Nonlocal Advantages of Quantum Imaginarity

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.

9 pages, 4 figures

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Cited by in corpus (7)

• Quantifying imaginarity in terms of pure-state imaginarity
• Two imaginarity monotones induced by unified $(\alpha ,\beta )$-relative entropy
• Analyzing the free states of one quantum resource theory as resource states of another
• Quantifying imaginarity of quantum operations
• Off-resonant preservation and generation of imaginarity in distributed scenarios
• Imaginarity as a Resource within Quantum Coherence: Geometric Decomposition and Operational Conversion
• Experimental certification of the nonlocal advantages of quantum imaginarity