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.

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

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• Maximally entangled three-qubit states via geometric measure of entanglement
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• From Ground States to Local Hamiltonians
• Reconstructing quantum states from single-party information
• Detecting genuine multipartite entanglement of pure states with bipartite correlations
• Experimental construction of a W-superposition state and its equivalence to the GHZ state under local filtration
• Duality and the geometric measure of entanglement of general multiqubit W states
• Generic detection-based error-mitigation using quantum autoencoders
• Self-testing using only marginal information
• Multi-partite $W-$type state is determined by its single particle reduced density matrices
• Experimental sample-efficient quantum state tomography via parallel measurements
• Uniquely determined pure quantum states need not be unique ground states of quasi-local Hamiltonians
• Correlations in excited states of local Hamiltonians
• Optimal reducibility of all Stochastic Local Operation and Classical Communication equivalent W states
• Reducible Correlations in Dicke States
• Distribution of Mutual Information in Multipartite States
• Determination of stabilizer states
• Generic pure quantum states as steady states of quasi-local dissipative dynamics
• An efficient numerical algorithm on irreducible multiparty correlations
• Universal behavior of the geometric entanglement measure of many-qubit W states
• Nonlocality of Quantum States can be Transitive
• Geometric Measure of Entanglement and Schmidt Decomposition of Multipartite Systems
• Three-qubit W state tomography via full and marginal state reconstructions on ibm_osaka