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arXiv:quant-ph/0511094 · Physica Scripta

Qubit rotation and Berry phase

Dipti Banerjee, Pratul Bandyopadhyay

Published May 11, 2006• 3 citations
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Abstract

A quantized fermion is represented by a scalar particle encircling a magnetic flux line. It has a spinor structure which can be constructed from quantum gates and qubits. We have studied here the role of Berry phase in removing dynamical phase during one qubit rotation of a quantized fermion. The entanglement of two qubits inserting spin-echo to one of them allows the trapped Berry phase to measure entanglement. Some effort is given to study the effect of noise on the Berry phase of spinors and their entangled states.

DOI
10.1088/0031-8949/73/6/008

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A quantized fermion is represented by a scalar particle encircling a magnetic flux line. It has a spinor structure which can be constructed from quantum gates and qubits. We have studied here the role of Berry phase in removing dynamical phase during one qubit rotation of a quantized fermion. The entanglement of two qubits inserting spin-echo to one of them allows the trapped Berry phase to measure entanglement. Some effort is given to study the effect of noise on the Berry phase of spinors and their entangled states.
A quantized fermion can be represented by a scalar particle encircling a magnetic flux line. It has the spinor structure which can be constructed from quantum gates and qubits. We have studied here the role of Berry phase in removing dynamical phase during one qubit rotation of a quantized fermion. The entanglement of two qubit inserting spin-echo to one of them results the change of Berry phase that can be considered as a measure of entanglement. Some effort is given to study the effect of noise on the Berry phase of spinor and their entangled states.
We have studied the entanglement of identical fermions in two spatial regions in terms of the Berry phase acquired by their spins. The analysis is done from the viewpoint of the geometrical interpretation of entanglement, where a fermion is visualized as a scalar particle attached to a magnetic flux quantum. The quantification of spin entanglement in terms of their Berry phases is novel and generalizes the relationship between the entanglement of distinguishable spins and that of delocalized fermions.
We have studied the entanglement of identical fermions in two spatial regions in terms of the Berry phase acquired by their spins. The analysis is done from the viewpoint of the geometrical interpretation of entanglement, where a fermion is visualized as a scalar particle attached with a magnetic flux quantum. The quantification of spin entanglement in terms of their Berry phases is novel and generalises the relationship between the entanglement of distinguishable spins and that of delocalised fermions.
This first show was that the spin system, the two nearest neighbour spin in the Entanglement of measuring compliance by the ground conditions are achieved Berry stage to the relation when it is a closed path developed is. It noted the need to share the stage in a kind of geometric phase as explained to go to which any deformations involved is not and it’s the first Stiefel-Whitney class which is to Zz–cohomology value takes. However for polarized fermions we can relate the exchange phase as the celebrated Berry phase as in this case the Zz-cohomology becomes irrelevant and is consistent with the first Chern class which involves curvature. This follows from the depiction of a fermion as a scalar particle attached with a magnetic flux line. As in this framework the measure of entanglement of two nearest neighbor spins in a spin system given by concurrence is found to be associated with the Berry phase acquired by a spin state when it evolves in a closed path we can consider that entanglement is a consequence of Fermi statistics. It has been noted that in terms of quantum field theory, the berry phase is related to the perpetual inconsistency caused by the breaking of the perpetual symmetry. As mentioned earlier the quantization procedure of a fermion in the framework of Nelson’s stochastic quantization procedure introduces an internal variable which appears as a direction vector and gives rise to spin degrees of freedom. It's pointing to is that when a spin- 1 state of two spin 1/2 state is a Entangle system as considered to be that, the most widely covered state longitudinal elements with the matching it.
The exchange phase for two spins is studied here from the point of view of the quantization of a fermion in the framework of Nelson’s stochastic mechanics. This introduces a direction vector attached to a space–time point depicting the spin degrees of freedom. In this formalism, a fermion appears as a scalar particle attached with a magnetic-flux quantum, and a quantum spin can be described in terms of an SU(2) gauge bundle. This helps us to recast the Berry–Robbins formalism where the exchange phase appears as an unfamiliar geometric phase arising out of the ‘exchange rotation’ in a transported spin basis in terms of gauge currents. However, for polarized fermions, the exchange phase is found to be given by the Berry phase.
We present measurements of the Berry Phase in a single solid-state spin qubit associated with the nitrogen-vacancy center in diamond. Our results demonstrate the remarkable degree of coherent control achievable in the presence of a highly complex solid-state environment. We manipulate the spin qubit geometrically by careful application of microwave radiation that creates an effective rotating magnetic field, and observe the resulting phase via spin-echo interferometry. We find good agreement with Berry's predictions within experimental errors. We also investigated the role of the environment on the geometric phase, and observed that unlike other solid-state qubit systems, the dephasing was primarily dominated by fast radial fluctuations in the path.