Faithful Squashed Entanglement
Fernando G. S. L. Brandao, Matthias Christandl, Jon Yard

TL;DR
This paper proves that squashed entanglement is a faithful measure of entanglement, strictly positive for entangled states, and explores its implications for quantum complexity theory.
Contribution
It establishes a lower bound for squashed entanglement based on the distance to separable states, proving its faithfulness and connecting it to quantum information measures.
Findings
Squashed entanglement is strictly positive iff the state is entangled.
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Abstract
Squashed entanglement is a measure for the entanglement of bipartite quantum states. In this paper we present a lower bound for squashed entanglement in terms of a distance to the set of separable states. This implies that squashed entanglement is faithful, that is, strictly positive if and only if the state is entangled. We derive the bound on squashed entanglement from a bound on quantum conditional mutual information, which is used to define squashed entanglement and corresponds to the amount by which strong subadditivity of von Neumann entropy fails to be saturated. Our result therefore sheds light on the structure of states that almost satisfy strong subadditivity with equality. The proof is based on two recent results from quantum information theory: the operational interpretation of the quantum mutual information as the optimal rate for state redistribution and the interpretation…
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