Talk:Bloch sphere

message: Thanks for correcting this. CSTAR 13:53, 8 Jul 2004 (UTC)

message: Hi, although the quantum description SU(2) appears to have more degrees of freedom, than the classical description SO(3), the length of the vector is fixed to one and the mixed state (called "pure" in the page)  is in fact equivalent to the classical description under that restriction.  
The Pauli matrices was the first link between a classical theory of a magnetic nuclear moment and a quantum theory using a two level system. The gap between both theory lead to consequences extremely hard to admit even today, therefore one has to use all possible tools to illustrate those equations. The Bloch vector model, the graphical equivalent of the Pauli model is a nice visual tool.
Alain Michaud 07:37, 11 June 2006 (UTC)
thread_title:  Answer to: why discussed so often? 

message: Is Bloch sphere related to the NMR physicist Felix Bloch? Thanks for any information or reference. --KasugaHuang 09:06, 3 March 2006 (UTC)
thread_title:  Relation to Felix Bloch? 

message: Yes the rotation of the Bloch vector on the Bloch sphere is nothing but the simple description of a NMR experiment. It was not until the 40th that the NMR experiment were done on solids (Purcel and xx), following the measurements of Rabi on atomic beams (1937).  
In the 30th, the situation was like this: The simplest system would have two levels, and the quantum mechanics at best would describe the probability that the system jumps from one state to the other. On the other hand the spectroscopists would measure 'common sense' physical properties like magnetic moment, etc...  
There were many people that were involved in the evolution from concept of shroedinger equation, which is the simplest wave equation, to the concept of "probability", the concept of "spin", the correspondence principle, the NMR experiments, etc... Among others, they were: Otto Stern who saw the first "doublet", Isidore Rabi, who induced a transition, Zeeman and Landé who made early spectroscopic measurements, Ulenbeck and Goudsmith who had the weird idea of an half integer cinetic moment, Pauli who gave a model for it, Bloch, Thomas, Dirac, etc...
During all those years, the gap between the classical and quantum theory remained and even today most of the literature for the general (non scientific) public is devoted to explain this apparent paradox. 
Nevertheless, the complete 'exact' theoritical description was given in the 50 with the work of von Neuman who introduced the concept density operator. This was the birth of what is now called "measurement theory": Measurements made on a large ensemble of identical particles show the "statistical" picture, while measurements made on an isolated particle reveal the "probabilistic" nature. 
(Also, it is worth mentioning the book of Hietler in 1935 which was very advanced for its time!)
Alain Michaud 06:55, 11 June 2006 (UTC)
thread_title:  Answer:

message: Hi,
I think this page goes too fast! In the first paragraph the "qubit" is introduced, while there is a section on the density operator at the end of the page. 
I did not change anything, as I do not want to destroy someone else's work. Here would my approach:
Section 1- Low level introduction:  Something that a High-school student could read: The bloch sphere realy is a visual aid for illustrating the link between the R^3 space to the U^2 space. The first one is easy to see while the second one is more "abstract" as the only "aspect" we can observe is the projection along one or two axis!
Section 2 - History: This model was introduced after the early spectroscopy measurements as link between classical (3D real) and quantum (2D complex) physics. This was only the tip of a gigantic iceberg!
Section 3 - A complete mathematical description requires the introduction of the density operator (introduced in the 50 by von Neuman) and also of the concept of spin (the simplest 2 level system model), etc...
Section 4 - A modern application is the use of the same formalism but on single particle or small systems, which leads to completely unexpected situations like entangled stated, etc... (All these phenomenons are a consequence of a "mismatch" between the R^3 ans U^2 spaces, which can be visualized by the bloch sphere)
As you see there is a lot here, but at least the first few paragraph should contain just the right information. very simple, but exact and not misleading.
Thank you for reading
Alain Michaud 05:53, 11 June 2006 (UTC)
thread_title:  Layout of the page 

message: Doing a disambig run on Natural, and I'm not enough of a mathematician to know if the word "natural" used in the "Generalization" section of this article should go to Nature or Natural transformation - or, indeed, somewhere else.  Could someone please help?  Thanks. Tevildo 04:05, 16 December 2006 (UTC)
thread_title:  "Natural"? 

message: Any reason this article doesn't mention the ability for the inside of the Bloch sphere to represent mixed states? — Preceding unsigned comment added by 207.171.180.101 (talk) 22:46, 7 February 2007 (UTC)
thread_title:  Only pure states? 

message: Slightly confused by the inclusion of a picture of a sphere that doesn't actually show any states on it.  In essense it then is just a sphere with an xyz axis, which is a pity since the whole beauty of the bloch sphere is that it allows a visualisation of the different possible states of a single qubit.
Would it be possible to update the picture.  I guess i could have a bash if that isn't stepping on anyone's feet.
I would imagine that something like the figure in this paper would be good:
http://arxiv.org/pdf/0803.1554
--Wideofthemark (talk) 12:06, 15 January 2009 (UTC)
replies: text: The picture includes a parametrization of states as described in the article in the body of the article. Why isn't that enough?--CSTAR (talk) 15:53, 15 January 2009 (UTC)
replies: text: Because it doesn't explicitly label the poles corresponding to |0> and |1>.  -KR 13:11, 2 June 2009 (UTC)
thread_title:  Lack of any actual states on the Bloch sphere figure? 

