Quantum uncertainty relations and stochastic mechanics

1984 ◽  
Vol 79 (2) ◽  
pp. 175-186 ◽  
Author(s):  
S. De Martino ◽  
S. De Siena
Keyword(s):  
Uncertainty Relations ◽  
Stochastic Mechanics ◽  
Quantum Uncertainty

Position-Momentum Uncertainty Relations in Stochastic Mechanics

1982 ◽  
Vol 49 (3) ◽  
pp. 181-183 ◽  
Author(s):  
Diego de Falco ◽  
Salvatore De Martino ◽  
Silvio De Siena
Keyword(s):  
Uncertainty Relations ◽  
Stochastic Mechanics

scholarly journals On the Uncertainty Relations in Stochastic Mechanics

2012 ◽  
Author(s):  
Dimitar A. Trifonov ◽  
Blagovest A. Nikolov
Keyword(s):  
Uncertainty Relations ◽  
Stochastic Mechanics

scholarly journals Uncertainty relations: An operational approach to the error-disturbance tradeoff

Quantum ◽  
2017 ◽  
Vol 1 ◽  
pp. 20 ◽  
Author(s):  
Joseph M. Renes ◽  
Volkher B. Scholz ◽  
Stefan Huber
Keyword(s):  
Quantum Theory ◽  
Uncertainty Relation ◽  
Uncertainty Relations ◽  
Actual Measurement ◽  
Quantum Uncertainty ◽  
Joint Measurability ◽  
Finite Dimensional ◽  
Wave Particle Duality ◽  
Heisenberg Type ◽  
Conceptual Difficulties

The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous measurements, and comparing the values of unmeasured observables is not necessarily meaningful according to quantum theory. To overcome these conceptual difficulties, we take a different approach and define error and disturbance in an operational manner. In particular, we formulate both in terms of the probability that one can successfully distinguish the actual measurement device from the relevant hypothetical ideal by any experimental test whatsoever. This definition itself does not rely on the formalism of quantum theory, avoiding many of the conceptual difficulties of usual definitions. We then derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems, as well as for the case of position and momentum. Our relations may be directly applied in information processing settings, for example to infer that devices which can faithfully transmit information regarding one observable do not leak any information about conjugate observables to the environment. We also show that Englert's wave-particle duality relation [PRL 77, 2154 (1996)] can be viewed as an error-disturbance uncertainty relation.

scholarly journals Universal quantum uncertainty relations: Minimum-uncertainty wave packet depends on measure of spread

2019 ◽  
Vol 383 (16) ◽  
pp. 1850-1855
Author(s):  
Anindita Bera ◽  
Debmalya Das ◽  
Aditi Sen(De) ◽  
Ujjwal Sen
Keyword(s):  
Wave Packet ◽  
Uncertainty Relations ◽  
Quantum Uncertainty ◽  
Universal Quantum ◽  
Minimum Uncertainty

scholarly journals Universal quantum uncertainty relations between nonergodicity and loss of information

2018 ◽  
Vol 97 (3) ◽  
Author(s):  
Natasha Awasthi ◽  
Samyadeb Bhattacharya ◽  
Aditi Sen(De) ◽  
Ujjwal Sen
Keyword(s):  
Uncertainty Relations ◽  
Loss Of Information ◽  
Quantum Uncertainty ◽  
Universal Quantum
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