01054nas a2200181   4500000000100000000000100001000000100002008004100003100001700044700002200061700002100083700002200104245006000126856005100186300001100237490000700248520061700255       2014                            d1 aŁ. Rudnicki1 aZbigniew Puchała1 aPaweł Horodecki1 aKarol Życzkowski00aConstructive entanglement test from triangle inequality  uhttps://doi.org/10.1088/1751-8113/47/42/424035  a4240350 v473 a<p>We derive a simple lower bound on the geometric measure of entanglement for mixed quantum states in the case of a general multipartite system. The main ingredient of the presented derivation is the triangle inequality applied to the root infidelity distance in the space of density matrices. The obtained bound leads to entanglement criteria with a straightforward interpretation. The proposed criteria provide an experimentally accessible, powerful entanglement test. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.</p>