Entropy, information and quantum measurements

The conditional entropy between two states of a quantum system is shown to be nonincreasing when a complete measurement is performed on the system. The information between two quantum systems is defined and is shown to be bounded above by the logarithmic correlation. This inequality is then applied to the measurement process. The entropy changes in the observed system and the measuring apparatus are compared with the information gain in the measurement.

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  L. Szilard.  über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen , 1929 .

[3]  E. M.,et al.  Statistical Mechanics , 2021, Manual for Theoretical Chemistry.

[4]  E. Wigner.  Die Messung quantenmechanischer Operatoren , 1952 .

[5]  H. Umegaki.  CONDITIONAL EXPECTATION IN AN OPERATOR ALGEBRA, II , 1954 .

[6]  S. Sherman,et al.  Monotone and convex operator functions , 1955 .

[7]  L. Brillouin,et al.  Science and information theory , 1956 .

[8]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[9]  Aleksandr Yakovlevich Khinchin,et al.  Mathematical foundations of information theory , 1959 .

[10]  R. Kunze.  _{} Fourier transforms on locally compact unimodular groups , 1958 .

[11]  H. Araki,et al.  Measurement of Quantum Mechanical Operators , 1960 .

[12]  A Note on the Entropy for Operator Algebras , 1961 .

[13]  R. Schatten, Norm Ideals of Completely Continuous Operators. (Ergebnisse der Mathematik und ihrer Grenzgebiete, Heft 27). VIII + 81 S. Berlin/Göttingen/Heidelberg 1960. Springer‐Verlag. Preis brosch. DM 23,60 , 1961 .

[14]  Mutsuo M. Yanase,et al.  Optimal Measuring Apparatus , 1961 .

[15]  A. Daneri,et al.  QUANTUM THEORY OF MEASUREMENT AND ERGODICITY CONDITIONS , 1962 .

[16]  H. Umegaki.  Conditional expectation in an operator algebra. IV. Entropy and information , 1962 .

[17]  W. Arveson.  Analyticity in Operator Algebras , 1967 .

[18]  Derek W. Robinson,et al.  Mean Entropy of States in Quantum‐Statistical Mechanics , 1968 .

[19]  R. Schatten,et al.  Norm Ideals of Completely Continuous Operators , 1970 .

[20]  H. Falk.  Inequalities of J. W. Gibbs , 1970 .

[21]  David M. Topping.  Lectures on von Neumann algebras , 1971 .

[22]  Göran Lindblad,et al.  An entropy inequality for quantum measurements , 1972 .