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Detecting entanglement through correlations between local observables
KTH, School of Information and Communication Technology (ICT), Optics and Photonics, Quantum Electronics and Quantum Optics, QEO.
KTH, School of Information and Communication Technology (ICT), Optics and Photonics, Quantum Electronics and Quantum Optics, QEO.
KTH, School of Information and Communication Technology (ICT), Optics and Photonics, Quantum Electronics and Quantum Optics, QEO.ORCID iD: 0000-0002-2082-9583
2007 (English)In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 84, 012010- p.Article in journal (Refereed) Published
Abstract [en]

We propose a measure of two-qubit entanglement that is invariant under local unitary transformations, and which is based on local measurements covariances. It measures the Hilbert-Schmidt distance between the state and the product state obtained by multiplying the local density matrices. The measure has the benefit that the experimentalist need not have any a priori knowledge of the state to make the measurements. For pure states, the measure provides the state's concurrence directly, without resorting to state tomography. For statistically mixed states, the measure provides bounds for the concurrence. The two-qutrit case is also studied.

Place, publisher, year, edition, pages
2007. Vol. 84, 012010- p.
National Category
Physical Sciences
URN: urn:nbn:se:kth:diva-34022DOI: 10.1088/1742-6596/84/1/012010ISI: 000295087600010ScopusID: 2-s2.0-36448967179OAI: diva2:418614

QC 20110524

Available from: 2011-05-23 Created: 2011-05-23 Last updated: 2012-09-17Bibliographically approved
In thesis
1. Applications and characterisation of correlations in quantum optics
Open this publication in new window or tab >>Applications and characterisation of correlations in quantum optics
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Quantum optics offers a huge variety of exciting phenomena. Many of them are still in their infancy and especially when it comes to implementing devices using these effects for more than a proof of principle demonstration still many things have to be investigated and understood. In this thesis I discuss the role of correlations in some areas of quantum optics and in some cases compare it to classical optics. Four papers form the core of the thesis.

In the first paper, I propose a new measure for entanglement. This measure is based on correlations between two states. I show, how this measure relates to another measure, the concurrence. It turns out that the measure is a bijective map of the concurrence for a pure state of two qubits. I motivate why the new measure is useful if one wants to implement it experimentally. I discuss its behaviour for the case of two qubits and show its properties when dealing with pure and with mixed states.

The second paper extends the result of the first one to the case where one has higher-dimensional states than qubits.

In the third paper I look at phase super-resolution. I show that it can be interpreted as a purely classical effect and I analyse what is needed and what is not needed to achieve it. Specifically, I show that quantum correlations in terms of entanglement is not needed to demonstrate phase super-resolution. By doing so I propose how one could achieve arbitrarily high phase super-resolution.

Finally, the last paper looks at the efficiency of quantum lithography and quantum imaging. It shows, that some basic assumptions in the original proposals of quantum lithography seems unfounded and that, as a consequence, the efficiency is poor. I give formulæ for the explicit scaling behaviour when changing the number of photons in a mode or when changing the number of pixels. The effect of the results on the future of quantum lithography is discussed as well.

Abstract [sv]

Kvantoptiken erbjuder ett stort antal spännande fenomen. Många av dem är fortfarande i sin linda och särskilt när man vill tillämpa kvantoptiska effekter snarare än att bara visa att principen fungerar så finns det många saker och ting som måste förstås och undersökas bättre. I denna avhandling ska jag diskutera vilken roll korrelationer spelar i några områden inom kvantoptik och i några fall ska jag jämföra dem med klassisk optik. Fyra vetenskapliga artiklar bildar kärnan i avhandlingen.

I det första pappret föreslår jag ett nytt sammanflätningsmått. Detta mått har sin ursprung i korrelationer mellan två tillstånd. Jag visar hur måttet förhåller sig till ett annat mått, den så kallade "concurrence". Det visar sig att måttet är en bijektiv avbildning av concurrence för rena tillstånd av två qubitar. Jag motiverar varför det nya måttet är användbart när man vill implementera det experimentellt. Jag diskuterar hur måttet beter sig för två qubitar och visar dess egenskaper för rena och blandade tillstånd.

Det andra pappret utvidgar första papprets resultat till situationer där man har tillstånd med högre dimension än qubitar.

I det tredje pappret undersöker jag superfasupplösning. Jag visar att man kan tolka detta som en rent klassisk effekt och jag undersöker vad man behöver och vad man inte behöver för att uppnå superfasupplösning. Jag visar särskilt att kvantkorrelationer genom sammanflätning inte behövs för att visa superfasupplösning. Därigenom ger jag förslag om hur man kan uppnå godtyckligt hög superfasupplösning.

Slutligen tittar jag i sista pappret på effektiviteten av kvantlitografi och kvantavbildning. Pappret visar att några grundläggande antaganden i originalförslaget till kvantlitografi verkar vara illa underbyggda och att därigenom kvantlitografins effektivitet reduceras kraftigt. Jag ger ekvationer för det exakta skalningsbeteendet när man ändrar antalet fotoner i en mod eller när man ändrar antalet pixlar. Jag diskuterar också implikationerna som det medför för kvantlitografins framtid.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. xix, 86 p.
Trita-ICT/MAP AVH, ISSN 1653-7610 ; 2011:06
National Category
Other Engineering and Technologies not elsewhere specified
urn:nbn:se:kth:diva-34024 (URN)978-91-7415-979-0 (ISBN)
Public defence
2011-06-07, FB52, AlbaNova Universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00 (English)
QC 20110524Available from: 2011-05-24 Created: 2011-05-23 Last updated: 2011-05-24Bibliographically approved

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