Logical loophole in random 3-bit sequence generator

In this note, we will provide an information-theoretic framework for the random 3-bit sequence {111, 110, 101, 100, 011, 010, 001, 000} that demonstrates (by using Wigner’s inequality) a logical loophole in the Bell-CHSH inequality [1, 2, 3], as also has recently been found experimentally for triples measurements [4]. As a consequence of this, both classical and quantum regimes can share their bounds within the same environment, which shows that maximally entangled states used in cryptography secure systems can be critically subverted via EPR (Einstein-Podolsky-Rosen) paradox [5]