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Quantum Information Processing

Protection of quantum Fisher information in entangled states via classical driving

Yu-Kun Ren, La-Mei Tang, Hao‐Sheng Zeng

Published Sep 28, 2016• 17 citations
Publisher
DOI
10.1007/s11128-016-1444-3

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Recently, researchers have found that not only entanglement but also quantum discord and even classical correlation can enhance the precision of parameter estimation. Thus the correlation which contributes quantum metrology should be treated as a new type of resource. In this paper, we directly construct a measure of the resource named as the relative quantum Fisher information (rQFI). It quantifies the improvement of QFI caused by correlations naturally. Operationally, rQFI quantifies the improvement of optimal precision achieved by joint measurement on a composite system, instead of the local measurement on the subsystem. Furthermore, rQFI itself is an alternative type of total correlation which captures effects of quantum entanglement, quantum discord, and classical correlation. It reduces to an entanglement measure for pure states. A detailed study for general two-qubit states is presented. Additionally, an alternative generalized discord measure can be extracted out of the rQFI.
Abstract Quantum Fisher information (QFI) has potential applications in quantum metrology tasks. QFI is investigated when the consecutive actions of a quantum channel on the sequence of qubits have partial classical correlations. The results showed that while the decoherence effect is detrimental to QFI, effects of such classical correlations on QFI are channel‐dependent. For the Bell‐type probe states, the classical correlations on consecutive actions of the depolarizing and phase flip channels can be harnessed to improve QFI, while the classical correlations in the bit flip and bit‐phase flip channels induce a slight decrease of QFI. For a more general parameterization form of the probe states, the advantage of using the initial correlated system on improving QFI can also remain in a wide regime of the correlated quantum channels.
Abstract We analytically investigate the dynamics of quantum Fisher information of two qubits in independent environments for both uncorrelated and entangled input states. Especially, we observe that, in the non-Markovian regime and resonant case, quantum Fisher information of uncorrelated input state vanishes only at discrete time point whereas that of entangled input state can disappear during finite time interval. It shows that quantum Fisher information, which determines the parameter estimation precision, is strongly affected by the environment memory effects, and the advantage of entanglement-enhance metrology no longer exists even for a very short time. We also note that quantum Fisher information for two kinds of input states can be preserved under appropriate qubit-reservoir detuning.