Tight lower bound on geometric discord of bipartite states

Abstract

We use singular value decomposition to derive a tight lower bound for geometric discord of arbitrary bipartite states. In a single shot this also leads to an upper bound of measurement-induced non locality which in turn yields that for Werner and isotropic states the two measures coincide. We also emphasize that our lower bound is saturated for all $2\otimes n$ states. Using this we show that both the generalized Greenberger-Horne-Zeilinger and $W$ states of $N$ qubits satisfy monogamy of geometric discord. Indeed, the same holds for all $N$-qubit pure states which are equivalent to $W$ states under stochastic local operations and classical communication. We show by giving an example that not all pure states of four or higher qubits satisfy monogamy.

4 pages

References in corpus (4)

• Necessary and sufficient condition for non-zero quantum discord
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Bloch vectors for qudits
• Transformations of $W$-Type Entangled States

Cited by in corpus (7)

• Evolution of Quantum Discord and its Stability in Two-Qubit NMR Systems
• Multipartite Quantum Correlations in Open Quantum Systems
• Quantum discord in quantum random access codes and its connection with dimension witness
• Correlation evolution and monogamy of two geometric quantum discords in multipartite systems
• Geometric quantum discord of an arbitrary two-qudit state: the exact value and general upper bounds
• Multipartite Generalization of Geometric measure of Discord
• Correlation and Entanglement dynamics for two atoms distributed in two isolated thermal cavities