Entanglement and Discord of superposition of Greenberger-Horne-Zeilinger states

Abstract

We calculate the analytic expression for geometric measure of entanglement for arbitrary superposition of two $N$-qubit canonical orthonormal Greenberger-Horne-Zeilinger ($GHZ$) states and the same for two $W$ states. In course of characterizing all kinds of nonclassical correlations, explicit formula for quantum discord (via relative entropy) for the former class of states has been presented. Contrary to the $GHZ$ state, the closest separable state to the $W$ state is not classical. Therefore, in this case the discord is different from the relative entropy of entanglement. We conjecture that the discord for the $N$-qubit $W$ state is ${\log }_{2}N$.

7 pages (2 columns), 2 figures

References in corpus (31)

• Entanglement detection
• Quantum discord and the power of one qubit
• Quantum discord for two-qubit X-states
• Unified View of Quantum and Classical Correlations
• Universal resources for measurement-based quantum computation
• Quantum Discord and the Geometry of Bell-Diagonal States
• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• The geometric measure of entanglement for symmetric states
• Multiqubit symmetric states with high geometric entanglement
• Witnessing quantum discord in 2 x N systems
• Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
• Fundamentals of universality in one-way quantum computation
• Visualizing elusive phase transitions with geometric entanglement
• Geometric measure of entanglement for pure multipartite states
• Closed formula for the relative entropy of entanglement
• Maximally entangled three-qubit states via geometric measure of entanglement
• Additivity and non-additivity of multipartite entanglement measures
• Geometric Entanglement in a One-Dimensional Valence Bond Solid State
• Relative entropy of entanglement for certain multipartite mixed states
• Connecting the generalized robustness and the geometric measure of entanglement
• Bounds on Negativity of Superpositions
• Concurrence of superposition
• Analytic Expressions for Geometric Measure of Three Qubit States
• Closed formula for the relative entropy of entanglement in all dimensions
• Difficulties in analytic computation for relative entropy of entanglement
• Reexamination of entanglement of superpositions
• Bounds on the multipartite entanglement of superpositions
• Duality and the geometric measure of entanglement of general multiqubit W states
• Analytical formula connecting entangled state and the closest disentangled state
• Multipartite entanglement of superpositions
• On the Geometric Measures of Entanglement

Cited by in corpus (14)

• The classical-quantum boundary for correlations: discord and related measures
• Theoretical and experimental aspects of quantum discord and related measures
• Building separable approximations for quantum states via neural networks
• Genuine multipartite system-environment correlations in decoherent dynamics
• Quantum Correlation in One-dimensional Extend Quantum Compass Model
• Various Correlations in Anisotropic Heisenberg XYZ Model with Dzyaloshinski-Moriya Interaction
• Entanglement swapping for Bell states and Greenberger-Horne-Zeilinger states in qubit systems
• Genuine Multipartite Entanglement of Superpositions
• Separability and entanglement in superpositions of quantum states
• Various correlations in a Heisenberg XXZ spin chain both in thermal equilibrium and under the intrinsic decoherence
• Geometric entanglement in the Laughlin wave function
• Distribution of Standard deviation of an observable among superposed states
• To share and not share a singlet: control qubit and nonclassicality in teleportation
• Unconditionally superposition-robust entangled state in all multiparty quantum systems