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 contribution||Parts of quantum states|
|Article number||Art. No. 012324|
|Journal||Physical Review A: Atomic, Molecular and Optical Physics|
|Publication status||Published - Jan 2005|
Bibliographical notePublisher: American Physical Soc
Other identifier: IDS Number: 901LF