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No-Broadcasting Theorem for Quantum Asymmetry and Coherence and a Trade-off Relation for Approximate Broadcasting
Iman Marvian1, Robert W Spekkens2
1Departments of Physics and Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA.
Physical Review Letters
|August 7, 2019
Summary
Quantum systems cannot broadcast asymmetry due to symmetric dynamics. A no-go theorem shows that creating asymmetry in one quantum subsystem necessarily reduces it in another, a uniquely quantum phenomenon.
Area of Science:
- Quantum mechanics
- Symmetry principles
- Information theory
Background:
- Symmetries impose constraints on both classical and quantum dynamics.
- Noether's theorem exemplifies constraints applicable to both classical and quantum systems.
- Existing constraints often have classical counterparts, but uniquely quantum consequences are of particular interest.
Purpose of the Study:
- To demonstrate a constraint arising from symmetric dynamics that has no classical analog.
- To establish the impossibility of broadcasting asymmetry in bounded-size quantum systems under continuous symmetry groups.
- To explore the fundamental nature of asymmetry in quantum information processing.
Main Methods:
- Formulation of a no-go theorem for asymmetry broadcasting.
- Analysis of interactions between initially uncorrelated quantum systems under symmetric dynamics.
- Investigation of the additivity properties of asymmetry measures.
- Connection to quantum information-disturbance principles.
Main Results:
- Demonstrated the impossibility of broadcasting asymmetry for bounded-size quantum systems.
- Established that if asymmetry is created in one subsystem, it must be reduced in another.
- Quantified the trade-off relationship between asymmetry in subsystems.
- Showed that faithful asymmetry measures violate both subadditivity and superadditivity.
- Linked these findings to an intrinsic quantum information-disturbance principle.
Conclusions:
- The broadcasting of asymmetry is fundamentally impossible in quantum mechanics for bounded systems.
- Asymmetry dynamics are governed by quantum information principles, not simple additivity.
- The use of quantum reference frames or coherence reservoirs for asymmetric operations leads to irreversible degradation of their quantum states.
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