Fundamental Limit to Qubit Control with Coherent Field@

Kazuhiro Igeta

Optical Science LaboratoryControlling matter qubits with coherent electromagnetic field is regarded as the most promising building block of quantum information processing systems. In practice, we can use the classical field theory which enables us to control a qubit perfectly as described by the Bloch rotation according to the pulse area of the field. However, classical fields exist only as an infinitely strong intensity limit. In reality, strong but finite strength coherent fields are available that will cause control errors because of their lack of infiniteness.

In this work, we formulate the full quantum mechanical interaction between a pure coherent field and a qubit in the general initial state including mixed states. While the fidelity error accompanied by /2 pulse control is shown to be inversely proportional to the average photon number in a way similar to that revealed by the former results [1, 2] our results show that the error depends strongly on the initial state of the qubit [3]. Our result (Fig. 1) reveals that the the entanglement built up between the field and the qubit is the origin of the error.

This work was partly supported by CREST of the Japan Science Technology Agency.[1] J.Gea-Banacloche, Phys. Rev. A

65(2002) 022308.

[2] M.Ozawa, Phys. Rev. Lett.89(2002) 057902.

[3] K. Igeta, N. Imoto, and M. Koashi, Phys. Rev. A87(2013) 022321.

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Fig. 1. Solid lines represent exact fidelity error rates for the initially up and initially down qubit states, respectively, plotted to the average photon number ( N) of the field on a log_{10}scale, along with the asymptotic curves for largeN(~1/N) and results of the former studies[1,2] as shown by dotted lines.

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