Module measure 

Observables, reduced states, entanglement, and ensemble analysis.

Structs

DiagonalEnsemble

DiagonalEnsembleColumn

NoncommutingGroup

One disjoint set of binary modes sharing an exchange phase.

Subspace

Gauge-independent finite-dimensional subspace.

Enums

EntropyOrder

Functions

analyze_diagonal_ensemble

Analyze one or more diagonal probability distributions in a shared eigensystem. Optional observable statistics are evaluated matrix-free in that eigensystem, so stored and matrix-free operators share one path.

apply_fermionic_subsystem_phases

Apply fermionic subsystem-ordering phases to a packed pure state.

apply_fermionic_subsystem_phases_density

Apply the same fermionic mode permutation to both density-matrix axes.

apply_noncommuting_subsystem_exchange_phases

Apply arbitrary selected exchange phases to a pure state.

apply_noncommuting_subsystem_exchange_phases_density

Apply arbitrary selected exchange phases to both density-matrix axes.

apply_noncommuting_subsystem_phases

Apply selected noncommuting-group exchange phases to a pure state.

apply_noncommuting_subsystem_phases_density

Apply selected noncommuting-group exchange phases to both density axes.

array_to_ints

Convert most-significant-site-first binary rows to integer states.

array_to_states

canonical_schmidt_spectrum_subsystem

Canonical Schmidt spectrum for a pure bipartition.

canonical_schmidt_spectrum_subsystem_with_exchange_phases

density_expectation

density_matrix_spectrum

Sorted eigenvalue spectrum of a row-major positive semidefinite density matrix.

density_quantum_fluctuation

Density-matrix fluctuation Tr(ρ A²) - Tr(ρ A)².

diagonal_density_matrix

diagonal_ensemble

diagonal_ensemble_density

diagonal_ensemble_from_probabilities

diagonal_ensemble_observable

ed_density_vs_time

Density-matrix counterpart of ed_state_vs_time, with row-major input and output matrices.

ed_state_vs_time

Exact time evolution from a complete eigendecomposition.

energy_window_indices

entanglement_entropy

entanglement_entropy_batch

entanglement_entropy_density

entanglement_entropy_density_subsystem

entanglement_entropy_sector

Entanglement entropy of a pure state represented in a binary sector.

entanglement_entropy_subsystem

entanglement_spectrum

entanglement_spectrum_density

entanglement_spectrum_density_subsystem

entanglement_spectrum_sector

Entanglement spectrum of a pure state represented in a binary sector.

entanglement_spectrum_subsystem

entropy_from_spectrum

Entropy of an already validated density-matrix spectrum.

expectation

fermionic_subsystem_phases

Fock-space signs induced by grouping selected fermionic modes into a subsystem. The returned phase is indexed by the original packed state.

ints_to_array

Convert integer states to most-significant-site-first binary rows.

kl_divergence

matrix_element

mean_level_spacing

Mean adjacent-gap ratio of an ordered spectrum.

noncommuting_subsystem_exchange_phases

General exchange phases induced by regrouping disjoint binary-mode groups.

noncommuting_subsystem_phases

Exchange phases induced by regrouping a tensor product with selected mutually anticommuting site groups.

observables_vs_time

partial_trace

Reduced density matrix of the first factor of a pure bipartite state.

partial_trace_density

Reduced density matrix of the first factor for a row-major mixed state.

partial_trace_density_subsystem

Mixed-state partial trace for an arbitrary retained site set.

partial_trace_sector_density

Reduced density matrix of a mixed state stored in an arbitrary binary sector basis.

partial_trace_sector_state

Reduced density matrix of a pure state stored in an arbitrary binary sector basis.

partial_trace_subsystem

Reduced density matrix for an arbitrary retained set of mixed-radix sites. Site zero is the least-significant local digit, matching the basis encodings.

project_operator

Compute P† A P one reduced column at a time.

quantum_fluctuation

Variance ||A psi||^2 - |<psi|A|psi>|^2 for a normalized state.

raw_quantum_fluctuation

Raw pure-state fluctuation ⟨ψ|A²|ψ⟩ - ⟨ψ|A|ψ⟩² without normalizing ψ.

states_to_array

subspace_fidelity

Mean squared principal-angle cosine between two subspaces.

subsystem_dimensions

Tensor-product dimensions selected by an arbitrary retained site set.