Physics:Quantum Kraus operators



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Quantum Kraus operators is a planned ScholarlyWiki page in the Quantum Collection about Kraus operators and the operator-sum representation.

Overview

Placeholder: explain how a set of Kraus operators represents the evolution of a quantum state under a channel or measurement process.

Key ideas

Placeholder: cover operator-sum representation, density matrices, quantum operations, measurement outcomes, complete positivity.

Operator-sum form

Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

Trace preservation

Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

Examples

Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

Connection to measurements

Placeholder: develop this section with definitions, examples, formulas, and links to related Quantum Collection pages.

Index

Core theory

1. Foundations

2. Conceptual and interpretations

3. Mathematical structure and systems

4. Atomic and spectroscopy

5. Wavefunctions and modes

6. Quantum dynamics and evolution

7. Measurement and information

8. Quantum information and computing

Applications and extensions

9. Quantum optics and experiments

10. Open quantum systems

11. Quantum field theory

12. Statistical mechanics and kinetic theory

13. Condensed matter and solid-state physics

14. Plasma and fusion physics

15. Timeline

16. Advanced and frontier topics

Book II

• Matter by scale

Book III

• Methods and tools

Book IV

• Data Analysis Techniques

Full contents

1. Foundations (14) Back to index

1. Physics:Quantum basics

2. Physics:Quantum photoelectric effect

3. Physics:Quantum black-body radiation

4. Physics:Quantum Planck constant

5. Physics:Quantum Postulates

6. Physics:Quantum Hilbert space

7. Physics:Quantum Observables and operators

8. Physics:Quantum mechanics

9. Physics:Quantum mechanics measurements

10. Physics:Quantum state

11. Physics:Quantum system

12. Physics:Quantum superposition

13. Physics:Quantum probability

14. Physics:Quantum Mathematical Foundations of Quantum Theory

2. Conceptual and interpretations (14) Back to index

15. Physics:Quantum Interpretations of quantum mechanics

16. Physics:Quantum Wave–particle duality

17. Physics:Quantum Complementarity principle

18. Physics:Quantum Uncertainty principle

19. Physics:Quantum Measurement problem

20. Physics:Quantum Bell's theorem

21. Physics:Quantum Hidden variable theory

22. Physics:Quantum nonlocality

23. Physics:Quantum contextuality

24. Physics:Quantum Darwinism

25. Physics:Quantum A Spooky Action at a Distance

26. Physics:Quantum A Walk Through the Universe

27. Physics:Quantum The Secret of Cohesion and How Waves Hold Matter Together

28. Physics:Quantum measurement problem

3. Mathematical structure and systems (15) Back to index

29. Physics:Quantum Density matrix

30. Physics:Quantum Exactly solvable quantum systems

31. Physics:Quantum many-body problem

32. Physics:Quantum Formulas Collection

33. Physics:Quantum A Matter Of Size

34. Physics:Quantum Symmetry in quantum mechanics

35. Physics:Quantum Noether theorem

36. Physics:Quantum Angular momentum operator

37. Physics:Quantum Runge–Lenz vector

38. Physics:Quantum Approximation Methods

39. Physics:Quantum Matter Elements and Particles

40. Physics:Quantum Dirac equation

41. Physics:Quantum Klein–Gordon equation

42. Physics:Quantum pendulum

43. Physics:Quantum configuration space

4. Atomic and spectroscopy (14) Back to index

44. Physics:Quantum Atomic structure and spectroscopy

45. Physics:Quantum Hydrogen atom

46. Physics:Quantum number

47. Physics:Quantum Multi-electron atoms

48. Physics:Quantum Fine structure

49. Physics:Quantum Hyperfine structure

50. Physics:Quantum Isotopic shift

