= Detection loophole
The <detection loophole> arises when missed events allow the retained sample to depend on settings and hidden variables. For example, a <local hidden-variable theory> may retain different underlying pairs at different <polarizer> angles. Applying the <CHSH inequality> to that selected sample does not test the original setting-independent ensemble. A valid protocol specifies outcomes and trials, including failures, or justifies an appropriate <fair sampling> assumption. Subtracting <accidental coincidences> addresses background contamination; it does not by itself repair this selection problem.
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