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Chinese Physics B

Influence of homodyne-based feedback control on the entropic uncertainty in open quantum system*

Juju Hu, Qin Xue

Published Jul 1, 2019• 7 citations
Publisher

Abstract

For an open quantum system containing two qubits under homodyne-based feedback control, we investigate the dynamical behaviors of quantum-memory-assisted entropic uncertainty. Moreover, we analyze the influence of feedback modes and coefficients on the entropic uncertainty. Numerical investigations show that the memory qubit should be placed in a non-dissipative channel if the single dissipative channel condition can be chosen, which helps reduce the entropic uncertainty of the system. For the homodyne feedback control F = λ σ x (or F = λ σ y ) , due to different roles of the entangled qubits A and B, when they are subject to feedback control with different feedback coefficients λ, the exchange of feedback coefficients will cause variations of the entropic uncertainty. When the feedback coefficient corresponding to the memory qubit B is larger ( λ B > λ A ) , the steady value of the entropic uncertainty will be small, which is conducive to enhancing the robustness of the system. However, for the feedback control F = λ σ z , the difference between the feedback coefficients has no effect on the steady values of the entropic uncertainty.

DOI
10.1088/1674-1056/28/7/070303

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For an open quantum system containing two qubits under homodyne-based feedback control, we investigate the dynamical behaviors of quantum-memory-assisted entropic uncertainty. Moreover, we analyze the influence of feedback modes and coefficients on the entropic uncertainty. Numerical investigations show that the memory qubit should be placed in a non-dissipative channel if the single dissipative channel condition can be chosen, which helps reduce the entropic uncertainty of the system. For the homodyne feedback control F = λ σ x (or F = λ σ y ) , due to different roles of the entangled qubits A and B, when they are subject to feedback control with different feedback coefficients λ, the exchange of feedback coefficients will cause variations of the entropic uncertainty. When the feedback coefficient corresponding to the memory qubit B is larger ( λ B > λ A ) , the steady value of the entropic uncertainty will be small, which is conducive to enhancing the robustness of the system. However, for the feedback control F = λ σ z , the difference between the feedback coefficients has no effect on the steady values of the entropic uncertainty.
Abstract Quantum objects are susceptible to noise from their surrounding environments, interaction with which inevitably gives rise to quantum decoherence or dissipation effects. In this work, we examine how different types of local noise under an open system affect entropic uncertainty relations for two incompatible measurements. Explicitly, we observe the dynamics of the entropic uncertainty in the presence of quantum memory under two canonical categories of noisy environments: unital (phase flip) and nonunital (amplitude damping). Our study shows that the measurement uncertainty exhibits a non-monotonic dynamical behavior—that is, the amount of the uncertainty will first inflate, and subsequently decrease, with the growth of decoherence strengths in the two channels. In contrast, the uncertainty decreases monotonically with the growth of the purity of the initial state shared in prior. In order to reduce the measurement uncertainty in noisy environments, we put forward a remarkably effective strategy to steer the magnitude of uncertainty by means of a local non-unitary operation (i.e. weak measurement) on the qubit of interest. It turns out that this non-unitary operation can greatly reduce the entropic uncertainty, upon tuning the operation strength. Our investigations might thereby offer an insight into the dynamics and steering of entropic uncertainty in open systems.
We investigate the dynamical behaviors of quantum-memory-assisted entropic uncertainty and its lower bound in the amplitude-damping channel. The influences of different placement positions of the quantum register on the dynamics of quantum coherence, quantum entanglement, and quantum discord are analyzed in detail. The numerical simulation results show that the quantum register should be placed in the channel of the non-Markovian effect. This option is beneficial to reduce the entropic uncertainty and its lower bound. We also find that this choice does not change the evolution of the quantum coherence and quantum entanglement, but changes the dynamical process of the quantum discord of the system. These results show that quantum coherence, quantum entanglement, and quantum discord are different quantum resources with unique characteristics and properties, and quantum discord can play a key role in reducing the uncertainty of quantum systems.
