scholarly journals Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 763 ◽  
Author(s):  
Ana Costa ◽  
Roope Uola ◽  
Otfried Gühne
Keyword(s):  
Relative Entropy ◽  
Uncertainty Relation ◽  
Uncertainty Relations ◽  
W States ◽  
Entropic Uncertainty Relations ◽  
Entropic Uncertainty Relation ◽  
Local Measurements ◽  
Action At A Distance ◽  
Quantum Steering ◽  
Joint Convexity

The effect of quantum steering describes a possible action at a distance via local measurements. Whereas many attempts on characterizing steerability have been pursued, answering the question as to whether a given state is steerable or not remains a difficult task. Here, we investigate the applicability of a recently proposed method for building steering criteria from generalized entropic uncertainty relations. This method works for any entropy which satisfy the properties of (i) (pseudo-) additivity for independent distributions; (ii) state independent entropic uncertainty relation (EUR); and (iii) joint convexity of a corresponding relative entropy. Our study extends the former analysis to Tsallis and Rényi entropies on bipartite and tripartite systems. As examples, we investigate the steerability of the three-qubit GHZ and W states.

scholarly journals Optimality of entropic uncertainty relations

2015 ◽  
Vol 13 (06) ◽  
pp. 1550045 ◽  
Author(s):  
Kais Abdelkhalek ◽  
René Schwonnek ◽  
Hans Maassen ◽  
Fabian Furrer ◽  
Jörg Duhme ◽  
...  
Keyword(s):  
Lower Bound ◽  
Numerical Investigation ◽  
Uncertainty Relation ◽  
Small Dimension ◽  
Uncertainty Relations ◽  
Complete Understanding ◽  
Entropic Uncertainty Relations ◽  
Entropic Uncertainty Relation ◽  
Analytical Results ◽  
Optimal Lower Bound

The entropic uncertainty relation proven by Maassen and Uffink for arbitrary pairs of two observables is known to be nonoptimal. Here, we call an uncertainty relation optimal, if the lower bound can be attained for any value of either of the corresponding uncertainties. In this work, we establish optimal uncertainty relations by characterizing the optimal lower bound in scenarios similar to the Maassen–Uffink type. We disprove a conjecture by Englert et al. and generalize various previous results. However, we are still far from a complete understanding and, based on numerical investigation and analytical results in small dimension, we present a number of conjectures.

scholarly journals Entropic Uncertainty Relations, Entanglement and Quantum Gravity Effects via the Generalised Uncertainty Principle

2018 ◽  
pp. 1-12
Author(s):  
Otto Gadea ◽  
Gardo Blado
Keyword(s):  
Shannon Entropy ◽  
Uncertainty Principle ◽  
Upper Bound ◽  
Uncertainty Relation ◽  
Uncertainty Relations ◽  
Single System ◽  
Entropic Uncertainty Relations ◽  
Entropic Uncertainty Relation ◽  
Gravity Effects ◽  
Entanglement Criterion

We apply the generalised uncertainty principle (GUP) to the entropic uncertainty relation conditions on quantum entanglement. In particular, we study the GUP corrections to the Shannon entropic uncertainty condition for entanglement. We combine previous work on the Shannon entropy entanglement criterion for bipartite systems and the GUP corrections to the Shannon entropy for a single system to calculate the GUP correction for an entangled bipartite system. As in an earlier paper of the second author, which dealt with variance relations, it is shown that there is an increase in the upper bound for the entanglement condition upon the application of the generalised uncertainty principle. Necessary fundamental concepts of the generalised uncertainty principle, entanglement and the entropic uncertainty relations are also discussed. This paper puts together the concepts of entanglement, entropic uncertainty relations and the generalised uncertainty principle all of which have been separately discussed in pedagogical papers by Schroeder, Majernik et al., Blado et al. and Sprenger.  

Limits on entropic uncertainty relations

2010 ◽  
Vol 10 (9&10) ◽  
pp. 848-858
Author(s):  
Andris Ambainis
Keyword(s):  
Quantum State ◽  
Uncertainty Relation ◽  
Mutually Unbiased Bases ◽  
Uncertainty Relations ◽  
Entropic Uncertainty Relations ◽  
Entropic Uncertainty Relation ◽  
Standard Construction ◽  
The One ◽  
Prime Dimension ◽  
Better Than

We consider entropic uncertainty relations for outcomes of the measurements of a quantum state in 3 or more mutually unbiased bases (MUBs), chosen from the standard construction of MUBs in prime dimension. We show that, for any choice of 3 MUBs and at least one choice of a larger number of MUBs, the best possible entropic uncertainty relation can be only marginally better than the one that trivially follows from the relation by Maassen and Uffink for 2 bases.

scholarly journals Entropic uncertainty relation in neutrino oscillations

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Dong Wang ◽  
Fei Ming ◽  
Xue-Ke Song ◽  
Liu Ye ◽  
Jing-Ling Chen
Keyword(s):  
Quantum Correlation ◽  
Neutrino Oscillations ◽  
Quantum Information Processing ◽  
Physical Phenomenon ◽  
Uncertainty Relations ◽  
Classical Counterpart ◽  
Entropic Uncertainty Relations ◽  
Entropic Uncertainty Relation ◽  
Neutrino Flavor ◽  
Potential Applications

