tag:blogger.com,1999:blog-3832136017893749497.post1094928724792485829..comments2023-09-29T08:49:30.765-04:00Comments on Elliptic Composability: Florin Moldoveanuhttp://www.blogger.com/profile/01087655914212705768noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-3832136017893749497.post-34988064050973844252015-08-04T05:39:49.387-04:002015-08-04T05:39:49.387-04:00Sure, but this may still take a while… :(Sure, but this may still take a while… :(bobhttp://www.cs.ox.ac.uk/bob.coecke/noreply@blogger.comtag:blogger.com,1999:blog-3832136017893749497.post-44974177576339550582015-08-03T12:08:26.626-04:002015-08-03T12:08:26.626-04:00Hi Bob, nice links, thanks.
Can I ask you a favor...Hi Bob, nice links, thanks.<br /><br />Can I ask you a favor? Can you drop a quick message here when your book becomes available?<br /><br />Thanks,<br />FlorinFlorin Moldoveanuhttps://www.blogger.com/profile/01087655914212705768noreply@blogger.comtag:blogger.com,1999:blog-3832136017893749497.post-70892120035163806482015-08-03T05:17:08.322-04:002015-08-03T05:17:08.322-04:00Hi Lawrence, here are diagrammatic accounts on GHZ...Hi Lawrence, here are diagrammatic accounts on GHZ/W/C*:<br /><br />1) A diagrammatic account on general multi-partite entanglement taking the GHZ-state and W-state as `generators':<br /><br />The compositional structure of multipartite quantum entanglement<br />Bob Coecke, Aleks Kissinger<br />http://arxiv.org/abs/1002.2540<br /><br />A Diagrammatic Axiomatisation for Qubit Entanglement<br />Amar Hadzihasanovic<br />http://arxiv.org/abs/1501.07082<br /><br />2) A diagrammatic derivation of non-locality based on the GHZ-state:<br /><br />Phase groups and the origin of non-locality for qubits<br />Bob Coecke, Bill Edwards, Robert W. Spekkens<br />http://arxiv.org/abs/1003.5005<br /><br />Generalised Compositional Theories and Diagrammatic Reasoning<br />Bob Coecke, Ross Duncan, Aleks Kissinger, Quanlong Wang<br />http://arxiv.org/abs/1506.03632<br /><br />3) C*-algebras diagrammatically (and generalised beyond `algebra'):<br /><br />Categories of Quantum and Classical Channels<br />Bob Coecke, Chris Heunen, Aleks Kissinger<br />http://arxiv.org/abs/1305.3821<br /><br />Compositional Quantum Logic<br />Bob Coecke, Chris Heunen, Aleks Kissinger<br />http://arxiv.org/abs/1302.4900<br /><br /><br /><br /><br /><br />bobhttp://www.cs.ox.ac.uk/bob.coecke/noreply@blogger.comtag:blogger.com,1999:blog-3832136017893749497.post-42271477555862357592015-07-29T22:19:48.658-04:002015-07-29T22:19:48.658-04:00Kashyap,
Hyperbolic QM was originally discovered ...Kashyap,<br /><br />Hyperbolic QM was originally discovered by Andrei Khrenikov, and re-discovered independently by Emile Grgin. In a nutshell you take ordinary QM and replace complex numbers with split-complex numbers (where instead of i = sqrt(-1) you have i=sqrt(+1) but i is not 1) https://en.wikipedia.org/wiki/Split-complex_number. <br /><br />This solution is stable under composition, but is nonphysical because the position and momentum representation give you distinct predictions. Moreover I was able to show that you encounter negative probabilities in this theory and there is no physical interpretation.<br /><br />Invariance under composition has only 3 solution: elliptic (QM), parabolic (CM), and hyperbolic (hyperbolic QM). My blog is called elliptic composability which is QM in disguise :)Florin Moldoveanuhttps://www.blogger.com/profile/01087655914212705768noreply@blogger.comtag:blogger.com,1999:blog-3832136017893749497.post-88051311527249051652015-07-29T22:10:31.365-04:002015-07-29T22:10:31.365-04:00Florin,
This is a new word for me, hyperbolic QM. ...Florin,<br />This is a new word for me, hyperbolic QM. Can you explain its basics in few lines?<br />Is it QM where you do not mind if probabilities become negative?kashyap vasavadahttps://www.blogger.com/profile/10732897306667764590noreply@blogger.comtag:blogger.com,1999:blog-3832136017893749497.post-34893364697294176802015-07-29T21:29:56.040-04:002015-07-29T21:29:56.040-04:00Lawrence,
