N-Qubit W States are Determined by their Bipartite Marginals

Abstract

We prove that the most general W class of N-qubit states are uniquely determined among arbitrary states (pure or mixed) by just their bipartite reduced density matrices. Moreover, if we consider only pure states, then (N-1) of them are shown to be sufficient.

RevTeX, 4+ pages, 2 figures, journal version includes an Appendix and slightly enlarged introduction and conclusions

References in corpus (3)

• General Monogamy Inequality for Bipartite Qubit Entanglement
• Three-party pure quantum states are determined by two two-party reduced states
• Only n-Qubit Greenberger-Horne-Zeilinger States are Undetermined by their Reduced Density Matrices

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• Experimental sample-efficient quantum state tomography via parallel measurements
• Uniquely determined pure quantum states need not be unique ground states of quasi-local Hamiltonians
• Determination of stabilizer states
• Universal behavior of the geometric entanglement measure of many-qubit W states
• Nonlocality of Quantum States can be Transitive
• Three-qubit W state tomography via full and marginal state reconstructions on ibm_osaka