For questions about quantum channels or more generally quantum maps and the related formalism. For questions about unitary operations, please use quantum-gate instead.
Questions tagged [quantum-operation]
472 questions
10
votes
3 answers
What is the "Stinespring Dilation"?
I've consulted Nielsen and Chuang to understand the Stinespring Dilation, but wasn't able to find anything useful. How does this operation relate to partial trace, Kraus operators, and purification?
Jimit Bavishi
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7
votes
1 answer
What's the difference between Kraus operators and measurement operators?
It is said in a lecture note[1] by John Preskill that,
Equivalently, we may imagine measuring system $B$ in the basis $\{|a\rangle\}$, but failing to record the measurement outcome, so we are forced to average over all the possible post-measurement…
Shuai
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7
votes
0 answers
Rotation resolutions in operations for qubits in commercial implementations
I have found information about Honeywell provider supporting operations with high-resolution rotations (i.e. around $\pi/500$) here.
What are typical maximal rotation resolution values supported by existing implementations and what is their…
Mariusz
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6
votes
2 answers
How to define a quantum channel for the partial trace?
I understand that the partial trace is a linear map, a completely positive map and a trace-preserving map. However, I have no idea how to define a quantum channel with the partial trace because partial trace depends on an index $i$(i.e. $i$ of…
John
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6
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1 answer
Do the eigenvalues of the Choi matrix have any direct physical interpretation?
Let $\Phi\in\mathrm T(\mathcal X,\mathcal Y)$ be a CPTP map, and let $J(\Phi)$ be its Choi representation.
As is well known, any such map can be written in a Kraus representation of the form
$$\Phi(X)=\sum_a p_a A_a X A_a^\dagger,\tag A$$
where…
glS
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6
votes
3 answers
What does the adjoint of a channel represent physically?
Given a quantum channel (CPTP map) $\Phi:\mathcal X\to\mathcal Y$, its adjoint is the CPTP map $\Phi^\dagger:\mathcal Y\to\mathcal X$ such that, for all $X\in\mathcal X$ and $Y\in\mathcal Y$,
$$\langle Y,\Phi(X)\rangle= \langle…
glS
- 24,708
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5
votes
1 answer
How to show there is a channel $\tilde\Lambda$ such that $\tilde\Lambda\circ\Lambda=\Lambda'$ with $\Lambda,\Lambda'$ dephasing channels?
I'm taking a quantum information course and one of my exercises says to find $p,p'$ for which there is a channel $\tilde\Lambda(\Lambda(\rho))=\Lambda'(\rho)$, where $\Lambda$ and $\Lambda'$ are dephasing channels with…
M.B.
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5
votes
2 answers
Validity of quantum channel given pairs of inputs and outputs
Given finitely many pairs of pure states $|x_1\rangle,|y_1\rangle,\ldots,|x_k\rangle,|y_k\rangle\in\mathcal{H}_n$, we can decide if there exists a unitary operator $U$ such that $U|x_i\rangle=|y_i\rangle$ for all $i$ by verifying the…
Wei Zhan
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5
votes
1 answer
Why are quantum channels described by linear maps?
Why should the quantum channels be described by linear maps?
Zubin
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5
votes
0 answers
When can a non-completely-positive evolution of a state be physical?
Definitions: a map $\Phi$ is called positive if $\Phi(\rho)$ is positive semidefinite for any positive semidefinite $\rho$, and completely positive (CP) if $\Phi \otimes \mathrm{Id}$ is a positive map with $\mathrm{Id}$ standing for an identity…
Yack
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4
votes
1 answer
Derive the form of an isometric extension of the erasure channel
Show that an isometric extension of the erasure channel is $$U^N_{A\to BE} =\sqrt{1−\epsilon}\left(|0\rangle_B \langle 0|_A +|1\rangle_B \langle 1|_A \right)\otimes|e\rangle_E+ \sqrt{\epsilon}|e\rangle_B \langle0|_A \otimes |0\rangle_E +…
tattwamasi amrutam
4
votes
2 answers
Image of a sum of positive operators contains the images of each individual operator?
In the proof of Proposition 2.52 of John Watrous' QI book, there is the statement that $\text{im}(\eta(a))\subset\text{im}(\rho)$, where $\rho=\sum_{i=1}^{N}\eta(i)$ is a sum of positive operators and $\rho$ has trace one.
I don't see…
wdc
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4
votes
1 answer
How to characterize the extreme points of the set of CPTP maps?
The set of CPTP maps is convex, therefore, it is enough to perform the needed optimizations over the set of extreme points. Is there any way of characterizing the said extreme points that would lend itself to optimization in general?
As I write…
Cain
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4
votes
2 answers
Are continuous probability distributions over quantum channels possible?
I am not an expert in the subject and apologize in advance for a strange question and (possible) abuse of the terminology.
I have learned that any convex combination of quantum channels (CPTP maps, following another nomenclature) is a quantum…
trurl
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4
votes
1 answer
What is a covariant quantum channel?
A novice to this topic, I am trying to understand the notion of (irreducible) Covariant Quantum Channels. This article provides a definition that is not very "physical".
My question:
What is the intuition behind the notion of covariant quantum…
Zubin
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