quantum-unified 0.0.1

Core utilities for the curvature–information invariant Y = sqrt(d_eff-1) * A^2 / I

quantum-unified

Curvature–Information utilities: compute and analyze the invariant

Y = sqrt(d_eff - 1) * A^2 / I

where

• A is the Bures (Uhlmann) angle between two density matrices,
• I is mutual information in bits from a Stinespring dilation, and
• d_eff = 1 / Tr(rho^2) is the effective dimension.

The package provides stable, dependency‑light helpers for fidelity/angle, effective dimension, entropies in bits, mutual information, and convenience functions to assemble Y from reduced or joint states.

Install

ash pip install quantum-unified

Quick start

`python import numpy as np from quantum_unified import ( bures_angle, effective_dimension, von_neumann_entropy_bits, mutual_information_bits, compute_Y, )

Two qubit states (example)

rho0 = np.array([[1,0],[0,0]], dtype=complex) rho1 = np.array([[0.9, 0.1],[0.1, 0.1]], dtype=complex)

A = bures_angle(rho0, rho1) # Uhlmann/Bures angle (radians) De = effective_dimension(rho1) # 1 / Tr(rho^2) Y = compute_Y(rho0, rho1, Ibits=0.5) # needs mutual information in bits print(A, De, Y) `

API

• ures_angle(rho, sigma) -> float: Bures angle A.
• effective_dimension(rho) -> float: Effective dimension d_eff.
• on_neumann_entropy_bits(rho) -> float: Entropy in bits.
• mutual_information_bits(rhoS, rhoE, rhoSE) -> float: I = S(S)+S(E)-S(SE) in bits.
• compute_Y(rhoS, rhoS_prime, Ibits) -> float: Y from reduced states and Ibits.
• partial_trace_SE(rhoSE, dims, subsystem) / compute_Y_from_SE(...): helpers with joint state.

Background: the curvature–information invariant

Y couples the Bures geometry of quantum states (via the fidelity angle) to informational change (mutual information). In isotropic/2‑design regimes, Y concentrates with mean Y0 + O(D^{-1}) and variance Θ(D^{-1}). This package exposes the building blocks to evaluate Y in your own models and data.

License

BSD 3‑Clause. See LICENSE.

Author

Anthony Olevester ([e-mail])