<p>Let 
$$P(0) = |a|^2 + |c|^2 + |e|^3 + |g|^2.$$
This is the probability of observing $0$. </p>

<p>Then
\begin{eqnarray*}
w &amp;=&amp; a \big/ \sqrt{P(0)}, \\
x &amp;=&amp; c \big/ \sqrt{P(0)}, \\
y &amp;=&amp; e \big/ \sqrt{P(0)}, \\
z &amp;=&amp; g \big/ \sqrt{P(0)}.
\end{eqnarray*}</p>

CC BY-SA 3.0
2016-06-29T08:48:33.313Z
Great, thanks for the help :) I was unsure whether the general form was that simple when talking about potentially entangled systems
Tim Atkinson
CC BY-SA 3.0
2016-06-28T15:19:15.227Z
2016-06-28T15:19:15.227Z
Peter Shor 
<p>Suppose I have a set of 3 qubits and I have the probabilities for their distribution. This could be arbitrarily entangled or pure:</p>

<ul>
<li>|000> -> a </li>
<li>|001> -> b</li>
<li>|010> -> c</li>
<li>|011> -> d</li>
<li>|100> -> e</li>
<li>|101> -> f</li>
<li>|110> -> g</li>
<li>|111> -> h</li>
</ul>

<p>With it holding that a^2 + b^2 ... h^2 = 1.</p>

<p>a) Now suppose I wanted to measure the third qubit. Would it be valid to <em>generally</em> take the probability of the measurement being 0 as a^2 + c^2 + e^2 + g^2?</p>

<p>b) Assume I had measured the third qubit as 0. How would I construct a new probability distribution across my remaining 2 qubits:</p>

<ul>
<li>|00> -> w </li>
<li>|01> -> x</li>
<li>|10> -> y</li>
<li>|11> -> z</li>
</ul>

<p>Where w, x, y and z are computed from a, b ... h</p>

<p>Thank you in advance for any guidance you can give me!</p>

<quantum-computing><quantum-information>
How are new probabilities computed when simulating measurement on a set of qubits?
Tim Atkinson
# How are new probabilities computed when simulating measurement on a set of qubits?

(Asked by: username_0 on 2016-06-28)

Suppose I have a set of 3 qubits and I have the probabilities for their distribution. This could be arbitrarily entangled or pure:

* |000> -> a
* |001> -> b
* |010> -> c
* |011> -> d
* |100> -> e
* |101> -> f
* |110> -> g
* |111> -> h

With it holding that a^2 + b^2 ... h^2 = 1.

a) Now suppose I wanted to measure the third qubit. Would it be valid to *generally* take the probability of the measurement being 0 as a^2 + c^2 + e^2 + g^2?

b) Assume I had measured the third qubit as 0. How would I construct a new probability distribution across my remaining 2 qubits:

* |00> -> w
* |01> -> x
* |10> -> y
* |11> -> z

Where w, x, y and z are computed from a, b ... h

Thank you in advance for any guidance you can give me!

**Tags:** quantum-computing, quantum-information

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## 1 answers

### Answer by username_1 on 2016-06-28. Score: 2 | Accepted answer

Let
$$P(0) = |a|^2 + |c|^2 + |e|^3 + |g|^2.$$
This is the probability of observing $0$.

Then
\begin{eqnarray\*}
w &=& a \big/ \sqrt{P(0)}, \\
x &=& c \big/ \sqrt{P(0)}, \\
y &=& e \big/ \sqrt{P(0)}, \\
z &=& g \big/ \sqrt{P(0)}.
\end{eqnarray\*}

> **Comments:**
> **username_0**: Great, thanks for the help :) I was unsure whether the general form was that simple when talking about potentially entangled systems  

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