Quantum Imaginarity in Quantum Mechanics
Summary
Quantum imaginarity denotes the essential role of imaginary components in the complex Hilbert space formulation of quantum theory. These imaginary parts give rise to phase coherence, interference phenomena and non-classical correlations that cannot be captured by a purely real formalism. The development of a resource-theoretic perspective has enabled the quantification and manipulation of imaginarity as an operationally valuable asset, akin to entanglement and coherence. Investigations have shown that certain discrimination tasks and networked measurement scenarios exhibit an intrinsic advantage only when complex amplitudes are permitted, thereby demonstrating that real-only quantum theories are fundamentally insufficient. The study of imaginarity thus unites foundational questions—such as the necessity of complex numbers in physics—with practical applications in quantum communication, sensing and computation.
Research from Nature Portfolio
Recent studies have formalised the resource theory of imaginarity in distributed quantum tasks, providing exact solutions for distillation and conversion protocols in bipartite systems of arbitrary dimension. Experimental realisations have confirmed the operational advantage of imaginarity in channel discrimination without auxiliary systems and have linked these protocols to assisted state discrimination under local operations and classical communication. A seminal network-based Bell-like experiment has been devised and implemented, demonstrating that formulations restricted to real numbers fail to reproduce the observed correlations in scenarios with independent states and measurements, thereby affirming the indispensability of complex amplitudes in genuine quantum descriptions.
Quantum Imaginarity in Quantum Mechanics publication trend
The graph below shows the total number of articles in quantum imaginarity in quantum mechanics across all publications each year (not limited to Nature Index journals).
Technical terms
Imaginarity: The total magnitude of imaginary components in quantum state vectors and operators, crucial for phase-dependent phenomena.
Resource theory: A formal framework for quantifying, manipulating and converting a specific quantum property as a resource under constrained operations.
Bell-like experiment: A generalisation of Bell tests to network scenarios designed to distinguish complex-valued predictions from real-only quantum models.
l1 norm of imaginarity: A measure equal to the sum of absolute values of all imaginary amplitudes in a quantum state, used to quantify imaginarity.
Real quantum operations: Quantum operations defined exclusively by real-number matrices, excluding complex phases and imaginary components.
References
- Resource theory of imaginarity in distributed scenarios. Communications Physics (2024).
- Quantum theory based on real numbers can be experimentally falsified. Nature (2021).
- Efficient discrimination between real and complex quantum theories. Quantum (2025).
- On complementarity and distribution of imaginarity in finite dimensions. Results in Physics (2024).
- Real quantum operations and state transformations. New Journal of Physics (2023).
About these summaries
This Nature Research Intelligence Topic summary is created with the cited references and a large language model. We take care to ground generated text with facts, and have systems in place to gain human feedback on the overall quality of the process in line with our AI principles. We strive to create accurate and useful summaries for people unfamiliar with the research topic and that supports this goal. These pages are a beta release and will be updated as we learn how best to help people gain value from a research topic summary.
Turn complex research questions into confident strategic decisions
When you're under pressure to set direction, justify investment, or understand your competitive position, you need more than raw data — you need trusted insights you can act on.
Benchmark your performance against global peers using robust, methodologically sound analysis.
Combine quantitative metrics with qualitative expert insight to uncover strengths, gaps and emerging opportunities.
Gain tailored, decision-ready recommendations aligned to your strategic priorities.
Talk to us to learn more about our data dashboards and bespoke strategy reports.
Grow research skills, confidence and careers with training built for every stage of the research lifecycle.
Developed with Nature Portfolio journal Editors and internationally renowned experts. Discover three ways to learn:
Self-paced, online courses in convenient bite-sized units, covering key skills across scientific writing, publishing, grant writing, data analysis, and more.
Expert trainer-led workshops with hands-on exercises and real-time feedback across core research skills, delivered via interactive group sessions.
Editor-led workshops combining core principles in writing and publishing, personalised 1:1 feedback from Nature Portfolio Editors and hands-on exercises.
Explore course catalogues and workshop agendas, enquire about the options or request institutional pricing.