Nick S. Jones, Noah Linden
Published 2004-07-15Version 1
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.
Comments: 10 pages, 1 figure
Journal: Phys. Rev. A 71, 012324 (2005)
On the set of reduced states of translation invariant, infinite quantum systems
Purification of Gaussian States by Photon Subtraction
Upper bound on three tangle of reduced states of four-qubit pure states
