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arXiv · 1610.00930

Nuclear Numerical Range and Quantum Error Correction Codes for non-unitary noise models

Patryk Lipka-Bartosik·Karol Życzkowski
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Abstract

We introduce a notion of nuclear numerical range defined as the set of expectation values of a given operator $A$ among normalized pure states, which belong to the nucleus of an auxiliary operator $Z$. This notion proves to be applicable to investigate models of quantum noise with block-diagonal structure of the corresponding Kraus operators. The problem of constructing a suitable quantum error correction code for this model can be restated as a geometric problem of finding intersection points of certain sets in the complex plane. This technique, worked out in the case of two-qubit systems, can be generalized for larger dimensions.

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Patryk Lipka-Bartosik, Karol Życzkowski. 2016-10-04. Nuclear Numerical Range and Quantum Error Correction Codes for non-unitary noise models. https://doi.org/10.1007/s11128-016-1484-8

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