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arXiv:2003.03015 · Annalen der Physik

Protecting Quantum Fisher Information in Correlated Quantum Channels

Ming‐Liang Hu, Hui‐Fang Wang

Published Dec 1, 2019• 33 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1002/andp.201900378

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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.
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We investigate how the correlated actions of quantum channels affect the robustness of entangled states. We consider the Bell-like state and random two-qubit pure states in the correlated depolarizing, bit flip, bit-phase flip, and phase flip channels. It is found that the robustness of two-qubit pure states can be noticeably enhanced due to the correlations between consecutive actions of these noisy channels, and the Bell-like state is always the most robust one. We also consider the robustness of three-qubit pure states in correlated noisy channels. For the correlated bit flip and phase flip channels, the result shows that although the most robust and most fragile states are locally unitary equivalent, they exhibit different robustness in different correlated channels, and the effect of channel correlations on them is also significantly different. However, for the correlated depolarizing and bit-phase flip channels, the robustness of two special three-qubit pure states is exactly the same. Moreover, compared with the random three-qubit pure states, they are neither the most robust states nor the most fragile states.
Abstract We explore the impact of channel correlations, resulting from consecutive uses of the channel, on the estimation of channel parameters. Specifically, we analyze the dynamics of quantum Fisher information (QFI) for correlation strength and coupling strength in a two-qubit system subjected to either a Random Telegraph (RT) noise channel or an Amplitude Damping (AD) noise channel. Our findings indicate that the correlation in the RT noise channel enhances the estimation precision of correlation strength but detracts from the precision of coupling strength estimation. However, the correlation in the AD noise channel exhibits a similar effect to that of the RT noise channel only in the initial stage of system’s evolution. In the long-term evolution, the correlation of the AD noise channel reduces the estimation precision of correlation strength but has no monotonic relationship with the estimation precision of coupling strength. Our study provides new insights into the effects of channel correlations on channel parameter estimation and has potential implications for controlling the precision of parameter estimation in quantum information processing.
We give the explicit expressions of quantum Fisher information and skew information for a two-qubit Bell states. We investigate their dynamics under the decoherence effects: phase-damping channel, depolarizing channel and amplitude-damping channel. We also discuss the thermal entanglement quantified by Wootters concurrence for these three decoherence channels and we compare its dynamical behavior with the quantum Fisher information and skew information. We then use this comparison to investigate the influence of noisy channels on thermal entanglement and its role in boosting the performance of metrology protocols. It is shown that the correlations in two-qubit Bell states are more resistant to phase-damping channel and depolarizing channels.
Quantum channel identification, a standard problem in quantum metrology, is the task of estimating parameter(s) of a quantum channel. We investigate dissonance (quantum discord in the absence of entanglement) as an aid to quantum channel identification and find evidence for dissonance as a resource for quantum information processing. We consider the specific case of dissonant Bell-diagonal probes of the qubit depolarizing channel, using quantum Fisher information as a measure of statistical information extracted by the probe. In this setting dissonant quantum probes yield more statistical information about the depolarizing probability than do corresponding probes without dissonance and greater dissonance yields greater information. This effect only operates consistently when we control for classical correlation between the probe and its ancilla and the joint and marginal purities of the ancilla and probe.