Composite Geometric Phase for Multipartite Entangled States

Abstract

When an entangled state evolves under local unitaries, the entanglement in the state remains fixed. Here we show the dynamical phase acquired by an entangled state in such a scenario can always be understood as the sum of the dynamical phases of its subsystems. In contrast, the equivalent statement for the geometric phase is not generally true unless the state is separable. For an entangled state an additional term is present, the mutual geometric phase, that measures the change the additional correlations present in the entangled state make to the geometry of the state space. For $N$ qubit states we find this change can be explained solely by classical correlations for states with a Schmidt decomposition and solely by quantum correlations for W states.

4 pages, 1 figure, improved presentation, results and conclusions unchanged from v1. Accepted for publication in PRA

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• Geometric phases for mixed states in interferometry
• Entangled Quantum States of Magnetic Dipoles
• Geometric phases and criticality in spin chain systems
• High Temperature Macroscopic Entanglement
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• Berry phase and fidelity susceptibility of the three-qubit Lipkin-Meshkov-Glick ground state
• Entanglement dynamics via geometric phases in quantum spin chains
• Unifying Geometric Entanglement and Geometric Phase in a Quantum Phase Transition
• Nonlinear behavior of geometric phases induced by photon pairs
• Preservation of quantum Fisher information and geometric phase of a single qubit system in a dissipative reservoir through the addition of qubits
• Separable states and the geometric phases of an interacting two-spin system
• Entanglement-induced geometric phase of quantum states
• Dimensionality induced entanglement in macroscopic dimer systems
• Experimentally testable geometric phase of sequences of Everett's relative quantum states
• Correlation induced non-Abelian quantum holonomies