Quantum metrological limits in noisy environments

          @misc{ pirsa_PIRSA:24050015,
            doi = {10.48660/24050015},
            url = {https://pirsa.org/24050015},
            author = {Zhou, Sisi},
            keywords = {Quantum Information},
            language = {en},
            title = {Quantum metrological limits in noisy environments},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {may},
            note = {PIRSA:24050015 see, \url{https://pirsa.org}}
          }
          

Abstract

The Heisenberg limit (HL) and the standard quantum limit (SQL) are two fundamental quantum metrological limits, which describe the scalings of estimation precision of an unknown parameter with respect to N, the number of one-parameter quantum channels applied. In the first part, we show the HL (1/N) is achievable using quantum error correction (QEC) strategies when the ``Hamiltonian-not-in-Kraus-span'' (HNKS) condition is satisfied; and when HNKS is violated, the SQL (1/N^1/2) is optimal and can be achieved with repeated measurements. In the second part, we identify modified metrological limits for estimating one-parameter qubit channels in settings of restricted controls where QEC cannot be performed. We prove unattainability of the HL and further show a ``rotation-generators-not-in-Kraus-span'' (RGNKS) condition that determines the achievability of the SQL.