Quantum-Computation-course-Basel/extra_resources/Entanglement_extra/2_locc.ipynb

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"""
LOCC cannot create entanglement. Simulate LOCC-like maps (local unitaries + classical randomness) on product states.

Exercises:
- Add classical mixing over different local unitaries and show separability persists for mixed states.
"""

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import numpy as np
from qiskit import QuantumCircuit
from qiskit.quantum_info import Statevector

def entangled(psi):
    s = np.linalg.svd(psi.data.reshape(2,2), compute_uv=False)
    return abs(s[0]*s[1])>1e-12 # Basically 0 if separable, i.e. not entangled.

psi = Statevector.from_label("00")
local = QuantumCircuit(2) # A separable state.
for q in range(2): local.rx(0.7,q); local.ry(0.3,q); local.rz(0.2,q) # Example local unitaries. Change as desired.
psi_local = psi.evolve(local)
print("Entangled after local?", entangled(psi_local)) #Whateve separable state, whatever local unitaries, should be False.

ent = QuantumCircuit(2); ent.rxx(0.6,0,1) # An entangling operation.
psi_ent = psi_local.evolve(ent)
print("Entangled after RXX?", entangled(psi_ent)) #Whatever entagnled state, whatever locc, should be True.

Entangled after local? False
Entangled after RXX? True