51. Physics:Quantum defect

52. Physics:Quantum Zeeman effect

53. Physics:Quantum Stark effect

54. Physics:Quantum Spectral lines and series

55. Physics:Quantum Selection rules

56. Physics:Quantum Fermi's golden rule

57. Physics:Quantum beats

5. Wavefunctions and modes (9) Back to index

58. Physics:Quantum Wavefunction

59. Physics:Quantum Superposition principle

60. Physics:Quantum Eigenstates and eigenvalues

61. Physics:Quantum Boundary conditions and quantization

62. Physics:Quantum Standing waves and modes

63. Physics:Quantum Normal modes and field quantization

64. Physics:Number of independent spatial modes in a spherical volume

65. Physics:Quantum Density of states

66. Physics:Quantum carpet

6. Quantum dynamics and evolution (21) Back to index

67. Physics:Quantum Time evolution

68. Physics:Quantum Schrödinger equation

69. Physics:Quantum Time-dependent Schrödinger equation

70. Physics:Quantum Stationary states

71. Physics:Quantum Perturbation theory

72. Physics:Quantum Time-dependent perturbation theory

73. Physics:Quantum Adiabatic theorem

74. Physics:Quantum Berry phase

75. Physics:Quantum Aharonov-Bohm effect

76. Physics:Quantum Aharonov-Casher effect

77. Physics:Quantum Scattering theory

78. Physics:Quantum Scattering matrix

79. Physics:Quantum S-matrix

80. Physics:Quantum tunnelling

81. Physics:Quantum speed limit

82. Physics:Quantum revival

83. Physics:Quantum reflection

84. Physics:Quantum oscillations

85. Physics:Quantum jump

86. Physics:Quantum boomerang effect

87. Physics:Quantum chaos

7. Measurement and information (9) Back to index

88. Physics:Quantum Measurement theory

89. Physics:Quantum Measurement operators

90. Physics:Quantum Projective measurement

91. Physics:Quantum POVM

92. Physics:Quantum Weak measurement

93. Physics:Quantum Measurement collapse

94. Physics:Quantum entanglement

95. Physics:Quantum Zeno effect

96. Physics:Quantum limit

8. Quantum information and computing (14) Back to index

97. Physics:Quantum information theory

98. Physics:Quantum Qubit

99. Physics:Quantum Entanglement

100. Physics:Quantum Bell state

101. Physics:Quantum Gates and circuits

102. Physics:Quantum BB84

103. Physics:Quantum No-cloning theorem

104. Physics:Quantum Computing Algorithms in the NISQ Era

105. Physics:Quantum Noisy Qubits

106. Physics:Quantum Boson sampling

107. Physics:Quantum random access code

108. Physics:Quantum pseudo-telepathy

109. Physics:Quantum network

110. Physics:Quantum money

9. Quantum optics and experiments (10) Back to index

111. Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy

112. Physics:Quantum Stern-Gerlach experiment

113. Physics:Quantum Experimental quantum physics

114. Physics:Quantum optics

115. Physics:Quantum optics beam splitter experiments

116. Physics:Quantum Mach-Zehnder interferometer

117. Physics:Quantum Hong-Ou-Mandel effect

118. Physics:Quantum eraser experiment

119. Physics:Quantum delayed-choice quantum eraser

120. Physics:Quantum Ultra fast lasers

121. Template:Quantum optics operators

10. Open quantum systems (13) Back to index

122. Physics:Quantum Open systems

123. Physics:Quantum channel

124. Physics:Quantum Kraus operators

125. Physics:Quantum Amplitude damping

126. Physics:Quantum Depolarizing channel

127. Physics:Quantum Master equation

128. Physics:Quantum Lindblad equation

129. Physics:Quantum Decoherence

130. Physics:Quantum dissipation

131. Physics:Quantum Markov semigroup

132. Physics:Quantum Markovian dynamics

133. Physics:Quantum Non-Markovian dynamics

134. Physics:Quantum Trajectories

11. Quantum field theory (23) Back to index

135. Physics:Quantum field theory (QFT) basics

136. Physics:Quantum field theory (QFT) core

