Quantum steering based on partial state information
TL;DR
It is shown that quantum correlations embodied through the proposed imaginarity steering inequality (ISI) can be witnessed by suitably constructed Hermitian operators that depend on fewer state parameters and require measurement of fewer observables than for witnessing other forms of quantum non-local correlations.
Abstract
Exploiting partial knowledge of a qubit in terms of its basis-dependent measure of imaginarity, we formulate a steering criterion for bipartite qubit systems, which requires two dichotomic measurements at the untrusted side and two mutually unbiased bases at the trusted side. We show that quantum correlations embodied through our proposed imaginarity steering inequality (ISI) can be witnessed by suitably constructed Hermitian operators that depend on fewer state parameters and require measurement of fewer observables than for witnessing other forms of quantum non-local correlations. The monogamy of such correlations is also demonstrated. We further underscore the steering of imaginarity as an efficient non-local resource in the presence of white noise and under unsharp measurements, showing the robustness of imaginarity steering compared with certain other steering criteria.