Peres Criterion

Entanglement can be tested by checking if the operator $T_A\otimes 1_B:{\mathcal{H}}_A\otimes {\mathcal{H}}_B\to {\mathcal{H}}_A\otimes {\mathcal{H}}_B$ is a Positive operator, where:

• ${\mathcal{H}}_A,{\mathcal{H}}_B$ are two Quantum Hilbert Spaces.
• $T_A$ is the transposition operator applied to system ${\mathcal{H}}_A$.
• $1_B$ is the identity map applied to system ${\mathcal{H}}_B$.