Questions tagged [quantum-channel]
In quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information. An example of quantum information is the state of a qubit. An example of classical information is a text document transmitted over the Internet. More formally, quantum channels are completely positive (CP) trace-preserving maps between spaces of operators. If appropriate, also use the [quantum-operation] tag.
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Real-life examples of classical-quantum channels
In quantum information theory, classical-quantum channels are considered to be channels whose input is the realizations $x\in\mathcal{X}$ of a classical random variable to a quantum state $\rho_x^B$, ...
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Kraus operators from POVM matrices
Is there a way to find Kraus operators if I know POVM matrices? For a simple example, how would you find the Kraus operators if the POVM matrices are the following:
\begin{bmatrix}
\frac{1}{2} &...
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Depolarizing channel operator sum representation
In Nielsen and Chuang, it is shown that the operator sum representation of a depolarizing channel $\mathcal{E}(\rho) = \frac{pI}{2} + (1-p)\rho$ is easily seen by substituting the identity matrix with
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How many Kraus operators are required to characterise a channel with different start and end dimensions?
If we have a quantum channel mapping from a $d$-dimensional state to a $d$-dimensional state, it can be described by at most $d^2$ Kraus operators. Suppose our channel maps instead from a $d_1$-...
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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 ...
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Isometric Extension of an 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\...
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1answer
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Confusion on the definition of the phase-damping channel
I am reading about the phase damping channel, and I have seen that some of the different references talking about such channel give different definitions of the Kraus operators that define the action ...
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Quantum channel Holevo information additivity: proof approach
I have an interesting idea for a proof approach that someone might find useful. Here it is.
Suppose we are given a quantum qubit channel $N$ (for example the amplitude damping channel) whose Holevo ...
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Three sender quantum simultaneous decoder conjecture
Recently I have started to read about network quantum information theory, where network problems are studied under the classical-quantum channel. For example, capacities of the cq-MAC, cq-broadcast or ...
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1answer
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Kraus operator of dephasing channel
I'm trying to deduce the Kraus representation of the dephasing channel using the Choi operator (I know the Kraus operators can be guessed in this case, I want to understand the general case).
The ...
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1answer
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Depolarizing channel implementation on IBM Q
Given a single qubit in the computational basis, $|\psi\rangle =\alpha |0\rangle + \beta|1\rangle$, the density matrix is $\rho=|\psi\rangle\langle\psi|=\begin{pmatrix} \alpha^2 & \alpha \beta^*\\
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Advances in Quantum Channel Capacity
I have been reading about the Quantum Channel Capacity and it seems to be an open problem to find such capacity in general. Quantum capacity is the highest rate at which quantum information can be ...
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Tensor product properties used to obtain Kraus operator decomposition of a channel
I work on a Quantum Information Science II: Quantum states, noise and error correction MOOC by Prof. Aram Harrow, and I do not understand which property of tensor products is used in one of the ...
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How to find the fidelity between two state when one is an operator?
I am going through Nielsen and Chuang and am finding the chapter on error-correction particularly confusing. At the moment I am stuck on exercise 10.12 which states
Show that the fidelity between the ...
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1answer
162 views
Quantum Channel Models
The so called depolarizing channel is the channel model that is mostly used when constructing quantum error correction codes. The action of such channel over a quantum state $\rho$ is
$\rho\...
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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 ...
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1answer
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Two notions of General Quantum Operators?
I understand that there are two ways to think about 'general quantum operators'.
Way 1
We can think of them as trace-preserving completely positive operators. These can be written in the form
$$\...
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2answers
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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 ...
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What is the difference between signaling and non-signaling quantum correlations, and what is a signaling channel?
This article talks about correlation and causality in quantum mechanics. In the abstract, under Framework for local quantum mechanics, it says (emphasis mine):
The most studied, almost epitomical, ...
