User:Jonnyelias/sandbox

Contributions to Bell state:

- separate block for Bell Basis: this will need to be elaborated on

- were going to have to find some more sources for this article. There is not too much literature on the internet about the Bell States, so maybe I'll go to the library

The Bell States

The Bell states are four specific maximally entangled quantum states of two qubits.

Bell Basis

In his famous paper of 1964, John S. Bell showed by simple probability theory arguments that these correlations (the one for the 0,1 basis and the one for the +,- basis) cannot both be made perfect by the use of any "pre-agreement" stored in some hidden variables—but that quantum mechanics predicts perfect correlations. In a more formal and refined formulation known as the Bell-CHSH inequality, it is shown that a certain correlation measure cannot exceed the value 2 if one assumes that physics respects the constraints of local "hidden variable" theory (a sort of common-sense formulation of how information is conveyed), but certain systems permitted in quantum mechanics can attain values as high as .

Four specific two-qubit states with the maximal value of  are designated as "Bell states". They are known as the four maximally entangled two-qubit Bell states, and they form a maximally entangled basis, known as the Bell basis, of the four-dimensional Hilbert space for two qubits:

(four equations)

Creating Bell States

Although there are many possible ways to create entangled Bell states through quantum circuits, the simplest takes two qubits as inputs, and contains a Hadamard gate and a CNOT gate (pictured below). As an example, the quantum circuit pictures takes the two qubit input $|00>$and transformed it to the first Bell state (1). Explicitly, the Hadamard gate transforms $|00>$ into a superposition of $(|0>+|1>)|0>/{\sqrt {2}}$. This will then act as a control input to he CNOT gate, which only inverts the target when the control is 1. Since the control is a 0, the CNOT gate transforms the qubit state to its final output of $(|00>+|11>){\sqrt {2}}$.

Quantum circuit to create Bell state.

For the four basic two qubit inputs, $|00>,|01>,|10>,|11>$, the circuit outputs a final Bell state in accordance with the equation

$|\beta (x,y)>=\left({\frac {|0,y>+(-1)^{x}|1,Y>}{\sqrt {2}}}\right)$

where $Y$is the negation of $y$.

Properties of Bell states

Upon measuring first qubit, you obtain two possible results for the second qubit, 0 with ½ probability, and 1 with ½ probability.  This implies that the measurement outcomes correlated. John Bell was the first to prove that the measurement correlations in the Bell State are stronger than could ever exist between classical systems.  This hints that quantum mechanics allows information processing beyond what is possible in the classical world. In addition, the Bell states form an orthonormal basis and can therefore be defined with an appropriate measurement.  Because Bell states are entangled states, information on the entire system may be know, while withholding information on the individual subsystems. For example, the Bell state is a pure state, but the reduced density operator of the first qubit is a mixed state.  The mixed state implies that not all the information on this first qubit is known. Bell States are either symmetric or antisymmetric with respect to the subsystems ( uses source 1).

Applications

Superdense Coding

Superdense coding allows two individuals to communicate two bits of classical information by only sending a single qubit. The basis of this phenomenon is the entangled states or Bell states of a two qubit system. In this example, Alice and Bob are very far distance from each other, and have each been given one qubit of the entangled state

$|\psi >={\frac {|00>+|11>}{\sqrt {2}}}$.

In this example, Alice is trying to communicate a two bits of classical information, one of four two bit strings: $'00','01','10',$or $'11'$. If Alice chooses to send the two bit message $'01'$, she would preform the phase flip $Z$to her qubit. Similarly, if Alice wants to send $'10'$, she would apply a quantum NOT gate; if she wanted to send $'11'$, she would apply the $iY$gate to her qubit; and finally, if Alice wanted to send the to bit message $'00'$, she would do nothing to her qubit. Alice preforms these quantum gate transformations locally, transforming the initial entangled state $|\psi >$ into one of the four Bell states.

The steps below show the necessary quantum gate transformation, and resulting Bell state, that Alice needs to apply to her qubit for each possible two bit message she desires to send to Bob.

$00:I={\begin{bmatrix}1&0\\0&1\end{bmatrix}}\longrightarrow |\psi >={\frac {|00>+|11>}{\sqrt {2}}}$

$01:X={\begin{bmatrix}0&1\\1&0\end{bmatrix}}\longrightarrow |\psi >={\frac {|00>-|11>}{\sqrt {2}}}$ $10:Z={\begin{bmatrix}1&0\\0&-1\end{bmatrix}}\longrightarrow |\psi >={\frac {|10>+|01>}{\sqrt {2}}}$
$11:iY\longrightarrow |\psi >={\frac {|01>-|10>}{\sqrt {2}}}$.

After Alice apply's her desired transformations to her qubit and sends it to Bob, who will then preform a measurement on the Bell state which projects the entangled state onto one of the four two qubit basis vectors, one of which will coincide with the original two bit message Alice was trying to send.

Response to Peer review:

- we have not received any peer reviews, so I'm not sure how we are supposed to respond

Add to an existing article:

- I will be adding to the Bell State article

- The Bell Basis equation are thrown in at the end of the Bell States section. I made these their own section, as they are extremely fundamental to understanding Bell States. We will improve on this section later.

Article Selection:

- The first article we looked at was the Bell State article (Bell state). We noticed a strong lack of math, as well as very little depth for the sections. We have learned more about this topic in class than we could learn from the article, so we could tell it needed improvement.

- the article was written neutraly, but certainly not in a lot of depth

- the citations are reliable, but there are only four references listed at the bottom of the page, which is not anywhere near enough to back up all the claims that were made in the article

Article Evaluation: (Audio engineer)

Content:

- the training section could be more in depth. Audio Engineering is a difficult profession and I imagine there could be a more in depth analysis of where and how to study. It only mentions audio engineering schools as places to learn the discipline, but what about non-audio engineering specific schools that offer the degree as a part of their engineering schools?

- There is nothing about the modern practices and equipment of an audio engineer; that could be drastically improved because, as a fan of music, I am aware of the constant change in resources producers have at their reach

Tone:

- The article definitely does not take sides, as there is really no side to be taken. It does not present the audio engineering field as one of the most challenging and hard to break into field, so it does not have a holier than thou way about the profession, which some might expect to see about field that require intense years of study during school, as all engineering majors do.

Sources:

- there are 27 references an all of them hold valid links to supporting articles or publications.

- the sources are also accurately cited, in that they are linked to relevant information

Talk page:

- interestingly, the most heavily debated thing about this article was the use of the word "engineer" in the description of the profession. There was a heavy argument between someone who claimed to be a professional engineer, who claimed the only audio engineers are the ones who design and create the equipment that producers and musicians use.

-In my opinion, while that is true that audio engineers are certainly the ones who create those machines, the use of "audio engineer" should not be limited to only those people. Audio engineers are very important to the production of music itself, are there is always one present in a studio when an artist of any genre is making new music.