Assisted optimal state discrimination without entanglement

A fundamental problem in quantum information is to explore the roles of different quantum correlations in a quantum information procedure. Recent work (Roa L. et al., Phys. Rev. Lett., 107 (2011) 080401) shows that the protocol for assisted optimal state discrimination (AOSD) may be implemented successfully without entanglement, but with another correlation, quantum dissonance. However, both the original work and the extension to discrimination of d states (Li B. et al., Phys. Rev. A, 85 (2012) 022328) have only proved that entanglement can be absent in the case with equal a priori probabilities. By improving the protocol in Zhang F.-L. et al., Sci. Rep., 3 (2013) 2134, we investigate this topic in a simple case to discriminate three nonorthogonal states of a qutrit, with positive real overlaps. In our procedure, the entanglement between the qutrit and an auxiliary qubit is found to be completely unnecessary. This result shows that the quantum dissonance may play a key role in optimal state discrimination assisted by a qubit for more general cases.