Two-qubit state recovery from amplitude damping based on weak measurement
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Two-qubit state recovery from amplitude damping based on weak measurement Sajede Harraz1 · Shuang Cong1
· Kezhi Li2
Received: 1 June 2019 / Accepted: 4 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we propose a feed-forward control approach to protect arbitrary two-qubit pure and mixed initial states using the weak measurement. A feed-forward operation and measurements are used before the noise channel, and afterward, a reversed operation and measurements are applied to recover the state back to its initial state. In the case of two-qubit pure states, we use the unraveling trick to describe the state of the system in each step of the control procedure. For two-qubit mixed states, a completely positive trace-preserving map is implemented. Finally, the fidelity and success probability are used to evaluate the effect of protection. The complete recovery conditions for the measurement strengths are derived, under which we achieve the optimal fidelity and the success probability of recovering the initial pure and mixed states. Keywords Quantum control · State protection · Amplitude damping · Quantum measurement
This work was supported by the National Natural Science Foundation of China under Grant Nos. 61973290 and 61720106009.
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Shuang Cong [email protected] Sajede Harraz [email protected] Kezhi Li [email protected]
1
Department of Automation, University of Science and Technology of China, Hefei 230027, China
2
Institute of Health information, University College London, London NW1 2DA, UK 0123456789().: V,-vol
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1 Introduction The dynamic of open quantum systems becomes decoherent easily due to the inevitable interaction with the environment [1]. To suppress the effect of decoherence, various strategies have been studied, such as decoherence-free subspaces [2], quantum error correction [3–7], quantum feedback control (QFBC) [8–11] and quantum feed-forward control (QFFC) [12–14]. In both quantum feedback control and quantum feed-forward control, the measurement plays an important role. The measurement in quantum theory significantly differs from that in classical theory. In quantum measurement, there is a trade-off between the information gain and the disturbance of the system caused by the measurement [15]. Hence, the quantum weak measurement technique is promising, since it has little effect on the dynamic of the quantum system. Weak measurements generalize ordinary quantum measurements, and they reveal some information about the quantum state. This process is achieved by leveraging a weak coupling between the measurement device and the system. Amplitude damping is a major decoherence that occurs in many quantum systems [16], such as a photon qubit in a leaky cavity, an atomic qubit subjected to spontaneous decay or a super-conduction qubit with zero-temperature energy relaxation. The specific control problem we are interested in here is the stabilization against amplitude damping for two-qubit pure and mixed s
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