Parts of quantum states

NS Jones, N Linden

Research output: Contribution to journalArticle (Academic Journal)peer-review

46 Citations (Scopus)


It is shown that generic N-party pure quantum states (with equidimensional subsystems) are uniquely determined by their reduced states of just over half the parties; in other words, all the information in almost all N-party pure states is in the set of reduced states of just over half the parties. For N even, the reduced states in fewer than N/2 parties are shown to be an insufficient description of almost all states (similar results hold when N is odd). It is noted that real algebraic geometry is a natural framework for any analysis of parts of quantum states: two simple polynomials, a quadratic and a cubic, contain all of their structure. Algorithmic techniques are described which can provide conditions for sets of reduced states to belong to pure or mixed states.
Translated title of the contributionParts of quantum states
Original languageEnglish
Article numberArt. No. 012324
JournalPhysical Review A: Atomic, Molecular and Optical Physics
Volume71 (1)
Publication statusPublished - Jan 2005

Bibliographical note

Publisher: American Physical Soc
Other identifier: IDS Number: 901LF


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