Phase Dynamics of Two Entangled Qubits

Abstract

We make a geometric study of the phases acquired by a general pure bipartite two level system after a cyclic unitary evolution. The geometric representation of the two particle Hilbert space makes use of Hopf fibrations. It allows for a simple description of the dynamics of the entangled state's phase during the whole evolution. The global phase after a cyclic evolution is always an entire multiple of $\pi$ for all bipartite states, a result that does not depend on the degree of entanglement. There are three different types of phases combining themselves so as to result in the $n\pi$ global phase. They can be identified as dynamical, geometrical and topological. Each one of them can be easily identified using the presented geometric description. The interplay between them depends on the initial state and on its trajectory and the results obtained are shown to be in connection to those on mixed states phases.

9 figures, slightly different version from the accepted one

References in corpus (16)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Observation of three-photon Greenberger-Horne-Zeilinger entanglement
• Geometric quantum computation with NMR
• Geometric Manipulation of Trapped Ions for Quantum Computation
• Geometric phases for mixed states in interferometry
• Geometric phase in open systems
• Geometry of entangled states, Bloch spheres and Hopf fibrations
• Multi-bit gates for quantum computing
• Spin-1/2 geometric phase driven by decohering quantum fields
• Mixed state geometric phases, entangled systems, and local unitary transformations
• Topological phase for entangled two-qubit states
• Relation between geometric phases of entangled bi-partite systems and their subsystems
• Geometric phases of mesoscopic spin in Bose-Einstein condensates
• Measurement of the degree of Polarization Entanglement Through Position Interference
• Representation of SO(3) Group by a Maximally Entangled State
• Local/Non-Local Complementarity in Topological Effects

Cited by in corpus (23)

• Topological phase for spin-orbit transformations on a laser beam
• Geometric phases in quantum information
• Geometric phases of light: insights from fibre bundle theory
• Experimental Observation of a Topological Phase in the Maximally Entangled State of a Pair of Qubits
• Environmentally-induced effects on a bipartite two-level system: geometric phase and entanglement properties
• Topological phases and multiqubit entanglement
• Observation of Entanglement-Dependent Two-Particle Holonomic Phase
• Geometric phases under the presence of a composite environment
• Topological phase structure of vector vortex beams
• Topological phase structure of entangled qudits
• Fractional topological phase on spatially encoded photonic qudits
• Experimental observation of fractional topological phases with photonic qudits
• Classification scheme of pure multipartite states based on topological phases
• Three-qubit topological phase on entangled photon pairs
• Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness
• Entanglement dynamics via geometric phases in quantum spin chains
• Geometrical, topological and dynamical description of $\mathcal{N}$ interacting spin-$\mathtt{s}$ under long-range Ising model and their interplay with quantum entanglement
• Two-qudit topological phase evolution under dephasing
• Tight lower bounds on the time it takes to generate a geometric phase
• Non Abelian structures and the geometric phase of entangled qudits
• Intrinsic bounds of a two-qudit random evolution
• iSWAP-type geometric gates induced by paths on Schmidt sphere
• Phase Analysis on the Error Scaling of Entangled Qubits in a 53-Qubit System