Abstract Neutrino oscillation is deemed as an interesting physical phenomenon and shows the nonclassical features made apparently by the Leggett–Garg inequality. The uncertainty principle is one of the fundamental features that distinguishes the quantum world to its classical counterpart. And the principle can be depicted in terms of entropy, which forms the so-called entropic uncertainty relations (EUR). In this work, the entropic uncertainty relations that are relevant to the neutrino-flavor states are investigated by comparing the experimental observation of neutrino oscillations to predictions. From two different neutrino sources, we analyze ensembles of reactor and accelerator neutrinos for different energies, including measurements performed by the Daya Bay collaboration using detectors at 0.5 and 1.6 km from their source, and by the MINOS collaboration using a detector with a 735km distance to the neutrino source. It is found that the entropy-based uncertainty conditions strengths exhibits non-monotonic evolutions as the energy increases. We also quantify the systemic quantumness measured by quantum correlation, and derive the intrinsic relationship between quantum correlation and EUR. Furthermore, we utilize EUR as a criterion to detect entanglement of neutrino-flavor state. Our results could illustrate the potential applications of neutrino oscillations on quantum information processing in the weak-interaction processes.

scholarly journals Additivity of entropic uncertainty relations

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 59 ◽  
Author(s):  
René Schwonnek
Keyword(s):  
Uncertainty Relation ◽  
Natural Generalization ◽  
Uncertainty Relations ◽  
Entanglement Witness ◽  
Separable States ◽  
Entropic Uncertainty Relations ◽  
Multipartite System ◽  
Positive Coefficients ◽  
Global Uncertainty ◽  
Projective Measurements

We consider the uncertainty between two pairs of local projective measurements performed on a multipartite system. We show that the optimal bound in any linear uncertainty relation, formulated in terms of the Shannon entropy, is additive. This directly implies, against naive intuition, that the minimal entropic uncertainty can always be realized by fully separable states. Hence, in contradiction to proposals by other authors, no entanglement witness can be constructed solely by comparing the attainable uncertainties of entangled and separable states. However, our result gives rise to a huge simplification for computing global uncertainty bounds as they now can be deduced from local ones. Furthermore, we provide the natural generalization of the Maassen and Uffink inequality for linear uncertainty relations with arbitrary positive coefficients.

scholarly journals Entropic uncertainty relation under correlated dephasing channels

2018 ◽  
Vol 96 (7) ◽  
pp. 700-704 ◽  
Author(s):  
Göktuğ Karpat
Keyword(s):  
Quantum Mechanics ◽  
Standard Deviation ◽  
Lower Bound ◽  
Quantum System ◽  
Quantum Channel ◽  
Uncertainty Relation ◽  
Open Quantum System ◽  
Uncertainty Relations ◽  
Entropic Uncertainty Relation ◽  
Incompatible Observables

Uncertainty relations are a characteristic trait of quantum mechanics. Even though the traditional uncertainty relations are expressed in terms of the standard deviation of two observables, there exists another class of such relations based on entropic measures. Here we investigate the memory-assisted entropic uncertainty relation in an open quantum system scenario. We study the dynamics of the entropic uncertainty and its lower bound, related to two incompatible observables, when the system is affected by noise, which can be described by a correlated Pauli channel. In particular, we demonstrate how the entropic uncertainty for these two incompatible observables can be reduced as the correlations in the quantum channel grow stronger.

scholarly journals Tripartite entropic uncertainty relation under phase decoherence

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
R. A. Abdelghany ◽  
A.-B. A. Mohamed ◽  
M. Tammam ◽  
Watson Kuo ◽  
H. Eleuch
Keyword(s):  
Lower Bound ◽  
Uncertainty Relation ◽  
Nearest Neighbors ◽  
The Other ◽  
Uncertainty In Measurement ◽  
Entropic Uncertainty Relation ◽  
Specific Choice ◽  
Phase Decoherence ◽  
Time Invariant ◽  
Incompatible Observables

AbstractWe formulate the tripartite entropic uncertainty relation and predict its lower bound in a three-qubit Heisenberg XXZ spin chain when measuring an arbitrary pair of incompatible observables on one qubit while the other two are served as quantum memories. Our study reveals that the entanglement between the nearest neighbors plays an important role in reducing the uncertainty in measurement outcomes. In addition we have shown that the Dolatkhah’s lower bound (Phys Rev A 102(5):052227, 2020) is tighter than that of Ming (Phys Rev A 102(01):012206, 2020) and their dynamics under phase decoherence depends on the choice of the observable pair. In the absence of phase decoherence, Ming’s lower bound is time-invariant regardless the chosen observable pair, while Dolatkhah’s lower bound is perfectly identical with the tripartite uncertainty with a specific choice of pair.

scholarly journals Tight entropic uncertainty relations for systems with dimension three to five

2017 ◽  
Vol 95 (3) ◽  
Author(s):  
Alberto Riccardi ◽  
Chiara Macchiavello ◽  
Lorenzo Maccone
Keyword(s):  
Uncertainty Relations ◽  
Entropic Uncertainty Relations

scholarly journals On Uncertainty Relations and Entanglement Detection with Mutually Unbiased Measurements

2015 ◽  
Vol 22 (01) ◽  
pp. 1550005 ◽  
Author(s):  
Alexey E. Rastegin
Keyword(s):  
The State ◽  
Uncertainty Relations ◽  
Trade Off ◽  
Entropic Uncertainty Relations ◽  
Finite Dimensional ◽  
State Dependent ◽  
Entanglement Detection

We formulate some properties of a set of several mutually unbiased measurements. These properties are used for deriving entropic uncertainty relations. Applications of mutually unbiased measurements in entanglement detection are also revisited. First, we estimate from above the sum of the indices of coincidence for several mutually unbiased measurements. Further, we derive entropic uncertainty relations in terms of the Rényi and Tsallis entropies. Both the state-dependent and state-independent formulations are obtained. Using the two sets of local mutually unbiased measurements, a method of entanglement detection in bipartite finite-dimensional systems may be realized. A certain trade-off between a sensitivity of the scheme and its experimental complexity is discussed.

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