- Conference date: 25-29 July 2004
- Location: Glasgow (United Kingdom)
The optimum quantum measurements that minimize the error probability for mixed‐state signals are considered. The square‐root measurement (SRM) is known to be the optimal measurement for many pure‐state signals, e.g., symmetric states, linear codes, etc. However, when the states are mixed, the SRM is no longer guaranteed to be optimal even if the states are symmetric. Here, we define the ‘pure’ square‐root measurement (pure‐SRM) which is the SRM for pure states and its optimality for mixed states. It is shown that the pure‐SRM is satisfied the necessary and sufficient conditions of the quantum Bayes strategy when the signals are mixed by transmission errors, and therefore the pure‐SRM is the optimal measurement.
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