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Entanglement Cost for Infinite-Dimensional Physical Systems
Hayata Yamasaki1,2, Kohdai Kuroiwa3,4, Patrick Hayden5
1Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 Japan.
We show that entanglement cost matches regularized entanglement of formation for infinite-dimensional quantum states with finite quantum entropy. This extends a key quantum information theory result to more complex systems.
Area of Science:
- Quantum Information Theory
- Mathematical Physics
Background:
- Entanglement cost and regularized entanglement of formation are crucial measures in quantum information.
- Previous results were limited to finite-dimensional quantum systems.
- Extending these concepts to infinite dimensions presents significant theoretical challenges.
Purpose of the Study:
- To generalize the equality of entanglement cost and regularized entanglement of formation to infinite-dimensional quantum states.
- To overcome limitations of conventional tools like strong typicality in infinite dimensions.
- To fully characterize the entanglement cost for all infinite-dimensional physical systems.
Main Methods:
- Development of a novel entanglement dilution protocol using local operations and one-way classical communication (LOCC) for infinite-dimensional states.
- Application of weak and strong typicality principles iteratively.
- Derivation of an integral representation for quantum entropy in infinite dimensions.
- Utilizing alternative forms of monotonicity and asymptotic continuity for entanglement of formation.
Main Results:
- Proved that entanglement cost equals regularized entanglement of formation for infinite-dimensional states with finite quantum entropy on at least one subsystem.
- Established the optimality of the new entanglement dilution protocol.
- Derived a new integral representation for quantum entropy.
Conclusions:
- The study successfully extends a foundational result in quantum information theory to infinite-dimensional systems.
- The developed methods provide new tools for analyzing entanglement in complex quantum systems.
- This work offers a complete characterization of the entanglement cost for infinite-dimensional physical systems.
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