Exploring the relationship between the faithfulness and entanglement of two qubits

• URL: http://arxiv.org/abs/2102.10121v2
• Date: Fri, 26 Feb 2021 11:24:59 GMT
• Title: Exploring the relationship between the faithfulness and entanglement of two qubits
• Authors: Gabriele Riccardi, Daniel E. Jones, Xiao-Dong Yu, Otfried G\"uhne and Brian T. Kirby
• Abstract summary: 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. 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. 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.
• Score: 2.400716652658002
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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