137. Physics:Quantum Fields and Particles

138. Physics:Quantum Second quantization

139. Physics:Quantum Fock space

140. Physics:Quantum Harmonic Oscillator field modes

141. Physics:Quantum Creation and annihilation operators

142. Physics:Quantum vacuum fluctuations

143. Physics:Quantum Casimir effect

144. Physics:Quantum Propagators in quantum field theory

145. Physics:Quantum Feynman diagrams

146. Physics:Quantum Path integral formulation

147. Physics:Quantum Renormalization in field theory

148. Physics:Quantum Renormalization group

149. Physics:Quantum Field Theory Gauge symmetry

150. Physics:Quantum Spontaneous symmetry breaking

151. Physics:Quantum Non-Abelian gauge theory

152. Physics:Quantum Electrodynamics (QED)

153. Physics:Quantum chromodynamics (QCD)

154. Physics:Quantum Electroweak theory

155. Physics:Quantum Standard Model

156. Physics:Quantum triviality

157. Physics:Quantum confinement problem

12. Statistical mechanics and kinetic theory (9) Back to index

158. Physics:Quantum Statistical mechanics

159. Physics:Quantum Partition function

160. Physics:Quantum Distribution functions

161. Physics:Quantum Liouville equation

162. Physics:Quantum Kinetic theory

163. Physics:Quantum Boltzmann equation

164. Physics:Quantum BBGKY hierarchy

165. Physics:Quantum Relaxation and thermalization

166. Physics:Quantum Thermodynamics

13. Condensed matter and solid-state physics (15) Back to index

167. Physics:Quantum Band structure

168. Physics:Quantum Fermi surfaces

169. Physics:Quantum Landau levels

170. Physics:Quantum Semiconductor physics

171. Physics:Quantum Phonons

172. Physics:Quantum Electron-phonon interaction

173. Physics:Quantum Exchange interaction

174. Physics:Quantum Superconductivity

175. Physics:Quantum Topological phases of matter

176. Physics:Quantum well

177. Physics:Quantum spin liquid

178. Physics:Quantum spin Hall effect

179. Physics:Quantum phase transition

180. Physics:Quantum critical point

181. Physics:Quantum dot

14. Plasma and fusion physics (8) Back to index

182. Physics:Quantum Fusion reactions and Lawson criterion

183. Physics:Quantum Plasma (fusion context)

184. Physics:Quantum Magnetic confinement fusion

185. Physics:Quantum Inertial confinement fusion

186. Physics:Quantum Plasma instabilities and turbulence

187. Physics:Quantum Tokamak core plasma

188. Physics:Quantum Tokamak edge physics and recycling asymmetries

189. Physics:Quantum Stellarator

15. Timeline (8) Back to index

190. Physics:Quantum mechanics/Timeline

191. Physics:Quantum mechanics/Timeline/Pre-quantum era

192. Physics:Quantum mechanics/Timeline/Old quantum theory

193. Physics:Quantum mechanics/Timeline/Modern quantum mechanics

194. Physics:Quantum mechanics/Timeline/Quantum field theory era

195. Physics:Quantum mechanics/Timeline/Quantum information era

196. Physics:Quantum mechanics/Timeline/Quantum technology era

197. Physics:Quantum mechanics/Timeline/Quiz

16. Advanced and frontier topics (16) Back to index

198. Physics:Quantum topology

199. Physics:Quantum battery

200. Physics:Quantum Supersymmetry

201. Physics:Quantum Black hole thermodynamics

202. Physics:Quantum Holographic principle

203. Physics:Quantum gravity

204. Physics:Quantum De Sitter invariant special relativity

205. Physics:Quantum Doubly special relativity

206. Physics:Quantum arithmetic geometry

207. Physics:Quantum unsolved problems

208. Physics:Quantum Yang-Mills mass gap

209. Physics:Quantum gravity problem

210. Physics:Quantum black hole information paradox

211. Physics:Quantum dark matter problem

212. Physics:Quantum neutrino mass problem

213. Physics:Quantum matter-antimatter asymmetry problem

References

Author: Harold Foppele

Source attribution: Physics:Quantum Kraus operators