bound-entangled

Reference implementations of several families of bound entangled states from the quantum information literature, as plain NumPy density matrices.

A bound entangled state is entangled yet has a positive partial transpose (PPT), so no pure entanglement can be distilled from it. This library collects constructions that are otherwise scattered across papers into a single, tested package, each factory returning the density matrix rho of the state.

📖 Documentation — one page per state, with the construction written out and what is known about it.

There is a TypeScript port of this package, also called bound-entangled — see js/README.md.

Installation

pip install bound-entangled

From a clone (the package lives in the python/ directory):

cd python && pip install -e ".[test]"

Requires Python ≥ 3.9. Depends on toqito and NumPy.

Usage

Packages are organized by the bipartite Hilbert space the states live in (c3_otimes_c3 = C³ ⊗ C³, cm_otimes_cn = C^m ⊗ C^n, etc.).

from bound_entangled.c3_otimes_c3 import chessboard_extremal_PPT, tiles_upb, pyramid_upb
from bound_entangled.cd_otimes_cd import yu_oh
from bound_entangled.c5_otimes_c5 import sn3_grid_state

rho = chessboard_extremal_PPT()          # 9x9 PPT-entangled chessboard state
rho = yu_oh(full_dim=3, x=0.5, y=0.1)    # Yu-Oh nonlocal bound entangled state

The two Horodecki states are both called horodecki, each in the package of the space it lives in: c2_otimes_c4 and c3_otimes_c3.

States

c2_otimes_c4 — C² ⊗ C⁴

c3_otimes_c3 — C³ ⊗ C³

c4_otimes_c4 — C⁴ ⊗ C⁴

c5_otimes_c5 — C⁵ ⊗ C⁵

cd_otimes_cd — C^d ⊗ C^d

cm_otimes_cn — C^m ⊗ C^n (parametric constructions)

multipartite — multipartite systems

utils

Development

pip install -e ".[test]"
pytest

License

MIT