Achieving the Heisenberg limit under general Markovian noise using quantum error correction without ancilla
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Achieving the Heisenberg limit under general Markovian noise using quantum error correction without ancilla Yi Peng1,2 · Heng Fan1,2,3,4 Received: 29 December 2019 / Accepted: 4 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Practical quantum metrology is generally hindered by environment noise which can demolish the advantage of breaching the shot-noise limit provided by quantum mechanics. Recently, quantum error-correction (QEC) codes have been developed for restoring the quantum advantage against Markovian noise for quantum metrology. This has been done by assuming either the existence of noiseless ancilla or specific noise types such as the spatially correlated noise and the so-called commuting noise. We consider the situation where all probing systems for metrology are infested by general uncorrelated Markovian noise; namely, there is neither noiseless ancilla nor spatial correlation of the noise. Under such circumstances, we have discussed the error-correction conditions in parallel metrology scheme where more than three probes are employed. We have shown the superiority of parallel schemes over sequential schemes in fighting Markovian noise by ancilla-free QEC with an explicit example. If we employ qubits for parameter sensing, it can be shown that one can restore Heisenberg limit (HL) via full and fast control without any ancilla, as long as the signal Hamiltonian of the probe system has nonvanishing component perpendicular to the noise. This is exactly the same requirement for restoring HL with the assistance of noiseless ancilla. Keywords Heisenberg limit · Markovian noise · Ancilla-free error correction · Parallel scheme
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Heng Fan [email protected]
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Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
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CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
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Songshan Lake Materials Laboratory, Dongguan 523808, Guangdong, China 0123456789().: V,-vol
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Y. Peng, H. Fan
1 Introduction Quantum metrology is one of the main streams in the thriving field of quantum information besides quantum communication and quantum computation [1]. Given the ideal noiseless condition, quantum resources such as entanglement and coherence can enhance the estimation precision of parameters to breach the shot-noise limit (SNL) √ 1/ N T which is the best precision allowed by classical theory. Here, T is the total probing time, while N is the number of probes employed. Ultimately, one can push the estimation precision to the Heisenberg limit (HL) 1/N T permitted by quantum mechanics [2–7]. The advantage provided by quantum mechanics in metrology has wide applications in many fields including spectroscopy [8], accurate clock construction [9–11], gravitational wave detection [12,13], fundamental biology research and medicine development [14] and some other technologies [2,
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