Almost all four-particle pure states are determined by their two-body marginals

Abstract

We show that generic pure states (states drawn according to the Haar measure) of four particles of equal internal dimension are uniquely determined among all other pure states by their two-body marginals. In fact, certain subsets of three of the two-body marginals suffice for the characterization. We also discuss generalizations of the statement to pure states of more particles, showing that these are almost always determined among pure states by three of their $(n-2)$-body marginals. Finally, we present special families of symmetric pure four-particle states that share the same two-body marginals and are therefore undetermined. These are four-qubit Dicke states in superposition with generalized GHZ states.

6 pages, 2 figures, v2: more results, final version

References in corpus (3)

• Spin squeezing and entanglement
• Entangling power of the quantum baker's map
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Cited by in corpus (17)

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• Investigating Pure State Uniqueness in Tomography via Optimization
• The additivity of states uniquely determined by marginals
• Refining ensemble $N$-representability of one-body density matrices from partial information
• Solving one-body ensemble N-representability problems with spin