Quantum limitations on the storage and transmission of information
Open accessAbstract
Information must take up space, must weigh, and its flux must be limited. Quantum limits on communication and information storage leading to these conclusions are described here. Quantum channel capacity theory is reviewed for both steady state and burst communication. An analytic approximation is given for the maximum signal information possible with occupation number signal states as a function of mean signal energy. A theorem guaranteeing that these states are optimal for communication is proved. A heuristic "proof" of the linear bound on communication is given, followed by rigorous proofs for signals with specified mean energy, and for signals with given energy budget. And systems of many parallel quantum channels are shown to obey the linear bound for a natural channel architecture. The time-energy uncertainty principle is reformulated in information language by means of the linear bound. The quantum bound on information storage capacity of quantum mechanical and quantum field devices is reviewed. A simplified version of the analytic proof for the bound is given for the latter case. Solitons as information caches are discussed, as is information storage in one-dimensional systems. The influence of signal self-gravitation on communication is considered. Finally, it is shown that acceleration of a receiver acts to block information transfer.
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The Bremermann-Bekenstein bound gives an upper limit on how much can be learned about inaccessible objects in the Universe, such as black holes.
“The Bremerman-Bekenstein bound [78,79] is an important result in cosmology, since it gives an upper bound on how much can be learned about non-accessible objects in the Universe, such as black holes.”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [79]
The Bekenstein-Hawking entropy of black holes saturates the Bremermann-Bekenstein bound.
“It is further interesting to note that the Bekenstein-Hawking entropy of black holes saturates the bound [78,79].”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [79]
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- Authors
- BEKENSTEIN, J. D., & SCHIFFER, M.
- Affiliations
- Ben-Gurion University of the Negev (IL)
- Insituto de Física Teórica, Rua Pamplona 145, São Paulo, S.P. 01405, Brazil
- Venue
- International Journal of Modern Physics C
- Publisher
- World Scientific Pub Co Pte Lt
- Published
- 1990-12
- Volume
- 01
- Issue
- 04
- Pages
- 355-422
- ISSN
- 0129-1831 (ISSN-L)
- 1793-6586
- OpenAlex
- W2950115942
- Cited by
- 86
- References
- 0
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 2 · 2023: 3 · 2022: 3 · 2021: 2 · 2020: 4 · 2019: 1 · 2018: 1 · 2017: 3 · 2016: 2 · 2015: 1 · 2014: 2 · 2012: 3
- FWCI
- 1.99
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- International Journal of Modern Physics C (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- quantum limit, quantum channel capacity, information storage, information transmission, time-energy uncertainty relation, burst communication
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