Quantum Exponential Families

This section is under development.

Introduction

Quantum exponential families represent quantum states in the form:

\[\rho(\theta) = \exp\left(\sum_a \theta_a F_a - \psi(\theta)\right)\]

where:

  • \(F_a\) are Hermitian operators (generators)

  • \(\theta_a\) are natural parameters

  • \(\psi(\theta)\) is the log-partition function

Creating an Exponential Family

from qig.exponential_family import QuantumExponentialFamily

# Qutrit with Gell-Mann operators
exp_fam = QuantumExponentialFamily(d=3, basis_type='gell-mann')

# With entangling pair operators
exp_fam_pairs = QuantumExponentialFamily(
    d=3,
    basis_type='gell-mann',
    include_pairs=True
)

See Also