Phase-space elementary information content of confined Dirac spinors
arXiv:2006.07255 · doi:10.1140/epjp/s13360-020-00692-2
Abstract
Reporting about the Wigner formalism for describing Dirac spinor structures through a covariant phase-space formulation, the quantum information quantifiers for purity and mutual information involving spin-parity (discrete) and position-momentum (continuous) degrees of freedom are consistently obtained. For Dirac spinor Wigner operators decomposed into Poincaré classes of spinor couplings, a definitive expression for quantum purity is identified in a twofold way: firstly, in terms of phase-space positively defined quantities, and secondly, in terms of the {\em spin-parity traced-out} associated density matrix in the position coordinate representation, both derived from the original Lorentz covariant phase-space Wigner representation. Naturally, such a structure supports the computation of relative (linear) entropies respectively associated to discrete (spin-parity) and continuous (position-momentum) degrees of freedom. The obtained theoretical tools are used for quantifying (relative) purities, mutual information as well as, by means of the quantum concurrence quantifier, the spin-parity quantum entanglement, for a charged fermion trapped by a uniform magnetic field which, by the way, has the phase-space structure completely described in terms of Laguerre polynomials associated to the quantized Landau levels. Our results can be read as the first step in the systematic computation of the elementary information content of Dirac-like systems exhibiting some kind of confining behavior.
arXiv comment27 pages, 3 figures
References in corpus (59)
- Spintronics: Fundamentals and applications
- Quantum entanglement
- Entanglement of Formation of an Arbitrary State of Two Qubits
- The electronic properties of bilayer graphene
- An Open-System Quantum Simulator with Trapped Ions
- 14-qubit entanglement: creation and coherence
- Electronic properties of graphene-based bilayer systems
- Onset of a Quantum Phase Transition with a Trapped Ion Quantum Simulator
- Quantum optics in the phase space - A tutorial on Gaussian states
- Long-lived qubit memory using atomic ions
- 'Designer atoms' for quantum metrology
- Microwave quantum logic gates for trapped ions
- Quantum Entanglement of Moving Bodies
- Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
- Quantum entropy and special relativity
- Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal
- Quantum simulation of open-system dynamical maps with trapped ions
- Relativistic Quantum Teleportation with Superconducting Circuits
- Entropy and Wigner Functions
- Relativistic entanglement and Bell's inequality
- Relativistic entanglement of two massive particles
- Local Detection of Quantum Correlations with a Single Trapped Ion
- Relativistic Einstein-Podolsky-Rosen correlation and Bell's inequality
- Klein tunneling and Dirac potentials in trapped ions
- Quantum frequency estimation with trapped ions and atoms
- Relativistic quantum mechanics with trapped ions
- Lorentz-covariant reduced spin density matrix and EPR-Bohm correlations
- Disentangling covariant Wigner functions for chiral fermions
- Relativistically invariant quantum information
- Comment on "Quantum entropy and special relativity" [by A. Peres, P. F. Scudo, and D. R. Terno, Phys. Rev. Lett. 88, 230402 (2002)]
- Absence of equilibrium chiral magnetic effect
- Wigner flow reveals topological order in quantum phase space dynamics
- Lorentz transformations that entangle spins and entangle momenta
- Black Holes and Phase Space Noncommutativity
- Wigner transformation, momentum space topology, and anomalous transport
- Entanglement and nonlocality of a single relativistic particle
- Probing phase-space noncommutativity through quantum beating, missing information and the thermodynamic limit
- Entanglement due to noncommutativity in the phase-space
- Phase-space noncommutative formulation of Ozawa's uncertainty principle
- Tachyon physics with trapped ions
- A physical framework for the Earth System, the Anthropocene Equation and the Great Acceleration
- Probing phase-space noncommutativity through quantum mechanics and thermodynamics of free particles and quantum rotors
- Trigonal Warping in Bilayer Graphene: Energy versus Entanglement Spectrum
- Lattice-layer entanglement in Bernal-stacked bilayer graphene
- Phase-space noncommutative extension of the Robertson-Schroedinger formulation of Ozawa's uncertainty principle
- Entanglement of Dirac bi-spinor states driven by Poincaré classes of $\mbox{SU}(2) \otimes \mbox{SU}(2)$ coupling potentials
- Global Dirac bispinor entanglement under Lorentz boosts
- Bell operator and Gaussian squeezed states in noncommutative quantum mechanics
- Non-classicality from the phase-space flow analysis of the Weyl-Wigner quantum mechanics
- Behaviour of entanglement and Cooper pairs under relativistic boosts
- Relativistic dynamics compels a thermalized Fermi gas to a unique intrinsic parity eigenstate
- Wigner's representation of quantum mechanics in integral form and its applications
- Quantum to classical transition in the Hořava-Lifshitz quantum cosmology
- Generation of maximally entangled states with sub-luminal Lorentz boost
- Quantum transitions and quantum entanglement from Dirac-like dynamics simulated by trapped ions
- Testing non-classicality with exact Wigner currents for an anharmonic quantum system
- Trapped ion emulation of electric dipole moment of neutral relativistic particles
- Coherent quantum squeezing due to the phase space noncommutativity
- Collapsing Shells and Black Holes: a quantum analysis