Nonlocal Properties of Two-Qubit Gates and Mixed States, and the Optimization of Quantum Computations

@article{Makhlin2002NonlocalPO,
  title={Nonlocal Properties of Two-Qubit Gates and Mixed States, and the Optimization of Quantum Computations},
  author={Yuriy Makhlin},
  journal={Quantum Information Processing},
  year={2002},
  volume={1},
  pages={243-252}
}
Entanglement of two parts of a quantum system is a nonlocal property unaffected by local manipulations of these parts. It can be described by quantities invariant under local unitary transformations. Here we present, for a system of two qubits, a set of invariants which provides a complete description of nonlocal properties. The set contains 18 real polynomials of the entries of the density matrix.We prove that one of two mixed states can be transformed into the other by single-qubit operations… CONTINUE READING