Logarithmic negativity: a full entanglement monotone that is not convex.

By Martin Bodo Plenio. Physical Review Letters, 2005

1,218 citations recorded by the source corpus.

It is proven that logarithmic negativity does not increase on average under a general positive partial transpose preserving operation (a set of operations that incorporate local operations and classical communication as a subset) and, in the process, a further proof is provided that the negativity does not increase on average under the same set of operations. Given that the logarithmic negativity is not a convex function this result is surprising, as it is generally considered that convexity describes the local physical process of losing information. The role of convexity and, in particular, its relation (or lack thereof) to physical processes is discussed and importance of continuity in this context is stressed.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/64435b0cfa00fafcfdca6d566eaca7dd6a824169

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Citations in the corpus

The resource theory of stabilizer quantum computation (2013, background): “Although convexity is a desirable feature it is possible to have interesting and useful monotones that are not convex (for example, the logarithmic entanglement negativity[39]).”
Gaussian quantum information (2011, background): “It was shown to be an entanglement monotone (Eisert, 2001; Plenio, 2005) and an upper bound of Dð̂Þ (Vidal and Werner, 2002).”
Quantum resource theories (2018, background): “However, as pointed out by Plenio and Virmani, this model for forgetting information is too simplistic (Plenio, 2005; Plenio and Virmani, 2007).”
Entanglement certification from theory to experiment (2018, methodology): “[79] Martin B.”
Entanglement detection (2008, background): “The logarithmic negativity is, however, not convex anymore [273].”