Quantum Bayes rule
  We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state of the N copies is exchangeable. As an illustration, we apply the rule to N qubits. Finally, we show that quantum state estimates derived via the principle of maximum entropy are fundamentally different from those obtained via the quantum Bayes rule. 
Ruediger Schack (Royal Holloway, University of London), Todd A. Brun   (Carnegie Mellon University), and Carlton M. Caves (U...