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On the efficiency of quantum error correction codes for the depolarising channel
KTH, Skolan för teknikvetenskap (SCI), Tillämpad fysik, Kvantelektronik och -optik, QEO.ORCID-id: 0000-0002-8721-3580
KTH, Skolan för teknikvetenskap (SCI), Tillämpad fysik, Kvantelektronik och -optik, QEO.ORCID-id: 0000-0002-2082-9583
(Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
Identifikatorer
URN: urn:nbn:se:kth:diva-180531OAI: oai:DiVA.org:kth-180531DiVA, id: diva2:894438
Anmärkning

QS 2016

Tillgänglig från: 2016-01-15 Skapad: 2016-01-15 Senast uppdaterad: 2016-01-15Bibliografiskt granskad
Ingår i avhandling
1. Quantum error correction
Öppna denna publikation i ny flik eller fönster >>Quantum error correction
2016 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Stockholm: KTH Royal Institute of Technology, 2016. s. xxiv, 144
Serie
TRITA-FYS, ISSN 0280-316X ; 2015:84
Nationell ämneskategori
Atom- och molekylfysik och optik
Forskningsämne
Fysik
Identifikatorer
urn:nbn:se:kth:diva-180533 (URN)978-91-7595-820-0 (ISBN)
Disputation
2016-01-29, Sal FA32, AlbaNova Universitetscentrum, Roslagstullsbacken 21, Stockholm, 14:00 (Engelska)
Opponent
Handledare
Anmärkning

QC 20160115

Tillgänglig från: 2016-01-15 Skapad: 2016-01-15 Senast uppdaterad: 2016-02-02Bibliografiskt granskad

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Björk, Gunnar G. E.

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Almlöf, JonasBjörk, Gunnar G. E.
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Kvantelektronik och -optik, QEO

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