Weak Values and the Reconstruction Problem

2016 ◽  
pp. 161-170
Author(s):  
Maurice A. de Gosson
Keyword(s):  
Weak Values ◽  
Reconstruction Problem

scholarly journals Quantum Polar Duality and the Symplectic Camel: A New Geometric Approach to Quantization

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Maurice A. de Gosson
Keyword(s):  
Uncertainty Principle ◽  
Convex Geometry ◽  
Geometric Approach ◽  
Point Of View ◽  
Reconstruction Problem ◽  
Orthogonal Projections ◽  
Topological Version ◽  
Mahler Conjecture ◽  
Quantum Indeterminacy ◽  
Dual Quantum

AbstractWe define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance ellipsoid of a quantum state on the configuration and momentum spaces form what we call a dual quantum pair. We thereafter show that quantum polarity allows solving the Pauli reconstruction problem for Gaussian wavefunctions. The notion of quantum polarity exhibits a strong interplay between the uncertainty principle and symplectic and convex geometry and our approach could therefore pave the way for a geometric and topological version of quantum indeterminacy. We relate our results to the Blaschke–Santaló inequality and to the Mahler conjecture. We also discuss the Hardy uncertainty principle and the less-known Donoho–Stark principle from the point of view of quantum polarity.

scholarly journals Identifying weak values with intrinsic dynamical properties in modal theories

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Devashish Pandey ◽  
Rui Sampaio ◽  
Tapio Ala-Nissila ◽  
Guillermo Albareda ◽  
Xavier Oriols
Keyword(s):  
Weak Values ◽  
Dynamical Properties

scholarly journals On a Reconstruction Problem for Sequences

1997 ◽  
Vol 77 (2) ◽  
pp. 344-348 ◽  
Author(s):  
I. Krasikov ◽  
Y. Roditty
Keyword(s):  
Reconstruction Problem

scholarly journals Manifestation of pointer-state correlations in complex weak values of quantum observables

2016 ◽  
Vol 94 (5) ◽  
Author(s):  
Som Kanjilal ◽  
Girish Muralidhara ◽  
Dipankar Home
Keyword(s):  
Weak Values ◽  
Quantum Observables

scholarly journals Comment on “Non-representative Quantum Mechanical Weak Values”

2017 ◽  
Vol 47 (4) ◽  
pp. 467-470 ◽  
Author(s):  
Alon Ben-Israel ◽  
Lev Vaidman
Keyword(s):  
Quantum Mechanical ◽  
Weak Values

scholarly journals COMBINATORIAL RECONSTRUCTION OF HALF-SIBLING GROUPS FROM MICROSATELLITE DATA

2010 ◽  
Vol 08 (02) ◽  
pp. 337-356 ◽  
Author(s):  
SAAD I. SHEIKH ◽  
TANYA Y. BERGER-WOLF ◽  
ASHFAQ A. KHOKHAR ◽  
ISABEL C. CABALLERO ◽  
MARY V. ASHLEY ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Experimental Results ◽  
Microsatellite Data ◽  
Reconstruction Problem ◽  
Full Sibling ◽  
Synthetic Datasets ◽  
Sibling Group ◽  
Half Sibling ◽  
Sibling Groups

While full-sibling group reconstruction from microsatellite data is a well-studied problem, reconstruction of half-sibling groups is much less studied, theoretically challenging, and computationally demanding. In this paper, we present a formulation of the half-sibling reconstruction problem and prove its APX-hardness. We also present exact solutions for this formulation and develop heuristics. Using biological and synthetic datasets we present experimental results and compare them with the leading alternative software COLONY. We show that our results are competitive and allow half-sibling group reconstruction in the presence of polygamy, which is prevalent in nature.

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