Linked Questions

4 votes
1 answer
196 views

What is the difference between $|0\rangle+|1\rangle$ and a balanced mixture of $|0\rangle$ and $|1\rangle$? [duplicate]

Suppose I have a quantum state $\frac{1}{\sqrt{2}}|0\rangle+\frac{1}{\sqrt{2}}|1\rangle$. Also I have a mixture of two quantum states $S_{1} = |0\rangle$ and $S_{2} = |1\rangle$. In this mixture $50\%$...
user27286's user avatar
  • 955
4 votes
1 answer
126 views

How is a qubit in superposition between $|0\rangle$ and $|1\rangle$ different from a mixture of $|0\rangle$ and $|1\rangle$? [duplicate]

Given that a qubit in equal superposition of $|0\rangle$ and $|1\rangle$ is represented by following wave function \begin{equation} \Psi = \frac{1}{\sqrt 2}(|0\rangle + |1\rangle) \end{equation} and ...
morpheus's user avatar
  • 359
30 votes
4 answers
40k views

What's the difference between a pure and mixed quantum state?

As per my limited understanding, a pure state is the quantum state where we have exact information about the quantum system. And the mixed state is the combination of probabilities of the information ...
Koder101's user avatar
  • 997
4 votes
4 answers
4k views

Why do computer scientists care about the phase of qubits?

When I design some classical register, flip-flop, binary counter, small byte of RAM, etc from scratch with classical logic gate, I never deal with such binary direction because classical bit doesn't ...
Muhammad Ikhwan Perwira's user avatar
7 votes
3 answers
2k views

What is the difference between $\vert 0 \rangle + \vert 1 \rangle$ and $\vert 0 \rangle \langle 0 \vert + \vert 1 \rangle \langle 1 \vert$?

In a discussion with Jay Gambetta on the QISKit Slack channel, Jay told me that "T2 is the time that $\vert 0 \rangle + \vert 1 \rangle$ goes to $\vert 0 \rangle \langle 0 \vert + \vert 1 \rangle \...
Adrien Suau's user avatar
  • 4,927
4 votes
4 answers
330 views

Are classical bits quantum?

A bit is a binary digit, typically 0 or 1. Until a value is assigned (or a measurement is made) a bit is in a superposition of the entangled binary pair, is it not?
user820789's user avatar
  • 3,302
2 votes
2 answers
406 views

How to understand combination states vs pure/mixed states?

I've learned that representing a combination of two states, I simply need to take the tensor product of the states. For example: $$\left|\Psi\right>=\alpha_0\left|0\right>+\beta_0\left|1\right&...
l3utterfly's user avatar
4 votes
3 answers
406 views

Explain the comparison between a state and density matrix

The density matrix $\rho = \frac{1}{2}(|0\rangle \langle0|+|1\rangle \langle1|)$ describes a system which is in state $|0\rangle$ and in $|1\rangle$ with equal probability. Also the state $|\psi\...
Soumyabrata hazra's user avatar
2 votes
3 answers
141 views

What is the difference between $|+\rangle$ and $|-\rangle$?

What is the difference between $|+\rangle$ and $|-\rangle$. I was reading about quantum states and found that $|+\rangle$ and $|-\rangle$ represent state in superposition of other states. I was just ...
Vinay Sharma's user avatar
0 votes
1 answer
123 views

What is the difference between $|\Phi^+\rangle=\frac1{\sqrt2}(|0,0\rangle+|1,1\rangle)$ and a mixture of $|00\rangle$ and $|11\rangle$?

I struggle to see the difference between $|\Phi^+\rangle = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |0\rangle_B + |1\rangle_A \otimes |1\rangle_B)$ and the mixed state defined with probabilities {0.5, ...
eternalstudent's user avatar