Entropy and asymptotics / Theorem
Schumacher quantum data-compression limit equality
Theorem statement
Let $\rho$ be a density operator on a finite-dimensional Hilbert space with von Neumann entropy $H(\rho)$. The optimal asymptotic Schumacher compression rate of the i.i.d. quantum source $\rho$, defined as the infimum over all achievable compression rates $R$, equals $H(\rho)$.
Sources
- From Classical to Quantum Shannon Theory
Mark M. Wilde, 2011
Lean context
- Lean declaration
QIT.State.schumacher_data_compression_limit
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