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The '''data processing inequality''' is an [[information theory|information theoretic]] concept that states that the information content of a signal cannot be increased via a local physical operation. This can be expressed concisely as 'post-processing cannot increase information'.<ref name= BeaudryArxiv>{{citation |journal=Quantum Information & Computation |volume=12 |issue=5–6 |pages=432–441 |last1=Beaudry |first1=Normand |title=An intuitive proof of the data processing inequality |date=2012 |doi=10.26421/QIC12.5-6-4 |arxiv=1107.0740|bibcode=2011arXiv1107.0740B |s2cid=9531510 }}</ref>
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Let three random variables form the [[Markov chain]] <math>X \rightarrow Y \rightarrow Z</math>, implying that the conditional distribution of <math>Z</math> depends only on <math>Y</math> and is [[Conditional independence|conditionally independent]] of <math>X</math>. Specifically, we have such a Markov chain if the joint probability mass function can be written as
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