Strong entropic uncertainty relations for multiple measurements

Xiao, Yunlong; Jing, Naihuan; Fei, Shao-Ming; Li, Tao; Li‐Jost, Xianqing; Ma, Teng; Wang, Zhi-Xi

doi:10.1103/physreva.93.042125

Cited by 52 publications

(48 citation statements)

References 18 publications

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“…Furthermore, QMA-EUR had been demonstrated experimentally [27,28] and also generalized by the Rényi entropy. [39] Canonically, a quantum system cannot escape from its surrounding environment and inevitably couples with the environmental noises, which will result in decoherence or dissipation effects. [39] Canonically, a quantum system cannot escape from its surrounding environment and inevitably couples with the environmental noises, which will result in decoherence or dissipation effects.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Measurement's Uncertainty in the Curved Space‐Time

2019

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The dynamical characteristics of measurement's uncertainty are investigated under two modes of Dirac field in the Garfinkle-Horowitz-Strominger dilation space-time. It shows that the Hawking effect induced by the thermal field would result in an expansion of the entropic uncertainty with increasing dilation-parameter value, as the systemic quantum coherence reduces, reflecting that the Hawking effect could undermine the systemic coherence. Meanwhile, the intrinsic relationship between the uncertainty and quantum coherence is obtained, and it is revealed that the uncertainty's bound is anti-correlated with the system's quantum coherence. Furthermore, it is illustrated that the systemic mixedness is correlated with the uncertainty to a large extent. Via the information flow theory, various correlations including quantum and classical aspects, which can be used to form a physical explanation on the relationship between the uncertainty and quantum coherence, are also analyzed. Additionally, this investigation is extended to the case of multi-component measurement, and the applications of the entropic uncertainty relation are illustrated on entanglement criterion and quantum channel capacity. Lastly, it is declared that the measurement uncertainty can be quantitatively suppressed through optimal quantum weak measurement. These investigations might pave an avenue to understand the measurement's uncertainty in the curved space-time.

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Section: Introductionmentioning

confidence: 99%

Dynamical Measurement's Uncertainty in the Curved Space‐Time

2019

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“…Example 2: Consider qutrite states with three measurements A k (k = 1, 2, 3) given by the vectors [29]: |a [29]. Our bound based on quadratic function for this case is 4a(1 − a); see Fig.…”

Section: Entropic Uncertainty Relation With State-independent Boundmentioning

confidence: 99%

“…(2) j (j = 1, 2, · · · , d), we have the following entropic uncertainty relation: (7) in Ref. [29] is represented by the dashed line, and the bound (6) in Ref. [26] is plotted by the dot-dashed line.…”

Section: Entropic Uncertainty Relation With State-dependent Boundmentioning

confidence: 99%

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Improved quantum entropic uncertainty relations

Chen

Xiao

et al. 2018

Phys. Rev. A

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We study entropic uncertainty relations by using stepwise linear functions and quadratic functions. Two kinds of improved uncertainty lower bounds are constructed: the state-independent one based on the lower bound of Shannon entropy and the tighter state-dependent one based on the majorization techniques. The analytical results for qubit and qutrit systems with two or three measurement settings are explicitly derived, with detailed examples showing that they outperform the existing bounds. The case with the presence of quantum memory is also investigated.PACS numbers:

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“…Similarly, the second quantum measure enables us to generalize the strong entropic uncertainty relations for multiple measurements [18] (i.e. admixture bound) to allow for quantum side information.…”

Section: Strong Entropic Uncertainty Relations In the Presence Of mentioning

confidence: 99%

Uncertainty under quantum measures and quantum memory

Xiao

Jing

Li‐Jost

2017

Quantum Inf Process

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The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty relation will vary. Based on the knowledge of correlations between the measured particle and quantum memory, we have investigated the entropic uncertainty relations for two and multiple measurements, and generalized the lower bounds on the sum of Shannon entropies without quantum side information to those that allow quantum memory. In particular, we have obtained generalization of Kaniewski-Tomamichel-Wehner's bound for effective measures and majorization bounds for noneffective measures to allow quantum side information. Furthermore, we have derived several strong bounds for the entropic uncertainty relations in the presence of quantum memory for two and multiple measurements. Finally, potential applications of our results to entanglement witnesses are discussed via the entropic uncertainty relation in the absence of quantum memory.

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Strong entropic uncertainty relations for multiple measurements

Cited by 52 publications

References 18 publications

Dynamical Measurement's Uncertainty in the Curved Space‐Time

Dynamical Measurement's Uncertainty in the Curved Space‐Time

Improved quantum entropic uncertainty relations

Uncertainty under quantum measures and quantum memory

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