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The parts determine the whole in a generic pure quantum state
1School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom.
Physical Review Letters
|January 7, 2003
Abstract:
We show that almost every pure state of multiparty quantum systems (each of whose local Hilbert space has the same dimension) is completely determined by the state's reduced density matrices of a fraction of the parties; this fraction is less than about two-thirds of the parties for states of large numbers of parties. In other words, once the reduced states of this fraction of the parties have been specified, there is no further freedom in the state.