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Quantum error correction
KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.ORCID iD: 0000-0002-8721-3580
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: urn:nbn:se:kth:diva-180533ISBN: 978-91-7595-820-0 (print)OAI: oai:DiVA.org:kth-180533DiVA: diva2:894450
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
List of papers
1. A short and efficient error correcting code for polarization coded photonic qubits in a dissipative channel
Open this publication in new window or tab >>A short and efficient error correcting code for polarization coded photonic qubits in a dissipative channel
2011 (English)In: Optics Communications, ISSN 0030-4018, E-ISSN 1873-0310, Vol. 284, no 1, 550-554 p.Article in journal (Refereed) Published
Abstract [en]

We propose a short and efficient non-degenerate quantum error correcting code that is adapted for qubits encoded on two orthogonal, single-photon states (e.g., horizontally and vertically polarized) subject to a dissipative channel. The proposed code draws its strength from the fact that it is adapted to the physical characteristics of the information-carrying basis states under the action of the channel. The code combines different energy manifolds and consists of only 3 spatio-temporal modes and on average 2 photons per code word.

Keyword
Quantum error correcting code, Photonic qubit, Dissipative channel
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-30519 (URN)10.1016/j.optcom.2010.09.006 (DOI)000285893200100 ()2-s2.0-78649652279 (Scopus ID)
Note
QC 20110304Available from: 2011-03-04 Created: 2011-02-28 Last updated: 2017-12-11Bibliographically approved
2. Fidelity as a figure of merit in quantum error correction
Open this publication in new window or tab >>Fidelity as a figure of merit in quantum error correction
2013 (English)In: Quantum information & computation, ISSN 1533-7146, Vol. 13, no 1-2, 0009-0020 p.Article in journal (Refereed) Published
Abstract [en]

We discuss the fidelity as a figure of merit in quantum error correction schemes. We show that when identifiable but uncorrectable errors occur as a result of the action of the channel, a common strategy that improves the fidelity actually decreases the transmitted mutual information. The conclusion is that while the fidelity is simple to calculate and therefore often used, it is perhaps not always a recommendable figure of merit for quantum error correction. The reason is that while it roughly speaking encourages optimisation of the "mean probability of success", it gives no incentive for a protocol to indicate exactly where the errors lurk. For small error probabilities, the latter information is more important for the integrity of the information than optimising the mean probability of success.

Keyword
Fidelity, Mutual information, Quantum error correction
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-107042 (URN)000315304700002 ()2-s2.0-84871693736 (Scopus ID)
Funder
Swedish Research Council
Note

QC 20130205. Updated from accepted to published.

Available from: 2012-12-06 Created: 2012-12-06 Last updated: 2017-12-07Bibliographically approved
3. On the efficiency of quantum error correction codes for the depolarising channel
Open this publication in new window or tab >>On the efficiency of quantum error correction codes for the depolarising channel
(English)Manuscript (preprint) (Other academic)
Identifiers
urn:nbn:se:kth:diva-180531 (URN)
Note

QS 2016

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

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