License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2021.22
URN: urn:nbn:de:0030-drops-144629
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14462/
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Branciard, Cyril ; Clément, Alexandre ; Mhalla, Mehdi ; Perdrix, Simon

Coherent Control and Distinguishability of Quantum Channels via PBS-Diagrams

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LIPIcs-MFCS-2021-22.pdf (0.9 MB)


Abstract

Even though coherent control of quantum operations appears to be achievable in practice, it is still not yet well understood. Among theoretical challenges, standard completely positive trace preserving (CPTP) maps are known not to be appropriate to represent coherently controlled quantum channels. We introduce here a graphical language for coherent control of general quantum channels inspired by practical quantum optical setups involving polarising beam splitters (PBS). We consider different situations of coherent control and disambiguate CPTP maps by considering purified channels, an extension of Stinespring’s dilation.
First, we show that in classical control settings, the observational equivalence classes of purified channels correspond to the standard definition of quantum channels (CPTP maps). Then, we propose a refinement of this equivalence class generalising the "half quantum switch" situation, where one is allowed to coherently control which quantum channel is applied; in this case, quantum channel implementations can be distinguished using a so-called transformation matrix. A further refinement characterising observational equivalence with general extended PBS-diagrams as contexts is also obtained. Finally, we propose a refinement that could be used for more general coherent control settings.

BibTeX - Entry

@InProceedings{branciard_et_al:LIPIcs.MFCS.2021.22,
  author =	{Branciard, Cyril and Cl\'{e}ment, Alexandre and Mhalla, Mehdi and Perdrix, Simon},
  title =	{{Coherent Control and Distinguishability of Quantum Channels via PBS-Diagrams}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{22:1--22:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14462},
  URN =		{urn:nbn:de:0030-drops-144629},
  doi =		{10.4230/LIPIcs.MFCS.2021.22},
  annote =	{Keywords: Quantum Computing, Diagrammatic Language, Quantum Control, Polarising Beam Splitter, Categorical Quantum Mechanics, Quantum Switch}
}

Keywords: Quantum Computing, Diagrammatic Language, Quantum Control, Polarising Beam Splitter, Categorical Quantum Mechanics, Quantum Switch
Collection: 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)
Issue Date: 2021
Date of publication: 18.08.2021


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