bound-entangled 0.1.3

Families of bound entangled states for Quantum Information

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.

Installation

pip install -e .
# with the test dependencies:
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(d=3, x=0.5, y=0.5)    # Yu-Oh nonlocal bound entangled state

States

c3_otimes_c3 — C³ ⊗ C³

Factory	State	Reference
chessboard, chessboard_extremal_PPT	Bruß–Peres chessboard states	quant-ph/9911056
cross_hatch	3×3 "cross-hatch" grid state (CCNR-detected)	1705.09261
steering_state	Steerable bound entangled state (counterexample to the stronger Peres conjecture)	1405.0262
tiles_upb, pyramid_upb	States from the Tiles / Pyramid unextendible product bases	quant-ph/9808030
parametrized_upb	Six-parameter family of UPBs generalizing Tiles / Pyramid	quant-ph/9908070
horodecki	3x3 Horodecki bound entangled state	quant-ph/9703004

c4_otimes_c4 — C⁴ ⊗ C⁴

Factory	State	Reference
breuer	Breuer bound-entangled state (PPT, detected by anti-linear map)	quant-ph/0605036
smolin	Smolin four-party unlockable bound entangled state	quant-ph/0001001
pianni	4×4 Benatti–Floreanini–Piani state	quant-ph/0411095

c5_otimes_c5 — C⁵ ⊗ C⁵

Factory	State	Reference
sn3_grid_state	Smallest known Schmidt-number-3 PPT bound entangled state	2402.12966

cd_otimes_cd — C^d ⊗ C^d

Factory	State	Reference
yu_oh, is_valid_yu_oh_input	Yu–Oh family of nonlocal bound entangled states	1509.08991
gen_tiles1	GenTiles1 UPB generalizing Tiles to d⊗d, even d≥4	quant-ph/9908070

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

Factory	State	Reference
grid_state	Quantum grid states from graph edges	1705.09261
generalized_grid_state	Grid states generalized to hyperedges	2402.12966
random_NPT, random_PPT, random_PPT_close_to_the_PPT_edge	Random density matrices by PPT class (rejection sampling)	—
gen_tiles2	GenTiles2 UPB generalizing Tiles to m⊗n, n>3, m≥3, n≥m	quant-ph/9908070

multipartite — multipartite systems

Factory	State	Reference
generalized_smolin	Generalized Smolin state on 2n qubits (bound entangled for all even n ≥ 2)	quant-ph/0411142

Documentation

Full API docs (built with MkDocs + mkdocstrings) are published to GitHub Pages on every push to main.

License

MIT