General quantum measurements optimally interpolate between measurement paradigms
July 18, 2022 - Francisco Elohim Becerra-Chavez
The ability to distinguish between two different quantum states can enable optical communication, cryptography, and networking. However, any overlap between the two states fundamentally limits how well they can be identified, and bounds how well various discrimination tasks can be achieved. Measurements for state discrimination include measurements that can identify the two states with the minimum possible error and measurements that can unambiguously discriminate the two states by introducing inconclusive results. However, quantum mechanics allows for more general quantum measurements encompassing these and other discrimination paradigms, which can be a powerful tool for quantum information and communications.
A particular strategy termed an optimal inconclusive measurement is a general measurement which can be adjusted to implement not only a minimum error or unambiguous strategy, but anything in between. Such a measurement strategy can yield a correct outcome, an error, or an inconclusive result, but with the optimal probabilities for each allowed by quantum mechanics. We experimentally demonstrate a proposed method (Nakahira & Usada PRA86, 052323 (2012)) to implement these optimal inconclusive measurements for phase encoded states of laser light based on optical interference, linear optics, single photon counting, and fast feedback operations.
Beyond the implementation of optimal inconclusive measurements, these same physical elements used in our demonstration could potentially be employed to implement arbitrary quantum measurements on binary states, an elusive task in the optical domain. Furthermore, extension of these techniques to discrimination of multiple states can illuminate how to reach the ultimate limits of information transfer in optical communication.
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