bibkey: gachechiladzewyderkaguhne2018ultrafine
authors: Gachechiladze, Mariami; Wyderka, Nikolai; Gühne, Otfried
year: 2018
title: "The structure of ultrafine entanglement witnesses"
doi: 10.1088/1751-8121/aad3dc
url: "https://arxiv.org/abs/1805.06404v2"
claim: "The paper characterizes when two product observables are useful for entanglement detection (necessary and sufficient for two qubits, with counterexamples for two qutrits), proves that a pair whose local factors commute on one side is useless, and asks for three product observables each pair of which is useless while the triple is useful."
strata_touched:
  - D5/S3/Quantum/Measurements/UltrafineThreeProductObservables
license: citation-only
triage: anchor

Gachechiladze, Wyderka and Gühne, The structure of ultrafine entanglement witnesses

M. Gachechiladze, N. Wyderka and O. Gühne, J. Phys. A: Math. Theor. 51, 365307 (2018), DOI 10.1088/1751-8121/aad3dc; arXiv:1805.06404v2. Quotations are from the arXiv v2 TeX source uew-iop-revision.tex; macros are expanded.

“The set of separable states is defined as the convex hull of all pure product states” (l. 113), and the observables considered are product observables $L=L_A\otimes L_B$, $C=C_A\otimes C_B$ (l. 156–157). A pair of observables is useless for entanglement detection when all possible combinations of their expectation values can originate from separable states (l. 504–507); in particular a pair with $[L_A,C_A]=0$ is useless (l. 679–683). The Summary asks (l. 748–752):

For instance, it would be interesting to identify three product observables, for which each pair is useless for entanglement detection, but the whole triple is useful.

Verified locator

• DOI: https://doi.org/10.1088/1751-8121/aad3dc
• Source: https://arxiv.org/abs/1805.06404v2