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A Short Course in Quantum Information Theory pp 61–77Cite as

Composite Q-System, Pure State

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Part of the book series: Lecture Notes in Physics ((LNP,volume 827))

Abstract

Even the simplest q-systems cannot exhaustively be discussed without the concept of composite systems. As we shall see, the reason is q-correlations between otherwise independent q-systems. While classical correlations permit separate treatment of local systems, q-correlations will only permit this with particular limitations. The mathematics of composite q-systems will be introduced from the aspect of q-correlations (entanglements). The reader may learn three historical instances of q-correlation. Two genuine q-informatic applications based on q-correlations will close the chapter.

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Notes

  1. 1.

    Sometimes we call them the principal system and the ancilla, or the system and the meter in case of the indirect measurement 8.3.

  2. 2.

    The factors of two \(\hat{\sigma}\)’s, when appear as \(\hat{\varvec{\sigma}}\otimes \hat{\varvec{\sigma}}\) or \(\hat{\varvec{\sigma}} \hat{\rho} \hat{\varvec{\sigma}}\), etc., should be understood as spatial scalar products. E.g.: \(\hat{\varvec {\sigma}} \otimes \hat{\varvec {\sigma}}= \hat{\sigma}_x\otimes \hat{\sigma}_x+ \hat{\sigma}_y\otimes \hat{\sigma}_y+ \hat{\sigma}_z\otimes \hat{\sigma}_z\).

  3. 3.

    This happens just because \({\mathcal{T}}\) belongs to non-completely positive maps, cf. Chap. 8, discovered by Stinespring [3].

  4. 4.

    It is the version by Clauser et al. [7].

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  1. MTA Budapest, KFKI Research Institute for Particle and Nuclear Physics (RMKI), Konkoly Thege Miklós út 29-33, 1525, Budapest, Hungary

    Lajos Diósi

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Diósi, L. (2011). Composite Q-System, Pure State. In: A Short Course in Quantum Information Theory. Lecture Notes in Physics, vol 827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16117-9_7

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  • DOI: https://doi.org/10.1007/978-3-642-16117-9_7

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