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Newest 'quantum-operation' Questions - Quantum Computing Stack Exchange
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Learn more about TeamsQuestions tagged [quantum-operation]
For questions about quantum channels or more generally quantum maps and the related formalism. For questions about unitary operations, please use quantum-gate instead.
548 questions
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Question about tracing out one subsystem when two qubits are entangled
I encountered one question when preparing for the exam.
(b) Suppose each of the qubits of the state $|\phi^+\rangle_{AB}$ undergoes a decoherence process of the form
$$
\rho \mapsto e^{-t} \rho + (1 - ...
3
votes
2
answers
104
views
Logical coset probabilities
Suppose we have an $n$-qubit stabilizer code with the logical state $\rho_L$, which goes through a quantum channel $\mathcal{E}(\rho_L)$. Here, I assume that the quantum channel is arbitrary, for ...
3
votes
2
answers
212
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Tensor submultiplicativity of diamond norm for non-CP maps (w.r.t Wilde's definition)
I am trying to prove the following submultiplicativity property of the diamond norm. Suppose
\begin{align*}
\mathcal{E}_1 : L(H_1) \to L(H_1') \quad \text{and} \quad \mathcal{E}_2 : L(H_2) \to L(H_2')
...
3
votes
2
answers
279
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Quantum Maximum Likelihood Decoding
In quantum maximum likelihood decoding (QMLD), the noise model is assumed to be the Pauli channel (or the depolarizing channel).
Is it possible to perform QMLD with other noise models as well? For ...
1
vote
0
answers
50
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Mutli-qubit depolarizing channel definition
I have seen multiple definitions of the depolaring channel on $N$ qubits :
$\varepsilon(\rho)=(1-p)\rho + \frac{pI}{2^N}Tr(\rho)$
(Depolarizing channel for $n$ qubits: why is there a trace term?)
$\...
4
votes
2
answers
219
views
Looking for a proof of a trace identity and (possibly) relationship to Kraus operators
$\DeclareMathOperator\PSU{PSU}\DeclareMathOperator\U{U}\DeclareMathOperator\SU{SU}\DeclareMathOperator\O{O}\DeclareMathOperator\SO{SO}\DeclareMathOperator\GL{GL}\DeclareMathOperator\ASL{ASL}\...
0
votes
1
answer
63
views
How to calculate the purity of a superoperator?
I know that the purity of a density matrix is calculated as the $tr (\rho^2)$.
Is there anything equivalent for superoperators? And if there are what are some examples where finding the purity of a ...
3
votes
1
answer
402
views
Legal to take inner product between a two-qubit and single-qubit state?
Given a single-qubit state $|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$, is it fine to calculate something like:
$$\langle\Phi^+|\psi\rangle = \frac{1}{\sqrt{2}}(\alpha\langle0| + \beta\langle1|),$$
...
4
votes
1
answer
161
views
Why do we assume a product state in the quantum process formalism?
In the quantum process formalism, we assume that we begin with a product state $$\rho \otimes |e_0\rangle \langle e_0|$$ where $\rho$ is a mixed state in a system of interest and where $|e_0\rangle$ ...
4
votes
1
answer
255
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Kraus operator sum rule for a convex-Gaussian channel
Consider a Gaussian operator$^{1}$ $M=Ce^{i\sum_{n,m=1}^N a^\dagger_n L_{nm} a_m}\equiv e^{ia^\dagger La}$, with $a_n^\dagger,a_n$ fermionic creation and annihilation operators, $C\in\mathbb{C}$, and $...
-3
votes
1
answer
96
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How does measuring one observable or a set of observables affect time complexity? [closed]
Okay, this is going to sound a little unprofessional. I asked ChatGPT if there is a significant difference between measuring a quantum circuit on the same observable or in a set of different ...
2
votes
1
answer
105
views
Is a single entanglement witness always weaker than the same positive map? Or is the adjoint really needed?
tl;dr: It is known that a single entanglement witness derived from a positive map is strictly weaker than the positivity criterion under the adjoint of said map, that is,
$${\rm tr}(\mathsf C(\Lambda_{...
0
votes
0
answers
80
views
Threshold Calculation for Good Quantum LDPC Codes
The threshold for different types of surface codes has been studied under various noise models (see this paper / arXiv and other references obtained by a quick literature search).
I am curious about ...
3
votes
1
answer
103
views
"Twisted" traces of Pauli strings
Consider a system of $L$ qubits. A generic string of Pauli operators acting on such a system can be written as (neglecting phases for simplicity)
$$\mathcal{O}(\vec{v},\vec{w}) = \bigotimes_{j=1}^{L}Z^...
0
votes
1
answer
71
views
Choi state of the completely decohering channel [closed]
Given the completely decohering channel $D\colon \rho \mapsto \sum_i\langle{i}| \rho |i \rangle |i\rangle \langle i |$, the Choi state is $ \sum_{i,j} |i\rangle \langle j | \otimes D(|i\rangle \...
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