90 research outputs found
Quantifying mixed-state quantum entanglement by optimal entanglement witness
We develop an approach of quantifying entanglement in mixed quantum states by
the optimal entanglement witness operator. We identify the convex set of mixed
states for which a single witness provides the exact value of an entanglement
measure, and show that the convexity, properties, and symmetries of
entanglement or of a target state considerably fix the form of the optimal
witness. This greatly reduces difficulty in computing and experimentally
determining entanglement measures. As an example, we show how to experimentally
quantify bound entanglement in four-qubit noisy Smolin states and three-qubit
Greenberger-Horne-Zeilinger (GHZ) entanglement under white noise. For general
measures and states, we provide a numerical method to efficiently optimize
witness.Comment: Supplemental material is include
Minimax optimization of entanglement witness operator for the quantification of three-qubit mixed-state entanglement
We develop a numerical approach for quantifying entanglement in mixed quantum
states by convex-roof entanglement measures, based on the optimal entanglement
witness operator and the minimax optimization method. Our approach is
applicable to general entanglement measures and states and is an efficient
alternative to the conventional approach based on the optimal pure-state
decomposition. Compared with the conventional one, it has two important merits:
(i) that the global optimality of the solution is quantitatively verifiable,
and (ii) that the optimization is considerably simplified by exploiting the
common symmetry of the target state and measure. To demonstrate the merits, we
quantify Greenberger-Horne-Zeilinger (GHZ) entanglement in a class of
three-qubit full-rank mixed states composed of the GHZ state, the W state, and
the white noise, the simplest mixtures of states with different genuine
multipartite entanglement, which have not been quantified before this work. We
discuss some general properties of the form of the optimal witness operator and
of the convex structure of mixed states, which are related to the symmetry and
the rank of states
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