Conditional probabilities and statistical independence in quantum theory

1978 ◽  
Vol 19 (8) ◽  
pp. 1705-1710 ◽  
Author(s):  
M. D. Srinivas
Keyword(s):  
Quantum Theory ◽  
Statistical Independence ◽  
Conditional Probabilities

Reasoning About Measurements

2021 ◽  
pp. 31-92
Author(s):  
Jochen Rau
Keyword(s):  
Probability Theory ◽  
Quantum Theory ◽  
Physical Theory ◽  
Logical Structure ◽  
Statistical Independence ◽  
Classical Probability ◽  
Multiple Systems ◽  
Classical Probability Theory ◽  
Operational Requirement

This chapter explains the approach of ‘operationalism’, which in a physical theory admits only concepts associated with concrete experimental procedures, and lays out its consequences for propositions about measurements, their logical structure, and states. It illustrates these with toy examples where the ability to perform measurements is limited by design. For systems composed of several constituents this chapter introduces the notions of composite and reduced states, statistical independence, and correlations. It examines what it means for multiple systems to be prepared identically, and how this is represented mathematically. The operational requirement that there must be procedures to measure and prepare a state is examined, and the ensuing constraints derived. It is argued that these constraint leave only one alternative to classical probability theory that is consistent, universal, and fully operational, namely, quantum theory.

More about systematic errors in charge-density studies

2014 ◽  
Vol 70 (5) ◽  
pp. 499-513 ◽  
Author(s):  
Julian Henn ◽  
Kathrin Meindl
Keyword(s):  
Experimental Data ◽  
Charge Density ◽  
Systematic Errors ◽  
Model Parameters ◽  
Statistical Independence ◽  
Conditional Probabilities ◽  
Density Data ◽  
Scientific Fields

In order to detect and graphically visualize the absence or presence of systematic errors in fit data, conditional probabilities are employed to analyze the statistical independence or dependence of fit residuals. This concept is completely general and applicable to all scientific fields in which model parameters are fitted to experimental data. The applications presented in this work refer to published charge-density data.

Quantum Theory

2017 ◽  
Author(s):  
Jochen Rau
Keyword(s):  
Quantum Theory ◽  
Mathematical Representation ◽  
General Notion ◽  
Projection Operators ◽  
Statistical Independence ◽  
Level System ◽  
Mixed States ◽  
Macroscopic System ◽  
Composite Systems ◽  
System A

From the outset statistical mechanics will be framed in the language of quantum theory. The typical macroscopic system is composed of multiple constituents, and hence described in some many-particle Hilbert space. In general, not much is known about such a system, certainly not the precise preparation of all its microscopic details. Thus, its description requires a more general notion of a quantum state, a so-called mixed state. This chapter begins with a brief review of the basic axioms of quantum theory regarding observables, pure states, measurements, and time evolution. Particular attention is paid to the use of projection operators and to the most elementary quantum system, a two-level system. The chapter then motivates the introduction of mixed states and examines in detail their mathematical representation and properties. It also dwells on the description of composite systems, introducing, in particular, the notions of statistical independence and correlations.

Comparing conditional probabilities and statistical independence in layers of protection analysis

2020 ◽  
Author(s):  
Timothy C. Mott ◽  
Paul Michael Kivistik ◽  
Anna K. Panorska ◽  
David C. Cantu
Keyword(s):  
Statistical Independence ◽  
Conditional Probabilities

scholarly journals Bell’s “Theorem”: loopholes vs. conceptual flaws

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 754-761
Author(s):  
A. F. Kracklauer
Keyword(s):  
Quantum Theory ◽  
Critical Analysis ◽  
Current Theory ◽  
Central Point ◽  
Bell’S Theorem ◽  
Historical Overview ◽  
Bell's Theorem ◽  
Conditional Probabilities

AbstractAn historical overview and detailed explication of a critical analysis of what has become known as Bell’s Theorem to the effect that, it should be impossible to extend Quantum Theory with the addition of local, real variables so as to obtain a version free of the ambiguous and preternatural features of the currently accepted interpretations is presented. The central point on which this critical analysis, due originally to Edwin Jaynes, is that Bell incorrectly applied probabilistic formulas involving conditional probabilities. In addition, mathematical technicalities that have complicated the understanding of the logical or mathematical setting in which current theory and experimentation are embedded, are discussed. Finally, some historical speculations on the sociological environment, in particular misleading aspects, in which recent generations of physicists lived and worked are mentioned.

Quantum theory of light in nonlinear media with dispersion and absorption

1998 ◽  
Vol 45 (2) ◽  
pp. 377-402 ◽  
Author(s):  
EDUARD SCHMIDT , JOHN JEFFERS , STEPHEN M.
Keyword(s):  
Quantum Theory ◽  
Nonlinear Media

The Constructive Thinking Inventory: Factorial Structure in Healthy Individuals and Patients with Chronic Skin Diseases

1998 ◽  
Vol 14 (3) ◽  
pp. 226-233 ◽  
Author(s):  
Jürgen Hoyer ◽  
Mechthild Averbeck ◽  
Thomas Heidenreich ◽  
Ulrich Stangier ◽  
Karin Pöhlmann ◽  
...  
Keyword(s):  
Skin Diseases ◽  
Principal Component ◽  
Initial Study ◽  
Statistical Independence ◽  
Constructive Thinking ◽  
Global Factor ◽  
Emotional Coping ◽  
Factor Congruence ◽  
Chronic Skin ◽  
Chronic Skin Diseases

Epstein's “Constructive Thinking Inventory” (CTI) was developed to measure the construct of experiential intelligence, which is based on his cognitive-experiential self-theory. Inventory items were generated by sampling naturally occurring automatic cognitions. Using principal component analysis, the findings showed a global factor of coping ability as well as six main factors: Emotional Coping, Behavioral Coping, Categorical Thinking, Personal Superstitious Thinking, Esoteric Thinking, and Naive Optimism. We tested the replicability of this factor structure and the amount of statistical independence (nonredundancy) between these factors in an initial study of German students (Study 1, N = 439) and in a second study of patients with chronic skin disorders (Study 2, N = 187). Factor congruence with the original (American) data was determined using a formula proposed by Schneewind and Cattell (1970) . Our findings show satisfactory factor congruence and statistical independence for Emotional Coping and Esoteric Thinking in both studies, while full replicability or independence could not be found in both for the other factors. Implications for the use and further development of the CTI are discussed.

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