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Quantum Information Processing

On the continuity of quantum correlation quantifiers

  • 01-08-2020
Published in:
Authors
T. M. Carrijo
A. T. Avelar
Published in
Quantum Information Processing | Issue 8/2020

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Abstract

We show an equivalence relation between different types of continuity of the generalized discord function (GDF) that leads to the continuity of the generalized quantum discord (GQD) in the finite-dimensional case. We extend the definition of the GQD to the case where the GDF is optimized over the set of all states with zero quantum discord and prove its continuity by showing that this set is topologically compact. However, for an unmeasured subsystem with infinite dimension, we find that this set is no longer compact while the set of locally measured states is shown to maintain this property in the space of Hilbert-Schmidt (HS) operators. This allows us to prove the continuity of the GQD when the GDF is jointly continuous in the infinite case. As an application, we obtain that the geometric discord is continuous (HS topology) and has the zero set given by the zero quantum discord set in the infinite-dimensional case as a consequence of our previous results.

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next article Comparison the performance of five-qubit IBM quantum computers in terms of Bell states preparation
Title
On the continuity of quantum correlation quantifiers
Authors
T. M. Carrijo
A. T. Avelar
Publication date
01-08-2020
Publisher
Springer US
Published in
Quantum Information Processing / Issue 8/2020
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-020-02709-2
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