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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 28th 2010

    Aleks Kissinger has contacted me about his aims to start a collection of nLab entries on quantum information from the point of view of the Bob Coecke school.

    Being very much delighted about this offer, I created a template entry quantum information for his convenience.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 28th 2010

    Aleks started adding some text. I added some links to his keywords.

    • CommentRowNumber3.
    • CommentAuthorIan_Durham
    • CommentTimeFeb 28th 2010
    I've made one or two additions and suggestions. We should probably be careful to make sure that anything that isn't specifically information-theoretic goes under the quantum mechanics heading since, as Zoran pointed out about my quantum channels entry, some things that we QI people may assume are purely QI-related may actually be more general.
    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeFeb 28th 2010

    Actually I've noticed that here the practice is that as long as the further generality is noted on the more specific page, the material can be duplicated on both pages (Urs is adept at this :) Corralling material into very specific pages needs to be balanced against making people jump through many links to find related information.

    Also, pages can be developed to be broad, and then split later, and I think that it is better to put any (appropriate) material in, than worry about the finer points of disciplinary delineation.

    But this is just my impression of how things go.

    • CommentRowNumber5.
    • CommentAuthorIan_Durham
    • CommentTimeFeb 28th 2010
    OK, cool. Then I won't worry too much about it.
    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeFeb 28th 2010
    • (edited Feb 28th 2010)

    yes, often only after a bunch of material has accumulated does it become clear how that material wants to be organized over different sections and maybe entries.

    of course somebody who cares and has the energy to deal with it has still to be around then...

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeFeb 28th 2010
    • (edited Feb 28th 2010)

    that said: I agree with Zoran and Ian, that we should try not to exclusively list under "quantum information" what genuinely belogs to quantum mechanics in general.

    • CommentRowNumber8.
    • CommentAuthorDavidRoberts
    • CommentTimeMar 1st 2010
    Having looked at the entry, I see your point Ian. _I_ wouldn't go into too much more detail than what is there now (only my own opinion). Familiarity with the appropriate level of background/back up information will come with time.
    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeApr 18th 2013

    I am about to split off quantum computing from quantum information (or rather: remove the redirect, since there is nothing yet to splitt off).

    First I am hereby moving an old and forgotten query boxes from there to here :

    [ begin forwarded text ]

    +–{: .query} Ian Durham: Should we maybe somehow link the quantum mechanics section to this? Teleportation and entanglement, to me, are quantum phenomena that transcend their use in quantum information theory (the others, I agree, are purely information-theoretical).

    Aleks Kissinger: Entanglement I agree with, though the description of teleportation as a protocol (as opposed to a phenomenon) probably belongs here.

    Ian Durham: Yes, I’d agree with that. It’s description is usually in terms of a protocol. Actually, I suppose it’s status as a “phenomenon” is somewhat debatable. =–

    [ end forwarded text ]

    • CommentRowNumber10.
    • CommentAuthorjuanmeleiro
    • CommentTimeJul 2nd 2020
    A nice introductory reference to the subject (which, in fact, discusses some of the topics that are not yet written), is Scott Aaronson's lecture notes [1]. I wouldn't know how to cite them, or even if it is appropriate to reference them.

    [1]: They can be found at
    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeNov 11th 2020

    added pointer to today’s

    • Sumeet Khatri, Mark M. Wilde, Principles of Quantum Communication Theory: A Modern Approach (arXiv:2011.04672)

    diff, v24, current

    • CommentRowNumber12.
    • CommentAuthorzskoda
    • CommentTimeJan 6th 2021
    • (edited Jan 6th 2021)
    • Reinhard Werner, Mathematical methods of quantum information theory, 18 lecture course (2017) video playlist yt

    diff, v26, current

    Contents, copied from Osborne’s blog

    Lecture 1: Hilbert spaces, scalar product, bra, ket, operators.

    Lecture 2: operators, diagonalization, functional calculus, qubit, composite systems, tensor product.

