Conditions for a class of entanglement transformations
Open accessAbstract
Suppose Alice and Bob jointly possess a pure state, $|\ensuremath{\psi}〉$. Using local operations on their respective systems and classical communication it may be possible for Alice and Bob to transform $|\ensuremath{\psi}〉$ into another joint state $|\ensuremath{\varphi}〉$. This Letter gives necessary and sufficient conditions for this process of entanglement transformation to be possible. These conditions reveal a partial ordering on the entangled states and connect quantum entanglement to the algebraic theory of majorization. As a consequence, we find that there exist essentially different types of entanglement for bipartite quantum systems.
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For pure bipartite states, a state |Ξ〉 can be prepared from |Φ〉 using only LOCC if and only if the Schmidt vector of |Ξ〉 majorises that of |Φ〉.
“It was shown that a state | Ξ 〉 can be prepared starting from a second state | Φ 〉 and using only LOCC, if and only if the vector ⃗ λ Ξ of Schmidt coefficients of | Ξ 〉 majorises ⃗ λ Φ [47]”
From Measures and dynamics of entangled states (2005) · cites this paper as [47]
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- Authors
- Nielsen, M. A.
- Affiliations
- California Institute of Technology (US)
- Corresponding author
- Nielsen, M. A.
- ORCID
- Nielsen, M. A.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1999-07-12
- Volume
- 83
- Issue
- 2
- Pages
- 436-439
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2141140927
- Cited by
- 1,036
- References
- 19
- Citations by year
- 2026: 31 · 2025: 51 · 2024: 40 · 2023: 72 · 2022: 41 · 2021: 53 · 2020: 41 · 2019: 61 · 2018: 44 · 2017: 30 · 2016: 39 · 2015: 29 · 2014: 51 · 2013: 34 · 2012: 30
- FWCI
- 41.65
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CaltechAUTHORS (California Institute of Technology) (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 › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- entanglement transformation, local operations and classical communication, majorization, bipartite quantum systems, necessary and sufficient conditions, quantum entanglement
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