scholarly journals Measurement Uncertainty Relations for Position and Momentum: Relative Entropy Formulation

Entropy ◽  
2017 ◽  
Vol 19 (7) ◽  
pp. 301 ◽  
Author(s):  
Alberto Barchielli ◽  
Matteo Gregoratti ◽  
Alessandro Toigo
Keyword(s):  
Measurement Uncertainty ◽  
Relative Entropy ◽  
Uncertainty Relations ◽  
Entropy Formulation

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 Measurement uncertainty relations

2014 ◽  
Vol 55 (4) ◽  
pp. 042111 ◽  
Author(s):  
Paul Busch ◽  
Pekka Lahti ◽  
Reinhard F. Werner
Keyword(s):  
Measurement Uncertainty ◽  
Uncertainty Relations

scholarly journals Limiting Uncertainty Relations in Laser-Based Measurements of Position and Velocity Due to Quantum Shot Noise

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 264 ◽  
Author(s):  
Andreas Fischer
Keyword(s):  
Measurement Uncertainty ◽  
Wave Vector ◽  
Shot Noise ◽  
Measurement Techniques ◽  
Time Of Flight ◽  
Wave Number ◽  
Uncertainty Relations ◽  
Position Measurement ◽  
Information Theoretic ◽  
Measurement Systems

With the ongoing progress of optoelectronic components, laser-based measurement systems allow measurements of position as well as displacement, strain and velocity with unbeatable speed and low measurement uncertainty. The performance limit is often studied for a single measurement setup, but a fundamental comparison of different measurement principles with respect to the ultimate limit due to quantum shot noise is rare. For this purpose, the Cramér-Rao bound is described as a universal information theoretic tool to calculate the minimal achievable measurement uncertainty for different measurement techniques, and a review of the respective lower bounds for laser-based measurements of position, displacement, strain and velocity at particles and surfaces is presented. As a result, the calculated Cramér-Rao bounds of different measurement principles have similar forms for each measurand including an indirect proportionality with respect to the number of photons and, in case of the position measurement for instance, the wave number squared. Furthermore, an uncertainty principle between the position uncertainty and the wave vector uncertainty was identified, i.e., the measurement uncertainty is minimized by maximizing the wave vector uncertainty. Additionally, physically complementary measurement approaches such as interferometry and time-of-flight positions measurements as well as time-of-flight and Doppler particle velocity measurements are shown to attain the same fundamental limit. Since most of the laser-based measurements perform similar with respect to the quantum shot noise, the realized measurement systems behave differently only due to the available optoelectronic components for the concrete measurement task.

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