Exploring the relationship between the faithfulness and entanglement of two qubits

A conceptually simple and experimentally prevalent class of entanglement witnesses, known as fidelity witnesses, detects entanglement via a state's fidelity with a pure reference state. While existence proofs guarantee that a suitable witness can be constructed for every entangled state, such assurances do not apply to fidelity witnesses. Recent results have found that entangled states that cannot be detected by a fidelity witness, known as unfaithful states, are exceedingly common among bipartite states. In this paper, we show that even among two-qubit states, which are the simplest of all entangled states, unfaithful states can be created through a suitable application of decoherence and filtering to a Bell state. We also show that the faithfulness is not monotonic to entanglement, as measured by the concurrence. Finally, we experimentally verify our predictions using polarization-entangled photons, and specifically we demonstrate a situation in which an unfaithful state is brought to faithfulness at the expense of further reducing the entanglement of the state.

Automated summary

The paper discusses a type of entanglement detection known as fidelity witnesses, finding that unfaithful states are common even among bipartite entangled states. It demonstrates that even the simplest two-qubit states can be transformed from unfaithful to faithful through suitable manipulation.