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Nuclear numerical range and quantum error correction codes for non-unitary noise models
Patryk Lipka-Bartosik, K. Życzkowski·October 4, 2016·DOI: 10.1007/s11128-016-1484-8
Computer ScienceMathematicsPhysics
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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.