The paper by Don N. Page explores the average entropy of a subsystem in a quantum system of Hilbert space dimension \( mn \) when the system is in a random pure state. The author conjectures that the average entropy \( S_{m,n} \) of a subsystem of dimension \( m \leq n \) is given by: \[ S_{m,n} = \sum_{k=n+1}^{mn} \frac{1}{k} - \frac{m-1}{2n} \] This conjecture is shown to be approximately equal to: \[ S_{m,n} \simeq \ln m - \frac{m}{2n} \] for \( 1 \leq m \leq n \). This implies that the smaller subsystem typically contains less than half a natural logarithmic unit of information, indicating that the smaller subsystem is very nearly maximally mixed, with little sign of the total system being pure. The result suggests that the correlations within the smaller subsystem contribute very little to the overall information, while the correlations between the larger and smaller subsystems play a significant role. The paper also discusses the asymptotic expansion of \( S_{m,n} \) for large \( n \) and provides an approximate expression for \( S_{m,n} \) in the limit of large \( m \) and \( n \).The paper by Don N. Page explores the average entropy of a subsystem in a quantum system of Hilbert space dimension \( mn \) when the system is in a random pure state. The author conjectures that the average entropy \( S_{m,n} \) of a subsystem of dimension \( m \leq n \) is given by: \[ S_{m,n} = \sum_{k=n+1}^{mn} \frac{1}{k} - \frac{m-1}{2n} \] This conjecture is shown to be approximately equal to: \[ S_{m,n} \simeq \ln m - \frac{m}{2n} \] for \( 1 \leq m \leq n \). This implies that the smaller subsystem typically contains less than half a natural logarithmic unit of information, indicating that the smaller subsystem is very nearly maximally mixed, with little sign of the total system being pure. The result suggests that the correlations within the smaller subsystem contribute very little to the overall information, while the correlations between the larger and smaller subsystems play a significant role. The paper also discusses the asymptotic expansion of \( S_{m,n} \) for large \( n \) and provides an approximate expression for \( S_{m,n} \) in the limit of large \( m \) and \( n \).