Measurement-device-independent entanglement witness with imprecise input states

TL;DR

This paper introduces sensitive measurement-device-independent entanglement witnesses that account for imprecise input states, providing a more realistic and robust method for entanglement detection in experimental settings.

Contribution

It develops criteria for sensitive MDI-EWs that fail under any input imprecision, and proposes a systematic way to modify existing criteria for practical robustness.

Findings

Sensitive MDI-EWs fail with any non-zero input imprecision

Two known MDI-EWs for Werner states are sensitive according to new criteria

Modified criteria improve robustness for experimental entanglement detection

Abstract

Measurement-device-independent entanglement witnesses (MDI-EWs) enable the detection of entanglement without relying on characterized measurements. However, the entanglement criteria for MDI-EWs typically assume the idealized condition that the lab input states are precisely the desired ones. In this work, we remove this idealization by considering the realistic scenario in which lab input states may be imprecise. We introduce a new class of MDI-EWs, termed sensitive MDI-EWs, whose entanglement criteria fail under any non-zero imprecision in the input states. We derive sufficient conditions for an MDI-EW to be classified as sensitive, revealing that a large class of MDI-EWs exhibit this sensitivity. Additionally, we demonstrate that two well-known MDI-EWs for Werner states are sensitive according to our criteria, one of which recovers the result from a previous study [Phys. Rev. A 104, 012429 (2021)]. Moreover, we clarify the concept of lab input states in a way that makes imprecisions experimentally measurable, and propose a systematic approach for modifying the criterion of any MDI-EW to accommodate small imprecisions, thus enhancing experimental relevance. A simple MDI-EW example is provided, where our modified criterion is already optimal. This work bridges the gap between idealized theoretical models and practical experimental conditions, paving the way for more robust and accessible entanglement detection in real-world settings.