message: Consider adding the following reference:
* Geometry of a Qubit by Maris Ozols.
In this essay I discuss various ways to represent a qubit state. Maybe this reference is relevant also for the article on Qubit.
— Preceding unsigned comment added by Marozols (talk • contribs) 22:32, 22 February 2009 (UTC)
thread_title:  Reference 

message: 2nd para, 2nd sentence:  "The space of pure states of a quantum system is given by the one-dimensional subspaces the Hilbert space (the "points" of projective Hilbert space)."
Should there be an "of" after subspaces?  Or am I even unable to read sentences on QP?  Forton (talk) 18:24, 16 November 2009 (UTC)
thread_title:  Grammar problem? 

message: The diagram is awful, not only is it ugly it also lacks vital information (what different points correspond to) making it unhelpful. If you have time and inclination, please replace it!  —Preceding unsigned comment added by 163.1.167.234 (talk) 21:19, 14 March 2010 (UTC)
thread_title:  image problem 

message: The presence of  and half-angles is never explained. There is the attempt,
:"To prove this fact, note that there is a natural group action of  on the set of states of ".
The blue link "natural" leads to abstract nonsense. Better might be to say simply that  is the (unique) group that preserves the standard Hermitian form (inner product) on , see classical group. Before I possibly do anything, I'd like some feedback. YohanN7 (talk) 16:35, 13 August 2014 (UTC)
thread_title:  Occurrence of U(n) (and half-angles) 

message: The Bloch CPU is a shpere that has many transistors on it's surface. It acts like a probabilistic CPU when noise inputs inserted, and many Bloch spheres usually work together as qubits do. It is zillion times slower than an actual quantum computer, also exports rounded results, but it may work well if many Bloch-sheres combine their states and if avegaged many results to provide a mean. It can be used as an input for a real quantum CPU,
when even the question we pose is complex enough and probabilistic. Also it can be used as a filter for the output of a quantum-CPU, when we require some extra rotations [usually fixed ones]  — Preceding unsigned comment added by 2.84.219.136 (talk) 22:18, 15 May 2015 (UTC)
replies: text: Unless there is a reliable source establishing some connection between the topic of this section and the Bloch sphere, beyond the name itself, I suggest that the section be removed from this talk page as being off topic.  Vaughan Pratt (talk) 03:06, 21 October 2017 (UTC)
thread_title:  the Bloch CPU 

message: The diagram uses theta and lower case phi but the definition uses theta and phi. Suggest to change one or the other to keep them consistent.  — Preceding unsigned comment added by 124.19.49.38 (talk) 22:28, 20 February 2018 (UTC)
thread_title:  Consistent variable naming 

message: It looks like somebody takes consistent fun in repeatedly replacing the image by an image which is wrong. The wrong image is labeled ẑ=|0> at the top and -ẑ=|1> at the bottom. Multiplying -ẑ=|1> with (-1) we obtain ẑ=-|1>. Together with ẑ=|0> and transitivity of equality we obtain the completely absurd result |0> = -|1> 
Please do Wikipedia a favor and stop replacing the corrected image by an image with this absurd annotation.  — Preceding unsigned comment added by 87.163.198.107 (talk) 22:06, 30 September 2018 (UTC)
replies: text: If you want to help, remove that absurd picture in all the other national variants of this article. — Preceding unsigned comment added by 87.163.198.107 (talk) 22:08, 30 September 2018 (UTC)

text: This confused me too and deserves an explanation, but the diagram is not wrong. The block sphere does not live in the same space as the |0>, |1> vector space because of the use of theta/2 instead of \theta in the first equation under Definition. "states which are orthogonal are not orthogonal vectors on the Bloch sphere. Thus for instance, |0⟩ and |1⟩ are orthogonal, but are represented on the Bloch sphere as θ = 0 and θ = pi" See this article by Dave Bacon. Pulu (talk) 04:17, 2 May 2019 (UTC)

text: Sigh. Well - NOW it is correct, but it WAS wrong before you came here :-)  — Preceding unsigned comment added by 217.95.163.145 (talk) 22:48, 5 December 2019 (UTC)
thread_title:  Image wrong wrong wrong 

message: The article states:
:For any state |\psi\rangle, the isotropy group of |\psi\rangle, (defined as the set of elements g  of  U(n) such that g |\psi\rangle = |\psi\rangle) is isomorphic to the product group
:: \operatorname{U}(n-1) \times \operatorname{U}(1). 
Actually, what is meant is the set of elements  such that g|\psi\rangle is some complex number (of absolute value 1) times |\psi\rangle. Could we make this clear? As it stands, the definition of this isotropy group is wrong and would be isomorphic only to \operatorname{U}(n-1). Eric Kvaalen (talk) 07:11, 2 April 2019 (UTC)
thread_title: Definition of isotropy group

message: As the article has some kind of a role as an introductory article for those wanting to develop concrete intuitions about qubits, would it benefit from examining a couple of examples of distinctively quantum logic gates? — Charles Stewart (talk) 07:31, 9 May 2022 (UTC)
thread_title:  [[Quantum logic gates]]