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Relation between concurrence and Berry phase of an entangled state of two spin 1/2 particles

Banasri Basu

Published Feb 10, 2006• 25 citations
OpenAlex

Abstract

We have studied here the influence of the Berry phase generated due to a cyclic evolution of an entangled state of two spin 1/2 particles. It is shown that the measure of formation of entanglement is related to the cyclic geometric phase of the individual spins. \\

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Correlation relations for the spin measurements on a pair of entangled particles scattered by the two separate arms of interferometers in hybrid setups of different types are investigated. Concurrence, entanglement of formation, quantum fidelity, Bures distance are used to clarify how the geometric phase affects the initial bipartite state. This affect causes a quantum interference due to the movement of charged particles in regions where electromagnetic fields are not present. We shown that in some cases the geometric phase information is carried over to the final bipartite entangled state.
The entanglement dependence of Berry's geometric phase is studied in the case of two spin-1/2 particles with a spin-spin interaction.Berry's phases for two spin-1/2 entanglement particles in the presence of spin-spin interaction and noninteraction are calculated,respectively.The expression of calculating geometric phase,when entanglement vanishes,is obtained.Moreover,the geometric phase is discussed when only one of the two particles is affected by the external magnetic field.It is shown that its geometric phase is not equal to that of single particle which is acted by the external magnetic field,and the result is related toαthat affect the strength of entanglement. A general entanglement-dependence geometric phase is formulated.
The geometric phase for states of two spin-1/2 particles in rotating magnetic field is calculated, in particular, the noncyclic and cyclic non-adiabatic phases for the general case are explicitly derived and discussed. We find that the cyclic geometric phase for the entangled state can always be written as a sum of the phases of the two particles respectively; the same cannot be said for the noncyclic phase. We also investigate the geometric phase of mixed state of one particle in a biparticle system, and we find that the geometric phase for one subsystem of an entangled system is always affected by another subsystem of the entangled system.
Above the work of E.Sjoqvist,the geometric phase and the entanglement of the system composed of a pair of noninteracting spin-1/ 2 particles pressing in an external time-independent magnetic field are considered using a new method.The relation between them is gained newly:only if the entanglement is zero will the geometric phase of the composite systems reduce to a sum of one-particle geometric phase.Further more,the Berry's phase and the entanglement of the system composed of a pair of noninteracting spin-1/2 particles pressing in a rotating magnetic field are studied.The same conclusion is gained.
The influence of the geometric phase, in particular the Berry phase, on an entangled spin-12\frac{1}{2}21​ system is studied. We discuss in detail the case, where the geometric phase is generated only by one part of the Hilbert space. We are able to cancel the effects of the dynamical phase by using the ``spin-echo'' method. We analyze how the Berry phase affects the Bell angles and the maximal violation of a Bell inequality. Furthermore we suggest an experimental realization of our setup within neutron interferometry.