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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.
Aleks started adding some text. I added some links to his keywords.
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.
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...
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.
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 ]
added pointer to today’s
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.
Tried to reorganize the list of references more usefully and more traditionally. Added pointer to:
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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.” :-)
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Added references on (entangled) quantum states as resources, not unlike the idea of resources in linear logic:
Charles H. Bennett, A resource-based view of quantum information, Quantum Information & Computation 4 6 (2004) 460–466 [doi:10.5555/2011593.2011598]
Igor Devetak; Aram W. Harrow; Andreas J. Winter, A Resource Framework for Quantum Shannon Theory, IEEE Transactions on Information Theory 54 10 (2008) [doi:10.1109/TIT.2008.928980]
Eric Chitambar, Gilad Gour, Quantum Resource Theories [arXiv:1806.06107]
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