Entanglement Negativity of Spin-Orbit Correlations in a general Qubit-Qudit Setup

Abstract

We present the complete eigenvalue spectrum of the partially transposed density matrix for a pure bipartite quantum state acting on a generic $2\otimes n$ Hilbert space. The spectrum contains four non-zero eigenvalues, as, \begin{eqnarray} λ_{1,2}=\pm \sqrt{A}, ~~~ λ_{3,4}= \frac{1}{2}(1\pm\sqrt{1-4 A}), \nonumber \end{eqnarray} where $A$ is the determinant of the reduced density matrix (traced over the larger subspace). As $0⩽A⩽1/4$, only one is negative among the four non-trivial eigenvalues. Within this qubit-qudit framework, we further studied the negativity as a measure of entanglement for the case of spin-orbit correlation of partons inside a proton. The entanglement negativity for spin-orbit correlations is found to be related to the gluon helicity PDF and the Hermitian angle of the associated Hilbert space for linearly polarized protons.

References in corpus (19)

• Quantum entanglement
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Separability Criterion for Density Matrices
• A computable measure of entanglement
• Separability of Mixed States: Necessary and Sufficient Conditions
• Entanglement of a Pair of Quantum Bits
• Deep inelastic scattering as a probe of entanglement
• Convex-roof extended negativity as an entanglement measure for bipartite quantum systems
• Entanglement Suppression and Emergent Symmetries of Strong Interactions
• The Color Glass Condensate density matrix: Lindblad evolution, entanglement entropy and Wigner functional
• Lower Bound on Entanglement of Formation for the Qubit-Qudit System
• Gluon saturation and entropy production in proton proton collisions
• Entanglement entropy and entropy production in the Color Glass Condensate framework
• Dynamical entropy of dense QCD states
• Investigating entanglement entropy at small-x in DIS off protons and nuclei
• Partial transpose as a direct link between concurrence and negativity
• Rapidity evolution of the entanglement entropy in quarkonium: parton and string duality
• Entanglement as a probe of hadronization
• Quantum entanglement correlations in double quark PDFs