Device independent Schmidt rank witness by using Hardy paradox

TL;DR

This paper introduces a device-independent method using Hardy's paradox to determine the Schmidt rank of an unknown bipartite quantum state, aiding in entanglement characterization without detailed device knowledge.

Contribution

It presents a novel application of Hardy's paradox as a device-independent Schmidt rank witness, linking quantum nonlocality with entanglement dimension assessment.

Findings

Hardy's test can determine Schmidt rank without device details

The method provides a practical tool for entanglement verification

It connects quantum nonlocality with entanglement dimension detection

Abstract

Schmidt rank of bipartite pure state serves as a testimony of entanglement. It is a monotone under local operation + classical communications (LOCC) and puts restrictions in LOCC convertibility of quantum states. Identifying the Schmidt rank of an unknown quantum state therefore seek importance from information theoretic perspective. In this work it is shown that a modified version of Hardy's argument, which reveals the contradiction of quantum theory with local realism, turns out to be useful for inspecting the minimal Schmidt rank of the unknown state and hence also the minimal dimension of the system. Use of Hardy's test in such task provides a practical advantage: the Schmidt rank can be determined without knowing the detailed functioning of the experimental devices i.e., Hardy's test suffices to be a device independent Schmidt rank witness.