Joint quantum entropy

The joint quantum entropy generalizes the classical joint entropy to the context of quantum information theory. Intuitively, given two quantum states ${\displaystyle \rho }$ and ${\displaystyle \sigma }$, represented as density operators that are subparts of a quantum system, the joint quantum entropy is a measure of the total uncertainty or entropy of the joint system. It is written ${\displaystyle S(\rho ,\sigma )}$ or ${\displaystyle H(\rho ,\sigma )}$, depending on the notation being used for the von Neumann entropy. Like other entropies, the joint quantum entropy is measured in bits, i.e. the logarithm is taken in base 2.

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