We investigate the quantum-memory-assisted entropic uncertainty for an entangled two-qubit system in a local quantum noise channel with -symmetric operation performing on one of the two particles. Our results show that the quantum-memory-assisted entropic uncertainty in the qubits system can be reduced effectively by the local -symmetric operation. Physical explanations for the behavior of the quantum-memory-assisted entropic uncertainty are given based on the property of entanglement of the qubits system and the non-locality induced by the re-normalization procedure for the non-Hermitian -symmetric operation.
Recently, Xu et al. [Phys. Rev. A 86, 012113(2012)] explored the behavior of the entropic uncertainty relation under the influence of local unital and nonunital noisy channels for a class of Bell-diagonal states. We here reform their results and investigate the entropic uncertainty relation under the influence of unital and nonunital noisy channels with memory. Different types of noisy channels with memory, such as amplitude damping channel(nonunitary), phase-damping and depolarizing channels(unitary) have been taken into account. Some analytical or numerical results are presented. The effect of channels with memory on dynamics of the entropic uncertainties (or their lower bounds) has been discussed in detail. Compare with previous results, our results show that, the entropic uncertainties (or their lower bounds) subjecting to amplitude damping channel with memory will be reduced at first and then be lifted with the memory coefficient of channel μμμ increasing, however they will be only reduced under phase-damping and depolarizing channels with memory. Especially, in the limit of μ→1μ\rightarrow1μ→1, the entropic uncertainties (or their lower bounds) could be well protected and immune to decoherence of channle. Moreover, the mechanism behind these phenomena are also explored by using the purity of state.
The uncertainty principle limits the ability for observer to precisely measure two incompatible observables, and plays a crucial role in quantum precision measurement in the quantum information science. When quantum systems interact with their surroundings, they inevitably result in decoherence, which increases the uncertainty of the system. In the process of quantum information processing, the effective regulation of uncertainty becomes a key problem that needs to be solved. In this work, we investigate the quantum-memory-assisted entropic uncertainty relation of a two-qubit system under correlated channels with dephasing colored noise. We demonstrate that it is possible to control the entropic uncertainty, U, and its lower bound, Ub, by combining correlations between successive uses of channels and the non-Markovianity of the dynamical evolution. Firstly, the evolutionary characteristics of the trace distance are employed to distinguish between Markovianity and non-Markovianity of the channel. Subsequently, the system is selected to be either a maximally entangled state or separated state initially. By adjusting the strength η of the correlations, we find that with the increase of η, the entropic uncertainty and its lower bound decrease. Especially, if the channel is fully correlated (η = 1), the entropic uncertainty and its lower bound remain constant under the channel, indicating that decoherence is completely suppressed. A comparison of Markovian channel with non-Markovian channel reveals that the entropic uncertainty and its lower bound exhibit oscillatory behaviour under non-Markovian channels. The combination of correlations and non-Markovianity of the channel demonstrates that the entropic uncertainty and its lower bound can be reduced under fully correlated channels where the non-Markovianity has no effect. This is because fully correlated channels suppress decoherence to a greatest extent. Under partially correlated channels, the combination of correlations and non-Markovianity can more effectively reduce the entropic uncertainty and its lower bound. Under such channels, correlations of the channel reduce the entropic uncertainty and its lower bound during the whole evolution, while the non-Markovianity contributes to their oscillations and reduce them in some specific time. Furthermore, the results show that the entropic uncertainty and its lower bound reach steady values that depend only on the strength of the correlations after long-time evolution. In other words, the stronger the correlations, the lower the entropy uncertainty and its lower bound of steady states will be. Finally, we analyse the physical nature of the decrease of the entropic uncertainty and its lower bound, and it is found that the decrease of the entropic uncertainty and its lower bound originate from the increase of the quantum correlations in the system.
We investigate the quantum-memory-assisted entropic uncertainty for an entangled two-qubit system in a local quantum noise channel with PT-symmetric operation performing on one of the two particles. Our results show that the quantum-memory-assisted entropic uncertainty in the qubits system can be reduced effectively by the local PT-symmetric operation. Physical explanations for the behavior of the quantum-memory-assisted entropic uncertainty are given based on the property of entanglement of the qubits system and the non-locality induced by the re-normalization procedure for the non-Hermitian PT-symmetric operation.