EkertOverlap

What a violation buys a key LENGTH: Lim et al.'s effective overlap

7/7 passed in 1ms

Test	What it does	Result
test_ceiling	A certified complementarity is never worth more than an assumed one, so the quality a CHSH value buys is at most the one bit pair_length reads off cbar = 1/2, with equality only at a maximal violation.	✅ pass
test_charge	The post-selection charge divides the whole excess over 1/2 by the surviving fraction, so it cannot help, and it cannot move a maximal violation.	✅ pass
test_crossing	The paper's Fig. 2 curves cross zero at the two surviving fractions its caption orders from left to right, so a coincidence-counted link, whose surviving fraction is its coincidence probability, is far below both.	✅ pass
test_endpoints	The certified overlap is exactly 1 at the local bound and exactly 1/2 at Tsirelson's, the value of a mutually unbiased qubit pair.	✅ pass
test_monotone	More violation certifies a smaller overlap across the whole domain, and the overlap never falls below the conjugate-pair value of 1/2.	✅ pass
test_secret	Feeding the charged overlap through the entropic uncertainty relation reproduces the paper's own Eq. (2) exactly, and at a maximal violation that fraction is BB84's 1 - 2h(Q), which is what the authors claim.	✅ pass
test_transcript	Both halves are the paper's two lemmas at every violation and surviving fraction, transcribed from the paper rather than read off the engine.	✅ pass