scholarly journals Uncertainty Relation between Detection Probability and Energy Fluctuations

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 595
Author(s):  
Felix Thiel ◽  
Itay Mualem ◽  
David Kessler ◽  
Eli Barkai
Keyword(s):  
Detection Probability ◽  
Uncertainty Relation ◽  
Finite Graph ◽  
Quantum Walks ◽  
Destructive Interference ◽  
Classical Counterpart ◽  
Random Walker ◽  
Search Processes ◽  
Local Measurements ◽  
Arrival Probability

A classical random walker starting on a node of a finite graph will always reach any other node since the search is ergodic, namely it fully explores space, hence the arrival probability is unity. For quantum walks, destructive interference may induce effectively non-ergodic features in such search processes. Under repeated projective local measurements, made on a target state, the final detection of the system is not guaranteed since the Hilbert space is split into a bright subspace and an orthogonal dark one. Using this we find an uncertainty relation for the deviations of the detection probability from its classical counterpart, in terms of the energy fluctuations.

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 A limit law of the return probability for a quantum walk on a hexagonal lattice

2015 ◽  
Vol 13 (07) ◽  
pp. 1550054 ◽  
Author(s):  
Takuya Machida
Keyword(s):  
Random Walks ◽  
Discrete Time ◽  
Hexagonal Lattice ◽  
Quantum Walk ◽  
Quantum Walks ◽  
The Other ◽  
View Point ◽  
Initial State ◽  
Random Walker ◽  
Return Probability

A return probability of random walks is one of the interesting subjects. As it is well known, the return probability strongly depends on the structure of the space where the random walker moves. On the other hand, the return probability of quantum walks, which are quantum models corresponding to random walks, has also been investigated to some extend lately. In this paper, we take care of a discrete-time three-state quantum walk on a hexagonal lattice from the view point of mathematics. The mathematical result shows a limit of the return probability when the walker starts off at the origin. The result of the limit tells us about a possibility of localization at the position and a dependence of localization on the initial state.

scholarly journals Continuous-time quantum walks on the threshold network model

2010 ◽  
Vol 20 (6) ◽  
pp. 1079-1090 ◽  
Author(s):  
YUSUKE IDE ◽  
NORIO KONNO
Keyword(s):  
Network Model ◽  
Continuous Time ◽  
Quantum Walks ◽  
Rigorous Results ◽  
Scale Free ◽  
Random Walker ◽  
Starting Point ◽  
Time Quantum ◽  
Threshold Network ◽  
Law Degree

It is well known that many real world networks have a power-law degree distribution (the scale-free property). However, there are no rigorous results for continuous-time quantum walks on such realistic graphs. In this paper, we analyse the space–time behaviour of continuous-time quantum walks and random walks on the threshold network model, which is a reasonable candidate model having the scale-free property. We show that the quantum walker exhibits localisation at the starting point, although the random walker tends to spread uniformly.

scholarly journals Eigenvalues, absolute continuity and localizations for periodic unitary transition operators

2019 ◽  
Vol 22 (02) ◽  
pp. 1950011 ◽  
Author(s):  
Tatsuya Tate
Keyword(s):  
Hilbert Space ◽  
Absolute Continuity ◽  
Transition Probabilities ◽  
Finite Graph ◽  
Quantum Walks ◽  
Transition Operator ◽  
Unitary Matrix ◽  
Initial State ◽  
Analytic Perturbation Theory ◽  
Transition Operators

The localization phenomenon for periodic unitary transition operators on a Hilbert space consisting of square summable functions on an integer lattice with values in a finite-dimensional Hilbert space, which is a generalization of the discrete-time quantum walks with constant coin matrices, is discussed. It is proved that a periodic unitary transition operator has an eigenvalue if and only if the corresponding unitary matrix-valued function on a torus has an eigenvalue which does not depend on the points on the torus. It is also proved that the continuous spectrum of a periodic unitary transition operator is absolutely continuous. As a result, it is shown that the localization happens if and only if there exists an eigenvalue, and when there exists only one eigenvalue, the long-time limit of transition probabilities coincides with the point-wise norm of the projection of the initial state to the eigenspace. The results can be applied to certain unitary operators on a Hilbert space on a covering graph, called a topological crystal, over a finite graph. An analytic perturbation theory for matrices in several complex variables is employed to show the result about absolute continuity for periodic unitary transition operators.

Uncertainty relation in broadband laser pulse shaping

2020 ◽  
Author(s):  
Konstantin B. Yushkov ◽  
Vladimir Ya. Molchanov ◽  
E.A. Khazanov
Keyword(s):  
Laser Pulse ◽  
Pulse Shaping ◽  
Uncertainty Relation ◽  
Broadband Laser ◽  
Laser Pulse Shaping

Recent advances on urban taxi sharing systems with the path arrival probability

2020 ◽  
Vol 13 ◽  
Author(s):  
Dui Hongyan ◽  
Zhang Chi
Keyword(s):  
Failure Probability ◽  
Traffic Congestion ◽  
Optimal Strategy ◽  
Time Windows ◽  
Optimal Path ◽  
Route Planning ◽  
Driving Time ◽  
Load Rate ◽  
Travel Efficiency ◽  
Arrival Probability

Background : Taxi sharing is an emerging transportation arrangement that helps improve the passengers’ travel efficiency and reduce costs. This study proposes an urban taxi sharing system. Methods: Considering each side congestion of the transport network, their corresponding reliability and failure probability are analyzed. Under the constraints of the number of passengers and their own time windows, the analysis is performed on passengers whose optimal path is inclusive. Results: According to the optimal strategy, the different passengers can be arranged into the same taxi to realize the taxi sharing. Then the shared taxi route can be optimized. Conclusion: Due to the reasonable vehicle route planning and passenger combination, these can effectively alleviate the traffic congestion, save the driving time, reduce the taxi no-load rate, and save the driving distance. At last, a numerical example is used to demonstrate the proposed method.

Local Measurements of Radial Plasma Velocity Fluctuations in the FT-2 Tokamak Using Equatorial Enhanced Scattering

2020 ◽  
Vol 46 (8) ◽  
pp. 767-770
Author(s):  
A. D. Gurchenko ◽  
E. Z. Gusakov ◽  
A. B. Altukhov ◽  
V. A. Ivanov ◽  
A. V. Sidorov ◽  
...  
Keyword(s):  
Plasma Velocity ◽  
Velocity Fluctuations ◽  
Local Measurements
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