Overview

• Core symbolic terms
  • Symbolic terms
    • Setup
    • Operator words with OpTerm
    • Normal-ordered monomials
    • Ket-like terms
    • Density-like terms
    • Choosing between the term types
    • API reference
• Modes
  • Overview
  • Physical motivation
  • Structure of a mode
  • Minimal example
  • Submodules
    • Mode labels
      • Overview
      • Examples
        • Constructing a mode label
        • Mode-label overlap
        • Replacing one component
        • Visualization
      • Design notes
    • Envelopes
      • Overview
      • Normalization
      • Time and frequency representations
      • Gaussian envelopes
      • Filtered and numerical envelopes
      • Examples
        • Gaussian envelope
        • Envelope overlap
        • Gaussian mixture (implicit)
      • Design notes
    • Transfer functions
      • Overview
      • Examples
      • Normalization and loss
      • Execution strategies
        • Gaussian-closed (analytic)
        • Numerical filtering
      • Gaussian transfer formalism
      • Structure-preserving operations
      • Examples
        • Gaussian band-pass filter (analytic)
        • Time delay (structure-preserving)
        • Numerical filtering fallback
      • Design notes
    • Polarization
      • Overview
      • Physical meaning
      • Built-in polarization states
      • Examples
        • Standard polarization states
        • Polarization overlaps
        • Visualization
        • Comparing linear and circular polarization
        • Linear polarization by angle
        • Rotation
        • Unitary transformation
      • Design notes
    • Path
      • Overview
      • Physical meaning
      • Examples
        • Constructing path labels
        • Path overlaps
      • Role in composite mode labels
      • Design notes
• CCR algebra
  • Ket algebra
    • Main ideas
    • Constructing from a normal-ordered monomial
    • Normal ordering from a word
    • Main operations
    • Example: symbolic inner product
    • API links
  • Density algebra
    • Main ideas
    • Constructing a pure density from a ket
    • Left and right actions
    • Main operations
    • Example: trace and purity
    • API links
  • Operator algebra
    • Main ideas
    • Basic constructors
    • Quadratures
    • Actions via @
    • API links
  • Normal ordering, expectation values, and trace
    • Background
    • Setup
    • Normal ordering example: \(a a^\dagger\)
    • Algorithmic picture
    • Step-by-step normal ordering
    • Two-mode expectation values
    • Already normal-ordered input
    • Constructing from operators vs words
    • Scalar overlaps
    • Operator action on kets
    • Expectation values
    • From kets to density operators
    • Trace
    • Purity
    • Left and right operator action
    • Partial trace
    • End-to-end example
    • Summary
    • See also