Tight lower bound on geometric discord of bipartite states

Details Tight lower bound on geometric discord of bipartite states Tight lower bound on geometric discord of bipartite states

2012-01-28

arxiv.org/abs/1201.5969v2

Phys. Rev. A 85, 024102 (2012)

Physics

Quantum Physics

4 pages

Scientific paper

10.1103/PhysRevA.85.024102

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.

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