    Lecture 3: composition, tensor product, channels, Heisenberg picture, Schrödinger picture, complete positivity, channel examples: unitary, depolarizing, von Neumann measurement.

    Lecture 4: state space, probabilites, composition positivity, geometry of cones.

    Lecture 5: geometry, extremal points, pure states, POVM, effect operators.

    Lecture 6: Choi-Jamiokowski isomorphism, Kraus operators.

    Lecture 7: Wigner’s theorem, anti unitary operators, symmetry groups, one-parameter groups, irreducible representations

    Lecture 8: How to construct a Hilbert space, positive kernel, kolmogorov dilation, completion, going to the larger Hilbert space.

    Lecture 9: Stinespring dilation Theorem and proof, Example: Naimark dilation, GNS representation, comparison theorem.

    Lecture 10: Corollary of Stinespring, Kraus Form.

    Lecture 11: Instrument, statistical structure; entanglement, Choi isomorphism and channels, classical models, Bell correlation.

    Lecture 12: Mixed state entanglement, Bell inequalites, Tsirelsons inequality, pure state entanglement, Schmidt decomposition, maximally entangled states.

    Lecture 13: Dispersion-free preparation, Joint measurement, measurement uncertainty relation, copying, transmitting a quantum state via a classical channel, signalling on correlations, teleportation.

    Lecture 14: quantum teleportation; dense coding

    Lecture 15: teleportation vs. dense coding, star trek

    Lecture 16: norms and fidelities, operator norms, Schatten norms, trace norm, diamond norm, cb norm.

    Lecture 17: some semidefinite tasks in QI SDPs, examples: unambiguous state discrimination, entanglement detection, code optimization, dual SDP, optimization on a convex cone (interior point method).

    Lecture 18: noisy resources and conversion rates classical-quantum information transmission, two-step encoding inequality.

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeMay 7th 2021

    Tried to reorganize the list of references more usefully and more traditionally. Added pointer to:

    diff, v29, current

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeMay 13th 2021

    added this pointer:

    diff, v30, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeAug 31st 2022

    added pointer to:

    diff, v37, current

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeSep 5th 2022

    Also added pointer to the newly available part II:

    Incidentally, it seems fair to say that these lecture notes indirectly demonstrate the achievement of Abramsky & Coecke 2004: While the latter may seem somewhat tautologous to the category-theoretically versed reader (certainly in hindsight, and that’s a positive for a foundational approach), this makes its utter dissimilarity with traditional texts such as Aaronson’s all the more remarkable.

    For example, after Aaronson’s course introduces the quantum teleportation protocol in components – where it is opaque – apparently the students were rightly left wondering: “How do people come up with this stuff ?” (p. 71). This would be the natural place to admit that quantum teleportation becomes a transparent triviality in string diagram notation (as e.g. in Bob Coecke’s “Quantum Picturalism”, p. 16), but the above lectures instead just say: “These sorts of protocols can be hard to find.” :-)

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeSep 6th 2022

    added pointer to:

    diff, v42, current

    • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeOct 17th 2022
    • (edited Oct 17th 2022)


    and doi-link for:

    diff, v47, current

    • CommentRowNumber19.
    • CommentAuthorUrs
    • CommentTimeDec 6th 2022

    added pointer to:

    diff, v51, current

    • CommentRowNumber20.
    • CommentAuthorUrs
    • CommentTimeDec 6th 2022


    diff, v51, current

    • CommentRowNumber21.
    • CommentAuthorUrs
    • CommentTimeJan 18th 2023
    • CommentRowNumber22.
    • CommentAuthorUrs
    • CommentTimeMar 29th 2023

    added this pointer:

    diff, v54, current

    • CommentRowNumber23.
    • CommentAuthorUrs
    • CommentTimeMar 30th 2023

    Added references on (entangled) quantum states as resources, not unlike the idea of resources in linear logic:

    diff, v55, current

    • CommentRowNumber24.
    • CommentAuthorUrs
    • CommentTimeSep 22nd 2023

    added pointer to:

    diff, v61, current