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

Abstract

The generalized n-qubit Greenberger-Horne-Zeilinger (GHZ) states and their local unitary equivalents are the only states of n qubits that are not uniquely determined among pure states by their reduced density matrices of n-1 qubits. Thus, among pure states, the generalized GHZ states are the only ones containing information at the n-party level. We point out a connection between local unitary stabilizer subgroups and the property of being determined by reduced density matrices.

arXiv comment4 pages

References in corpus (5)

• Three qubits can be entangled in two inequivalent ways
• Observation of three-photon Greenberger-Horne-Zeilinger entanglement
• Three-party pure quantum states are determined by two two-party reduced states
• Compatibility conditions from multipartite entanglement measures
• Maximum stabilizer dimension for nonproduct states

Cited by in corpus (26)

• System-reservoir dynamics of quantum and classical correlations
• Partial separability and entanglement criteria for multiqubit quantum states
• Majorana representation of symmetric multiqubit states
• Irreducible multi-particle correlations in states without maximal rank
• Uniqueness of Quantum States Compatible with Given Measurement Results
• 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
• From Ground States to Local Hamiltonians
• Reconstructing quantum states from single-party information
• Experimental construction of a W-superposition state and its equivalence to the GHZ state under local filtration
• The Parts Determine the Whole except for n-Qubit Greenberger-Horne-Zeilinger States
• Self-testing using only marginal information
• Irreducible MultiQutrit Correlations in Greenberger-Horne-Zeilinger Type States
• Neural-Shadow Quantum State Tomography
• 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
• Distribution of Mutual Information in Multipartite States
• Determination of stabilizer states
• An efficient numerical algorithm on irreducible multiparty correlations
• Alternative Decomposition of Two-Qutrit Pure States and Its Relation with Entanglement Invariants
• The additivity of states uniquely determined by marginals
• Three-qubit W state tomography via full and marginal state reconstructions on ibm_osaka
• Nonlocal Variable-Strength Measurements of N Qubits Using GHZ-like Entanglement
• Undetermined states: how to find them and their applications
• Locally undetermined states, generalized Schmidt decomposition, and an application in distributed computing