Refers to the state of an isolated quantum system. A quantum state provides a probability distribution for the value of each observable, i.e. for the outcome of each possible measurement on the system. A mixture of quantum states is again a quantum state.
6
votes
3answers
140 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 \...
5
votes
1answer
558 views
Solving linear systems represented by NxN matrices with N not power of 2
As far as I have seen, when it comes to solving linear systems of equations it is assumed to have a matrix with a number of rows and columns equal to a power of two, but what if it is not the case?
...
5
votes
1answer
72 views
Stabilizer state verification and specification from state vector
Given an arbitrary $n$-qudit state vector $|\psi\rangle =\sum_i c_i| i \rangle \in \mathbb{C}_d^n$ for some orthonormal basis $\{|i\rangle\}$, what is the most efficient way one can:
Verify whether ...
11
votes
6answers
2k views
Quantum states are unit vectors… with respect to which norm?
The most general definition of a quantum state I found is (rephrasing the definition from Wikipedia)
Quantum states are represented by a ray in a finite- or infinite-dimensional Hilbert space over ...
3
votes
1answer
63 views
How the joint state of these qubits is derived?
Can someone show to me the steps to derive the joint state at the bottom of this image, please?
I tried to follow his explanation but I didn't get the same results…
This is taken from the lecture ...
8
votes
2answers
181 views
What are the possible ways to visualise large, entangled states?
What are the prominent visualisations used to depict large, entangled states and in what context are they most commonly applied?
What are their advantages and disadvantages?
3
votes
2answers
140 views
What does negative probability represent?
"Negative energies and probabilities should not be considered as nonsense. They are well-defined concepts mathematically, like a negative of money." -Paul Dirac
The abstract from Photon-phonon-photon ...
6
votes
1answer
53 views
Are Absolutely Maximally Entangled states maximally entangled under all entanglement monotones?
In Ref. [1] absolutely maximally entangled (AME) states are defined as:
An $\textrm{AME}(n,d)$ state (absolutely maximally entangled state) of $n$ qudits of dimension $d$, $|\psi\rangle \in \mathbb{...
6
votes
2answers
76 views
Density matrices for pure states and mixed states
What is the motivation behind density matrices? And, what is the difference between the density matrices of pure states and density matrices of mixed states?
This is a self-answered sequel to What&#...
11
votes
1answer
633 views
How to interpret a quantum circuit as a matrix?
If a circuit takes more than one qubit as its input and has quantum gates which take different numbers of qubits as their input, how would we interpret this circuit as a matrix?
Here is a toy example:...
5
votes
1answer
104 views
What is the $\left| 22\right>$ state?
I came across with a problem that involves $2$ quantum trits in state $\left| 22 \right>.$ What is it's tensor product interpretation and a matrix interpretation?
4
votes
2answers
155 views
How to check if 2 qubits are entangled? [duplicate]
I know that 2 qubits are entangled if it is impossible to represent their joint state as a tensor product. But when we are given a joint state, how can we tell if it is possible to represent it as a ...
6
votes
1answer
86 views
How to apply single and two qubit gates to 2 qubits multiple times?
Let's say we have the following quantum circuit:
Let's say we input the state $|00\rangle$ . Both of the $H$ gates produce the output $1/\sqrt{2}$, but which one of the following $2$ vectors is the ...
9
votes
3answers
189 views
Positive maps on pure states?
In the comments to a question I asked recently, there is a discussion between user1271772 and myself on positive operators.
I know that for a positive trace-preserving operator $\Lambda$ (e.g. the ...
3
votes
1answer
78 views
What does the notation $\lvert \underline{x} \rangle$ mean?
I recently read hand-written notes about the "secret mask" or "secret string" algorithm (which I can't share here) with the following notation $\lvert \underline{x} \rangle$, i.e. a letter with a line ...
3
votes
1answer
69 views
What exactly is a phase vector?
The following $2\times 2$ matrix
$$
P =
\begin{bmatrix}
e^{i\theta} & 0 \\
0 & e^{i\phi}
\end{bmatrix}
$$
represents a quantum gate because it's a unitary matrix.
If we multiply $P$ by ...
9
votes
1answer
1k views
What is the difference between a qubit and a quantum state?
In general, a qubit is mathematically represented as a quantum state of the form $\lvert \psi\rangle = \alpha \lvert 0\rangle + \beta \lvert 1\rangle$, using the basis $\{ \lvert 0\rangle, \lvert 1\...
3
votes
2answers
151 views
How are EPR Pairs used in quantum computing?
Context
Lately, I have been reading a scholarly paper entitled An Introduction to Quantum Computing for Non-Physicists which discusses the EPR Paradox.
The paper states that:
Einstein, Podolsky ...
13
votes
2answers
2k views
Significance of The Church of the Higher Hilbert space
The term "Church of the Higher Hilbert Space" is used in quantum information frequently when analysing quantum channels and quantum states.
What does this term mean (or, alternately, what does the ...
7
votes
2answers
135 views
What is the difference between superpositions and mixed states?
My understanding so far is: a pure state is a basic state of a system, and a mixed state represents uncertainty about the system, i.e. the system is in one of a set of states with some (classical) ...
6
votes
3answers
225 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 ...
