Tighter generalized entropic uncertainty relations in multipartite systems

Wu, Lin; Liu, Ye; Wang, Dong

doi:10.1103/physreva.106.062219

Cited by 23 publications

(12 citation statements)

References 53 publications

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“…Riding the waves of information theory, a variety of characterizations and quantifications of uncertainty relations have been established, including but not limited to the ones in terms of variance [4][5][6][7][8][9][10][11][12][13], entropy [14][15][16][17], noise and disturbance [18], successive measurement [19,20], majorization technique [21,22], skew information [23][24][25][26][27], etc.. These uncertainty relations play an important role in a wide range of applications in such as quantum gravity [28], quantum cryptography [29,30], entanglement detection [31,32], nonlocality [33], quantum steering [34] and quantum metrology [35].…”

Section: Introductionmentioning

confidence: 99%

Tighter sum uncertainty relations via variance and Wigner–Yanase skew information for N incompatible observables

Zhang

Fei

2021

Quantum Inf Process

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The Wigner-Yanase skew information stands for the uncertainty about the information on the values of observables not commuting with the conserved quantity. The Wigner-Yanase skew information-based uncertainty relations can be regarded as a complementarity to the conceptual Heisenberg uncertainty principle. We present tight uncertainty relations in both product and summation forms for two quantum channels based on the Wigner-Yanase skew information. We show that our uncertainty inequalities are tighter than the existing ones.

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Section: Introductionmentioning

confidence: 99%

Tighter sum uncertainty relations via variance and Wigner–Yanase skew information for N incompatible observables

Zhang

Fei

2021

Quantum Inf Process

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“…We can now lower the result's uncertainty by using Bob's measurement data [11]. The uncertainty standard deviation for two observables X and Y, can be represented as [12][13][14][15]…”

Section: The Entropic Uncertainty Measurementioning

confidence: 99%

Biqubit Heisenberg spin chain correlations and entropic uncertainty

Rahman¹,

Zangi²,

Yang³

et al. 2023

Preprint

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We investigate the dynamics of quantum correlations and entropic uncertainty in a system of two-qubit XXZ-type Heisenberg spin chain when exposed to a magnetic and classical field simultaneously. To demonstrate entanglement, coherence, entropic uncertainty and mixedness disorder, we utilize negativity and 1 -norm of coherence, quantum memory-assisted entropic uncertainty and linear entropy functions, respectively. Besides, a dephasing static noise is considered affecting the joint scheme of the external magnetic and classical channel. The dynamics of entanglement, coherence, uncertainty, and disorder have been explicitly investigated against various several parameters of the current configuration, such as qubit-channel coupling, static noise strength, spin-spin coupling, Heisenberg spin exchange interaction, Dzyaloshinskii-Moriya interaction (DM), Kaplan, Shekhtman, Entin-Wohlman, and Aharony (KSEA) and anisotropy parameters. We show that compared to the individual application of the classical and magnetic field, their simultaneous application is more appropriate for the quantum correlations preservation. The entanglement and coherence functions have been shown to have opposite relationship with the entropic uncertainty and entropy disorder. Finally, compared to the entanglement, coherence remains strengthened in the two-qubit Heisenberg spin chain system.

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“…[ 22 ] Additionally, in ref. [23], the authors derived a tighter lower bound of three‐qubit entropic uncertainty relation in terms of the Holevo quantity along with the generalization for multiple measurements in multipartite systems. Including a pairing of mutual unbiased bases in terms of incompatibility, a bound is presented that remained very tight for the case of tripartite X‐states coinciding with uncertainty based on entropy and can be traced back to the associated Renes and Boileau's bound.…”

Section: Introductionmentioning

confidence: 99%

Control of Quantum‐Memory Induced by Generated Thermal XYZ‐Heisenberg Entanglement: y‐Component DM Interaction

et al. 2023

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This study explores the thermal quantum-memory-assisted entropic uncertainty relation (QM-EUR) and entanglement in a general two-qubit XYZ-Heisenberg spin chain model in the presence of the Dzyaloshinskii-Moriya (DM) interaction. The characterization of y-component DM and spin-spin interactions are particularly focused. It is found that the DM and spin-spin interaction strengths highly regulate the flow behavior and the initial final levels of QM-EUR and entanglement. In comparison, the spin-spin interaction strength in the z-direction remains useful in both ferromagnetic and anti-ferromagnetic regimes for entropic uncertainty suppression and entanglement generation. Additionally, the negative and the positive y-directed DM values can usefully turn classical states into resourceful quantum states. The dynamics of thermal QM-EUR and entanglement-of-formation have symmetric behaviors only with respect to y-component DM and z-component spin-spin interaction. Finally, different critical points of temperature, y-component DM as well as spin-spin interaction are encountered, which should be opted to preserve quantum correlations and degrade uncertainty.

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Tighter generalized entropic uncertainty relations in multipartite systems

Cited by 23 publications

References 53 publications

Tighter sum uncertainty relations via variance and Wigner–Yanase skew information for N incompatible observables

Tighter sum uncertainty relations via variance and Wigner–Yanase skew information for N incompatible observables

Biqubit Heisenberg spin chain correlations and entropic uncertainty

Control of Quantum‐Memory Induced by Generated Thermal XYZ‐Heisenberg Entanglement: y‐Component DM Interaction

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