Quantifying imaginarity in terms of pure-state imaginarity

Abstract

Complex numbers are widely used in quantum physics and are indispensable components for describing quantum systems and their dynamical behavior. The resource theory of imaginarity has been built recently, enabling a systematic research of complex numbers in quantum information theory. In this work, we develop two theoretical methods for quantifying imaginarity, motivated by recent progress within resource theories of entanglement and coherence. We provide quantifiers of imaginarity by the convex roof construction and quantifiers of the imaginarity by the least imaginarity of the input pure states under real operations. We also apply these tools to study the state conversion problem in resource theory of imaginarity.

9 pages, 1 figure, 50 references

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Cited by in corpus (7)

• Imaginarity measures induced by real part states and the complementarity relations
• 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
• Quantum-state block texture and its quantification
• Experimental certification of the nonlocal advantages of quantum imaginarity
• Imaginarity as a Resource within Quantum Coherence: Geometric Decomposition and Operational Conversion