Polytopes of Absolutely Wigner Bounded Spin States
arXiv:2304.09006 · doi:10.22331/q-2024-12-04-1550
Abstract
Quasiprobability has become an increasingly popular notion for characterising non-classicality in quantum information, thermodynamics, and metrology. Two important distributions with non-positive quasiprobability are the Wigner function and the Glauber-Sudarshan function. Here we study properties of the spin Wigner function for finite-dimensional quantum systems and draw comparisons with its infinite-dimensional analog, focusing in particular on the relation to the Glauber-Sudarshan function and the existence of absolutely Wigner-bounded states. More precisely, we investigate unitary orbits of mixed spin states that are characterized by Wigner functions lower-bounded by a specified value. To this end, we extend a characterization of the set of absolutely Wigner positive states as a set of linear eigenvalue constraints, which together define a polytope centred on the maximally mixed state in the simplex of spin- states. The lower bound determines the relative size of such absolutely Wigner bounded (AWB) polytopes and we study their geometric characteristics. In each dimension a Hilbert-Schmidt ball representing a tight purity-based sufficient condition to be AWB is exactly determined, while another ball representing a necessary condition to be AWB is conjectured. Special attention is given to the case where the polytope separates orbits containing only positive Wigner functions from other orbits because of the use of Wigner negativity as a witness of non-classicality. Comparisons are made to absolute symmetric state separability and spin Glauber-Sudarshan positivity, with additional details given for low spin quantum numbers.
17 pages, 8 figures [published version in Quantum]
References in corpus (37)
- Three qubits can be entangled in two inequivalent ways
- Atom chip based generation of entanglement for quantum metrology
- Contextuality supplies the magic for quantum computation
- The Resource Theory of Stabilizer Computation
- Positive Wigner functions render classical simulation of quantum computation efficient
- Negative Quasi-Probability as a Resource for Quantum Computation
- Resource theory of quantum non-Gaussianity and Wigner negativity
- Phase-space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries
- Entanglement with Negative Wigner Function of Three Thousand Atoms Heralded by One Photon
- Estimating outcome probabilities of quantum circuits using quasiprobabilities
- Convex resource theory of non-Gaussianity
- Quantifying the magic of quantum channels
- Classicality of spin states
- A General Theory of Phase-Space Quasiprobability Distributions
- Equivalence between contextuality and negativity of the Wigner function for qudits
- Discrete Moyal-type Representations for a Spin
- Overview of the phase space formulation of quantum mechanics with application to quantum technologies
- Uniqueness of noncontextual models for stabilizer subtheories
- Continuous phase-space representations for finite-dimensional quantum states and their tomography
- Quasiprobabilities in quantum thermodynamics and many-body systems
- Tomographic reconstruction of the Wigner function on the Bloch sphere
- Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements
- Phase-Space Methods for Simulating the Dissipative Many-Body Dynamics of Collective Spin Systems
- Tests of multimode quantum non-locality with homodyne measurements
- Hybrid discrete-continuous truncated Wigner approximation for driven, dissipative spin systems
- Collective Radiative Interactions in the Discrete Truncated Wigner Approximation
- Partial transpose criteria for symmetric states
- Wigner negativity in spin- systems
- Contracting the Wigner-Kernel of a Spin to the Wigner-Kernel of a Particle
- Quantum state tomography of a single electron spin in diamond with Wigner reconstruction
- Absolutely classical spin states
- Spectral Properties of Symmetric Quantum States and Symmetric Entanglement Witnesses
- On the family of Wigner functions for N-level quantum system
- Absolute separability witnesses for symmetric multiqubit states
- Maximum entanglement of mixed symmetric states under unitary transformations
- Kenfack Zyczkowski indicator of nonclassicality for two non-equivalent representations of Wigner function of qutrit
- On measures of classicality/quantumness in quasiprobability representations of finite-dimensional quantum systems