Monogamy of entanglement without inequalities

Gilad Gour1 and Guo Yu2

1Department of Mathematics and Statistics and Institute for Quantum Science and Technology, University of Calgary, Calgary, Alberta T2N 1N4, Canada
2Institute of Quantum Information Science, Shanxi Datong University, Datong, Shanxi 037009, China

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Abstract

We provide a fine-grained definition for monogamous measure of entanglement that does not invoke any particular monogamy relation. Our definition is given in terms an equality, as oppose to inequality, that we call the "disentangling condition". We relate our definition to the more traditional one, by showing that it generates standard monogamy relations. We then show that all quantum Markov states satisfy the disentangling condition for any entanglement monotone. In addition, we demonstrate that entanglement monotones that are given in terms of a convex roof extension are monogamous if they are monogamous on pure states, and show that for any quantum state that satisfies the disentangling condition, its entanglement of formation equals the entanglement of assistance. We characterize all bipartite mixed states with this property, and use it to show that the G-concurrence is monogamous. In the case of two qubits, we show that the equality between entanglement of formation and assistance holds if and only if the state is a rank 2 bipartite state that can be expressed as the marginal of a pure 3-qubit state in the W class.

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The above citations are from Crossref's cited-by service (last updated successfully 2023-09-21 20:23:05) and SAO/NASA ADS (last updated successfully 2023-09-21 20:23:06). The list may be incomplete as not all publishers provide suitable and complete citation data.