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On the efficiency of quantum error correction codes for the depolarising channel
KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.ORCID iD: 0000-0002-2082-9583
(English)Manuscript (preprint) (Other academic)
Identifiers
URN: urn:nbn:se:kth:diva-180531OAI: oai:DiVA.org:kth-180531DiVA: diva2:894438
Note

QS 2016

Available from: 2016-01-15 Created: 2016-01-15 Last updated: 2016-01-15Bibliographically approved
In thesis
1. Quantum error correction
Open this publication in new window or tab >>Quantum error correction
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Quantum error correction is the art of protecting quantum states from the detrimental influence from the environment. To master this art, one must understand how the system interacts with the environment and gives rise to a full set of quantum phenomena, many of which have no correspondence in classical information theory. Such phenomena include decoherence, an effect that in general destroys superpositions of pure states as a consequence of entanglement with the environment. But decoherence can also be understood as “information leakage”, i.e., when knowledge of an encoded code block is transferred to the environment. In this event, the block’s information or entanglement content is typically lost.

In a typical scenario, however, not all types of destructive events are likely to occur, but only those allowed by the information carrier, the type of interaction with the environment, and how the environment “picks up” information of the error events. These characteristics can be incorporated into a code, i.e., a channel-adapted quantum error-correcting code.

Often, it is assumed that the environment’s ability to distinguish between error events is small, and I will denote such environments “memory-less”. But this assumption is not always valid, since the ability to distinguish error events is related to the temperature of the environment, and in the particular case of information coded onto photons, kBTR «ℏω typically holds, and one must then assume that the environment has a “memory”. In the thesis I describe a short quantum error-correction code adapted for photons interacting with a “cold” reservoir, i.e., a reservoir which continuously probes what error occurred in the coded state.

I also study other types of environments, and show how to distill meaningful figures of merit from codes adapted for these channels, as it turns out that resource-based figures reflecting both information and entanglement can be calculated exactly for a well-studied class of channels: the Pauli channels. Starting from these resource-based figures, I establish the notion of efficiency and quality and show that there will be a trade-off between efficiency and quality for short codes. Finally I show how to incorporate, into these calculations, the choices one has to make when handling quantum states that have been detected as incorrect, but where no prospect of correcting them exists, i.e., so-called detection errors.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. xxiv, 144 p.
Series
TRITA-FYS, ISSN 0280-316X ; 2015:84
National Category
Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-180533 (URN)978-91-7595-820-0 (ISBN)
Public defence
2016-01-29, Sal FA32, AlbaNova Universitetscentrum, Roslagstullsbacken 21, Stockholm, 14:00 (English)
Opponent
Supervisors
Note

QC 20160115

Available from: 2016-01-15 Created: 2016-01-15 Last updated: 2016-02-02Bibliographically approved

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