Quantum coding
Abstract
A theorem is proven for quantum information theory that is analogous to the noiseless coding theorem of classical information theory. In the quantum result, the von Neumann entropy S of the density operator describing an ensemble of pure quantum signal states is equal to the number of spin-1/2 systems (``quantum bits'' or ``qubits'') necessary to represent the signal faithfully. The theorem holds whether or not the signal states are orthogonal. Related results are also presented about the fidelity of quantum coding and about representing entangled quantum states.
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Quantum data compression allows quantum data to be transmitted with asymptotically perfect fidelity using a number of qubits asymptotically approaching the source's von Neumann entropy.
“quantum data compression [2,3] allows quantum data to be transmitted, with asymptotically perfect fidelity, using a number of 2-state quantum systems or qubits ( e.g. spin1 2 particles) asymptotically approaching the source's von Neumann entropy”
From Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels (1996) · cites this paper as [2]
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- Authors
- Schumacher, B.
- Affiliations
- Kenyon College (US)
- Corresponding author
- Schumacher, Benjamin
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1995-04-01
- Volume
- 51
- Issue
- 4
- Pages
- 2738-2747
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W4231127907
- Semantic Scholar
- f6e8937d89ad84080f3181be87c4f19f3a29fa39
- Cited by
- 1,090
- References
- 13
- Citations by year
- 2026: 33 · 2025: 60 · 2024: 62 · 2023: 48 · 2022: 51 · 2021: 42 · 2020: 53 · 2019: 42 · 2018: 33 · 2017: 35 · 2016: 42 · 2015: 34 · 2014: 26 · 2013: 18 · 2012: 27
- FWCI
- 39.37
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review A (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum coding, quantum information, von Neumann entropy, qubits, quantum states, fidelity, entangled states, density matrix
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