Density Matrix Derivations
Density-matrix derivations clarify when a state is mixed, how subsystem states are computed, and why the trace rule is the representation-independent way to compute probabilities and expectation values.
State and Trace Rules
Section titled “State and Trace Rules”- Density Operators
- Pure versus Mixed States
- Classical Mixtures versus Quantum Superpositions
- Trace-Rule Expectation Values
- Density Matrix Expectation Formula Card
Subsystems and Entanglement
Section titled “Subsystems and Entanglement”- Partial Trace
- Reduced Density Operators
- Reduced Density Matrices
- Schmidt Decomposition
- Subsystem Entropy
Entropy and Purification
Section titled “Entropy and Purification”- Entropy Overview
- von Neumann Entropy Formula Card
- Purification Overview
- Renyi Entropies
- Mutual Information
Measurement
Section titled “Measurement”References
Section titled “References”- J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955.
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2010.
- J. Watrous, The Theory of Quantum Information, Cambridge University Press, 2018.