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Operational Resource Theory of Imaginarity
Kang-Da Wu1,2, Tulja Varun Kondra3, Swapan Rana3,4,5
1CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China.
Physical Review Letters
|March 22, 2021
Summary
Complex numbers are essential in quantum mechanics, despite debates. This study shows that while real quantum states are easier to create, complex numbers are indispensable for phenomena like state discrimination, confirmed experimentally.
Area of Science:
- Quantum Physics
- Quantum Information Theory
Background:
- Wave-particle duality necessitates complex numbers in quantum mechanics.
- The necessity of complex numbers has been a long-standing debate in quantum theory.
Purpose of the Study:
- To theoretically and experimentally investigate the essentiality of complex numbers in quantum mechanics.
- To explore the role of 'imaginarity' as a quantum resource.
Main Methods:
- Utilized quantum resource theories, specifically the resource theory of imaginarity.
- Investigated state-conversion and distillation problems for quantum states.
- Conducted experimental verification using linear optics and two-photon quantum states.
Main Results:
- Quantum states with real elements are operationally easier to create and manipulate.
- Imaginarity is crucial for distinguishing certain quantum states, even when real states can be perfectly discriminated.
- Experimental results confirm the theoretical predictions regarding the role of imaginarity in state discrimination.
Conclusions:
- Complex numbers are an indispensable component of quantum mechanics.
- The resource theory of imaginarity provides operational meaning to the necessity of complex numbers.
- Quantum states and their discrimination fundamentally rely on the properties described by complex numbers.
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