Discriminating mixed qubit states with collective measurements

It is a central fact in quantum mechanics that non-orthogonal states cannot be distinguished perfectly. In general, the optimal measurement for distinguishing such states is a collective measurement. However, to the best our knowledge, collective measurements have not been used to enhance quantum state discrimination to date. One of the main reasons for this is the fact that, in the usual state discrimination setting with equal prior probabilities, at least three copies of a quantum state are required to be measured collectively to outperform separable measurements. This is very challenging experimentally. In this work, by considering unequal prior probabilities, we propose and experimentally demonstrate a protocol for distinguishing two copies of single qubit states using collective measurements which achieves a lower probability of error than can be achieved by any non-entangling measurement. Additionally, we implemented collective measurements on three and four copies of the unknown state and found they performed poorly. Non-orthogonal quantum states cannot be perfectly distinguished - a fact of central importance in quantum mechanics, from both a fundamental and practical viewpoint. The authors introduce an approach to this problem, using entangled measurements to distinguish quantum states better than what is possible with direct measurements.

Automated summary

The study introduces a protocol for using collective measurements to distinguish quantum states, which achieves a lower probability of error compared to non-entangling measurements. Experimental results demonstrate the effectiveness of this approach.