I do not use the channel-state duality...Lawrence, <br /><br />I do not use the channel-state duality in my case as invariance under composition has 3 solutions: QM, CM, and hyperbolic QM. In hyperbolic QM one does not have completely positive maps. C-J isomorphism arises only after introducing positivity as another physical principle.<br /><br />The interesting problem is to find out what happens beyond C* algebras, in the realm of Hilbert modules (where we have QM over SL(2,C)). And I don't yet know the answer to this. Florin Moldoveanuhttps://www.blogger.com/profile/01087655914212705768noreply@blogger.comtag:blogger.com,1999:blog-3832136017893749497.post-19754138977006357722015-07-29T19:43:16.111-04:002015-07-29T19:43:16.111-04:00What does Choy-Jamilkowsky isomorphism imply with ...What does Choy-Jamilkowsky isomorphism imply with respect to your tensor product formalism? Also this seems to work with bipartite entanglements. What about tripartite, W and GHZ entanglements? I think one needs to extend this into a C* algebra.<br /><br />LCLawrence Crowellhttps://www.blogger.com/profile/12090839464038445335noreply@blogger.comtag:blogger.com,1999:blog-3832136017893749497.post-46720335178344533142015-07-29T07:09:27.638-04:002015-07-29T07:09:27.638-04:00Florin,
Thanks. OK! So we will wait! BTW, by nume...Florin,<br />Thanks. OK! So we will wait! BTW, by numerical methods, I did mean computational software in contrast to paper and pencil!kashyap vasavadahttps://www.blogger.com/profile/10732897306667764590noreply@blogger.comtag:blogger.com,1999:blog-3832136017893749497.post-57467036733736966252015-07-29T00:04:18.645-04:002015-07-29T00:04:18.645-04:00Kashyap,
I may be biased, but I see a very bright...Kashyap,<br /><br />I may be biased, but I see a very bright future for this approach and I think it is premature to pass judgment at this stage. Conceptually category theory is the right paradigm for quantum mechanics and at least it helped me to validate my approach and understand why and how it worked. When you are exploring a brand new area, there is a lot of confusion and wrong steps, but category theory lifted the fog and now I can attack with clarity new problems. (The pictorial formalism is simply a way to visually represent categorical arguments).<br /><br />On Feynman diagrams I am not an expert in this area of numerical simulation and my answer is that I don't know. I know there are powerful symbolic software packages which compute Feynman diagrams exactly, so I don't quite see the need for numerical methods. Mathematica was started by Stephen Wolfram to help with his Feynman diagram computations (I heard him give a talk at UMCP about it).Florin Moldoveanuhttps://www.blogger.com/profile/01087655914212705768noreply@blogger.comtag:blogger.com,1999:blog-3832136017893749497.post-42559989289313746272015-07-28T23:03:13.327-04:002015-07-28T23:03:13.327-04:00I had the same question as this person on Twitter,...I had the same question as this person on Twitter, i.e. what is the real utility of pictorial representation? I am willing to accept that this may be an early stage. So we have to wait! But to calculate any observable, you have to write the full Hamiltonian and calculate matrix elements or solve Schrodinger equation anyway. Does this approach make numerical evaluation easier or combine various matrix elements to give one grand answer? As for utility of Feynman diagrams, I would say that once you have Feynman rules, you do not have to go back to Lagrangian every time you want to evaluate a higher order diagram with lots of loops etc. Although I never evaluated any Feynman diagram numerically, my guess is that such rules make numerical evaluation possible and easier. What do you think? kashyap vasavadahttps://www.blogger.com/profile/10732897306667764590noreply@blogger.com