Another Short and Elementary Proof of Strong Subadditivity of Quantum Entropy

Abstract

A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz inequality in elementary courses. Several consequences are proved in a way which allow an elementary proof of strong subadditivity in a few more lines. Some expository material on Schwarz inequalities for operators and the Holevo bound for partial measurements is also included.Comment: The proof given here is short and more elementary that in either quant-ph/0404126 or quant-ph/0408130. The style is intended to be suitable to classroom presentation. For a Much More Complicated approach, see Section 6 of quant-ph/050619