Exploring entropic uncertainty relation in the Heisenberg XX model with inhomogeneous magnetic field

Huang, Ai-Jun; Wang, Dong; Wang, Jiaming; Shi, Jia-Dong; Sun, Wen; Liu, Ye

doi:10.1007/s11128-017-1657-0

Cited by 46 publications

(18 citation statements)

References 31 publications

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“…In practice, a physical system is remarkably susceptible to ambient environments, which may unavoidably inject decoherence effects. In this regard, it is of fundamental importance to pursue an understanding of the influence of various decoherence effects on QMA‐EUR; these effects have been shown to be nontrivial in the domain of quantum information science . Recently, Fan et al., and Jing et al have explored the dynamic characteristics of the QMA‐EUR while the particle to be measured is taken to be curved space‐time (e.g., Schwarzschild and de Sitter spaces); Huang et al .…”

Section: Introductionmentioning

confidence: 99%

Effects of Hawking Radiation on the Entropic Uncertainty in a Schwarzschild Space‐Time

et al. 2018

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The Heisenberg uncertainty principle describes a basic restriction on an observer's ability of precisely predicting the measurement of a pair of noncommuting observables, and virtually is at the core of quantum mechanics. Herein, the aim is to study the entropic uncertainty relation (EUR) under the background of a Schwarzschild black hole and its control. Explicitly, dynamical features of the measuring uncertainty via entropy are developed in a practical model where a stationary particle interacts with its surrounding environment while another particle-serving as a quantum memory reservoir-undergoes free fall in the vicinity of the event horizon of the Schwarzschild space-time. It shows higher Hawking temperatures would give rise to an inflation of the entropic uncertainty on the measured particle. This is suggestive of the fact the measurement uncertainty is strongly correlated with degree of mixing present in the evolving particles. Additionally, based on information flow theory, a physical interpretation for the observed dynamical behaviors related with the entropic uncertainty in such a genuine scenario is provided. Finally, an efficient strategy is proposed to reduce the uncertainty by non-tracing-preserved operations. Therefore, our explorations may improve the understanding of the dynamic entropic uncertainty in a curved space-time, and illustrate predictions of quantum measurements in relativistic quantum information sciences.

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Section: Introductionmentioning

confidence: 99%

Effects of Hawking Radiation on the Entropic Uncertainty in a Schwarzschild Space‐Time

et al. 2018

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“…Huang et al . investigated the nonunital and non‐semiclassical local channels, such as the amplitude damping channel characterized by the Kraus operators

E_{0}^{A D} = e^{- Γ t / 2} false| 0 false⟩ false⟨ 0 false| + false| 1 false⟩ false⟨ 1 false|

and

E_{1}^{A D} = \sqrt{1 - e^{- Γ t}}

| 1 ⟩ ⟨ 0 |

.…”

Section: The Dynamical Uncertainty In Open Systems and Its Manipulationmentioning

confidence: 99%

“…If

J_{x} = J_{y}

and

J_{z} = 0

, the corresponding Heisenberg chains is called the XX model, and its system Hamiltonian for a two‐spin system was given by

\begin{matrix} true \\ right H_{A B} = \frac{1}{2} ([], J_{x} σ_{1}^{x} σ_{2}^{x} + J_{y} σ_{1}^{y} σ_{2}^{y} + (G + g) σ_{1}^{z} + (G - g) σ_{2}^{z}) \end{matrix}

when an inhomogeneous magnetic field is applied along the z ‐direction, where G and g correspond the degree of inhomogeneity and the degree of inhomogeneity, respectively. The quantum‐memory‐assisted EUR was first studied in a two‐qubit Heisenberg

X X

model by Huang et al . Their results reflect that the larger coupling coefficient between two spin qubits can decrease the uncertainty of interest and the entropic uncertainty will even reach to zero for the relatively large coupling coefficients.…”

Section: The Dynamical Uncertainty In Open Systems and Its Manipulationmentioning

confidence: 99%

“…Explicitly, the filtering operation can be described by

\begin{matrix} true \\ right F = ((), \begin{matrix} \sqrt{1 - k_{f}} & 0 \\ 0 & \sqrt{k_{f}} \end{matrix}) \end{matrix}

where

k_{f} \in false[0, 1 false]

is the strength of the operation. Huang et al . first studied the reduction of quantum‐memory‐assisted entropic uncertainty by performing the filtering operation, which is influenced by the unital and nonunital channels.…”

Section: The Dynamical Uncertainty In Open Systems and Its Manipulationmentioning

confidence: 99%

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Quantum‐Memory‐Assisted Entropic Uncertainty Relations

Wang

Ming

et al. 2019

Annalen der Physik

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Uncertainty relations take a crucial and fundamental part in the frame of quantum theory, and are bringing on many marvelous applications in the emerging field of quantum information sciences. Especially, as entropy is imposed into the uncertainty principle, entropy-based uncertainty relations lead to a number of applications including quantum key distribution, entanglement witness, quantum steering, quantum metrology, and quantum teleportation. Herein, the history of the development of the uncertainty relations is discussed, especially focusing on the recent progress with regard to quantum-memory-assisted entropic uncertainty relations and dynamical characteristics of the measured uncertainty in some explicit physical systems. The aims are to help deepen the understanding of entropic uncertainty relations and prompt further explorations for versatile applications of the relations on achieving practical quantum tasks.

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“…The dynamics of QMA‐EUR in non‐inertial frame had also spurred a lot of interest in recent years . On the other hand, in order to reduce the entropic uncertainty under noises, several methods have been employed, such as quantum weak measurement, filtering operation, as well as quantum feedback control …”

Section: Introductionmentioning

confidence: 99%

The Entropic Uncertainty Relation for Two Qubits in the Cavity‐Based Architecture

Bai

Xue

et al. 2019

Annalen der Physik

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Based on a simple cavity-engineered architecture, the dynamics of quantum memory-assisted entropic uncertainty relation (QMA-EUR) for two qubits initially prepared in a generic Werner state is investigated. The effects of cavity decay rate, qubit-cavity couplings, and cavity-cavity couplings on the uncertainty are explored. It is found that the damped oscillation of uncertainty can be induced by the increase of two types of coupling strengths mentioned above. It is demonstrated that the maximum value of uncertainty is closely related to the purity of the initial state. The uncertainty can be either increased or decreased, depending on the threshold value of coupling strength between the two cavities. Finally, in agreement with a recent observation, an asynchronous relation between uncertainty and mixedness is found during the initial time evolution.

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Exploring entropic uncertainty relation in the Heisenberg XX model with inhomogeneous magnetic field

Cited by 46 publications

References 31 publications

Effects of Hawking Radiation on the Entropic Uncertainty in a Schwarzschild Space‐Time

Effects of Hawking Radiation on the Entropic Uncertainty in a Schwarzschild Space‐Time

Quantum‐Memory‐Assisted Entropic Uncertainty Relations

The Entropic Uncertainty Relation for Two Qubits in the Cavity‐Based Architecture

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