Entropic uncertainty relations for successive measurements of canonically conjugate observables

Rastegin, Alexey E.

doi:10.1002/andp.201600130

Cited by 25 publications

(24 citation statements)

References 78 publications

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“…[17,18] Therefore, EUR has became a hot topic in the domain of quantum information science and many authors paid much attention on reforming the uncertainty relations in refs. [19][20][21][22][23][24][25]. Specifically, Berta and cooperators in 2010 had suggested a brand new uncertainty relation when a quantum memory emerges, [25] namely, quantum-memory-assisted entropic uncertainty relations (QMA-EUR).…”

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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“…More special properties of the above conditional entropy with some applications were addressed in [58,59]. The entropy (28) has been used in formulating the uncertainty principle in successive measurements [60,61]. This scenario is very close to that is dealt with in quantum key distribution with eavesdropping.…”

Section: Information-theoretic Functions Of the Rényi Typementioning

confidence: 99%

Individual attacks with generalized discrimination and inadequacy of some information measures

Rastegin

2019

Quantum Inf Process

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We accomplish studies of properly quantifying eavesdropper's information gain in individual attacks on the BB84 system of quantum key distribution. A noticeable sensitivity of conclusions to the choice of information measures is brightly revealed, when generalized state discrimination is used at the last stage. To realize her aims, Eve intrudes into the communication channel with some entangling probe. The Fuchs-Peres-Brandt (FPB) probe is known as a powerful individual attack on the BB84 protocol. In the simplest formulation, Eve uses the Helstrom scheme to distinguish output probe states. In conclusive eavesdropping, the unambiguous discrimination is utilized. In the intermediate scenario, she can apply a generalized discrimination scheme that interpolates between the Helstrom and unambiguous discrimination schemes. We analyze Eve's probe performance from the viewpoint of various measures for quantifying mutual information.

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“…We will follow the strategy already justified in the previous papers [50,51,59]. Here, the basic idea is to deal with inequalities between norm-like functionals of the form (6).…”

Section: Entanglement Criteria For a Multipartite Quantum Systemmentioning

confidence: 99%

“…When the bins all tend to zero, these histograms reproduce the original distributions. Assuming a > 1 > b > 0, we can prove the inequalities [51,59] …”

Section: Criteria In Terms Of Discretized Distributionsmentioning

confidence: 99%

Rényi formulation of entanglement criteria for continuous variables

Rastegin

2017

Phys. Rev. A

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Entanglement criteria for an n-partite quantum system with continuous variables are formulated in terms of Rényi entropies. Rényi entropies are widely used as a good information measure due to many nice properties. Derived entanglement criteria are based on several mathematical results such as the Hausdorff-Young inequality, Young's inequality for convolution and its converse. From the historical viewpoint, the formulations of these results with sharp constants were obtained comparatively recently. Using the position and momentum observables of subsystems, one can build two total-system measurements with the following property. For product states, the final density in each global measurement appears as a convolution of n local densities. Hence, restrictions in terms of two Rényi entropies with constrained entropic indices are formulated for n-separable states of an n-partite quantum system with continuous variables. Experimental results are typically sampled into bins between prescribed discrete points. For these aims, we give appropriate reformulations of the derived entanglement criteria.

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Entropic uncertainty relations for successive measurements of canonically conjugate observables

Cited by 25 publications

References 78 publications

Dynamical Measurement's Uncertainty in the Curved Space‐Time

Dynamical Measurement's Uncertainty in the Curved Space‐Time

Individual attacks with generalized discrimination and inadequacy of some information measures

Rényi formulation of entanglement criteria for continuous variables

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