress
• Entanglement between total intensity and polarization for pairs of coherent states
• Quantum Estimation of the Stokes Vector Rotation for a General Polarimetric Transformation
• Orthonormal bases of extreme quantumness
• Equivalence of classicality and separability based on P phase-space representation of symmetric multiqubit states
• Superselection rules and bosonic quantum computational resources
• Finding maximal quantum resources
• Majorization of quantum polarization distributions
• Stellar representation of extremal Wigner-negative spin states
• Entangling power of symmetric multiqubit systems: a geometrical approach
• Minimal-noise estimation of noncommuting rotations of a spin
• Non-Gaussianity from superselection rules
• Spin coherence scale: operator-ordering sensitivity beyond the Heisenberg-Weyl group
• Polynomial deformations of $sl(2)$ and unified algebraic framework for solutions of a class of spin models