Nonlocal Advantages of Quantum Imaginarity

TL;DR

This paper explores the relationship between quantum imaginarity and nonlocality in two-qubit states, introducing the concept of nonlocal advantage of quantum imaginarity (NAQI) and analyzing its implications for quantum steerability.

Contribution

It establishes a connection between quantum imaginarity and nonlocality, introduces NAQI, and investigates its properties and implications in multi-qubit states.

Findings

NAQI indicates quantum steerability in two-qubit states.

NAQI has an exclusion property in three-qubit pure states.

Complementary relations among quantum imaginarities are derived.

Abstract

Quantum imaginarity and quantum nonlocality capture the essence of quantumness of a physical system from different aspects. We establish a connection between the imaginarity and quantum nonlocality in any two-qubit states. Based on the imaginarity $l_1$-norm and relative entropy, we first derive complementary relations among the quantum imaginarities with respect to any set of mutually unbiased bases for arbitrary qubit states. Based on these complementary relations, we introduce the nonlocal advantage of quantum imaginarity (NAQI). We show that any two-qubit state with NAQI is quantum steerable, but not the vice-versa. In addition, we investigate the exclusion property of NAQI in three-qubit pure states.