Exploring the relationship between the faithfulness and entanglement of two qubits

TL;DR

This paper investigates the relationship between the faithfulness of entanglement witnesses and the entanglement of two-qubit states, revealing that unfaithful states are common and can be transformed into faithful states through decoherence and filtering, with experimental validation.

Contribution

It demonstrates that unfaithful states are prevalent among two-qubit states and shows how they can be converted into faithful states, challenging assumptions about the monotonicity of faithfulness with entanglement.

Findings

Unfaithful states can be created from Bell states via decoherence and filtering.

Faithfulness is not necessarily correlated with entanglement levels.

Experimental verification using polarization-entangled photons confirms theoretical predictions.

Abstract

A conceptually simple and experimentally prevalent class of entanglement witnesses, known as fidelity witnesses, detect 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, 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 demonstrate a situation where an unfaithful state is brought to faithfulness at the expense of further reducing the entanglement of the state.