Efficient utilization of imaginarity in quantum steering

TL;DR

This paper explores how complex numbers, specifically imaginarity, influence quantum steering, proposing a new criterion that is more measurement-efficient and robust against noise, highlighting imaginarity as a valuable nonlocal resource.

Contribution

It introduces a novel imaginarity-based steering inequality requiring fewer measurements and demonstrates its robustness and monogamy properties in noisy quantum systems.

Findings

Imaginarity steering inequality witnesses quantum correlations with fewer observables.

The proposed criterion is more measurement-efficient than existing methods.

Imaginarity steering remains robust under white noise and unsharp measurements.

Abstract

We illustrate the role of complex numbers in quantum information processing through the phenomenon of quantum steering. Exploiting partial knowledge of a qubit in terms 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 can be witnessed by suitably constructed Hermitian operators that depend on fewer state parameters and require measurement of a lesser number of observables than for witnessing other forms of quantum nonlocal correlations. The monogamy of such correlations is also demonstrated. We further underscore the steering of imaginarity as an efficient nonlocal resource in the presence of white noise and under unhsarp measurements, showing the robustness of imaginarity steering compared to certain other steering criteria.