The Parts Determine the Whole except for n-Qubit Greenberger-Horne-Zeilinger States

Abstract

The generalized n-qubit Greenberger-Horne-Zeilinger (GHZ) states and their local unitary equivalents are the only pure states of n qubits that are not uniquely determined (among arbitrary states, pure or mixed) by their reduced density matrices of n-1 qubits. Thus, the generalized GHZ states are the only ones containing information at the n-party level.

4 pages

References in corpus (1)

• Only n-Qubit Greenberger-Horne-Zeilinger States are Undetermined by their Reduced Density Matrices

Cited by in corpus (17)

• System-reservoir dynamics of quantum and classical correlations
• Majorana representation of symmetric multiqubit states
• Monogamy of quantum correlations in three qubit pure states using Rajagopal-Rendell (RR) quantum deficit
• N-Qubit W States are Determined by their Bipartite Marginals
• Reconstructing quantum states from single-party information
• Experimental construction of a W-superposition state and its equivalence to the GHZ state under local filtration
• Irreducible MultiQutrit Correlations in Greenberger-Horne-Zeilinger Type States
• Uniquely determined pure quantum states need not be unique ground states of quasi-local Hamiltonians
• Optimal reducibility of all Stochastic Local Operation and Classical Communication equivalent W states
• Reducible Correlations in Dicke States
• The meaning of redundancy and consensus in quantum objectivity
• Determination of stabilizer states
• Alternative Decomposition of Two-Qutrit Pure States and Its Relation with Entanglement Invariants
• The additivity of states uniquely determined by marginals
• Nonlocal Variable-Strength Measurements of N Qubits Using GHZ-like Entanglement
• Three-qubit W state tomography via full and marginal state reconstructions on ibm_osaka
• Undetermined states: how to find them and their applications