a class of stochastic maps, or channels, whose action (when tensored with the identity) on an entangled state always yields a separable state.
Questions tagged [entanglement-breaking-channels]
10 questions
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What channels preserve the purity of all pure inputs?
Consider channels $\Phi$ such that $\Phi(|\psi\rangle\!\langle\psi|)$ is pure for all $|\psi\rangle$. Is there a simple way to characterise channels with this property?
Let's suppose $\Phi$ acts between input and output spaces of the same dimension.…
glS
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Is the square of a separable state again separable?
Famously, a bipartite quantum state $\rho\in\mathbb C^{n\times n}\otimes\mathbb C^{m\times m}$ is defined to be separable if and only if
$$
\rho\in{\rm conv}\{ \omega\otimes\sigma : \omega\in\mathbb C^{n\times n},\sigma\in\mathbb C^{m\times m}\text{…
Frederik vom Ende
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Coherent Information and Entanglement Breaking channels
The book by John Watrous, "The Theory of Quantum Information" is an exciting read for anyone wanting to research quantum information theory. The following question presumes some background covered in the book, which I will do my best to…
K Gautam Shenoy
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How to write the joint action of a CP map that acts on a single qubit of a bipartite state?
The question
Say I have a completely-positive (CP) map $\mathcal{A}_{ij}$ defined in terms of two projectors $\Pi_i = |i\rangle \langle i |$ and $\Pi_j = |j\rangle \langle j |$ that acts on a density operator as:
$$\mathcal{A}_{ij}[\rho] =…
RobMuNu
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How can one check if a given quantum channel is unitary?
A unitary channel is a channel $\mathcal{U}$ of the following form:
$\mathcal{U}(\rho) = U\rho U^{\dagger}$.
A mixed unitary channel is a channel $\mathcal{U}_m$ of the form: $\mathcal{U}_m(\rho) = \sum_{k=1}^n p_kU_k\rho U_k^{\dagger}$, where each…
Hari krishnan S V
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Why are entanglement breaking channels, defined as $\Phi(\rho)=\sum_a \operatorname{Tr}(\mu(a)\rho)\sigma_a$, entanglement breaking?
Define an entanglement breaking channel $\Phi$ as a channel (CPTP map) of the form
$$\Phi(\rho) = \sum_a \operatorname{Tr}(\mu(a)\rho) \sigma_a\tag A$$
for some POVM $\{\mu(a)\}_a$ and states $\sigma_a$.
It is mentioned e.g. in (Horodecki, Shor,…
glS
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Unital qubit channels as a convex combination of entanglement-breaking and unitary channel
I am trying to show that for $T:B(\mathbb{C}^{2})\rightarrow B(\mathbb{C}^{2})$ a unital qubit channel, that T is a convex combination $T=pB+(1-p)Ad_{V}$, where B is a Entanglement-Breaking(EB) channel and $Ad_{V}(X)=VXV^{\dagger}$, for V…
Pink Elephants
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Is there a notion of approximate entanglement breaking (EB) channels?
Is there a notion of approximate entanglement breaking (EB) channels? Say, e.g. the output is always close to a separable state. If so, do the nice properties of the EB channels, such as additive classical capacity, carry over to the approximate…
Shadumu
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Are entanglement breaking channels of any use?
As the name suggests, an entanglement breaking channel $\Phi$ is such that $(Id \otimes \Phi)[\rho]$ is always separable, even when $\rho$ is entangled. Won't such channels be useless, as they destroy entanglement? Does it make sense to say a…
Zubin
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A way to check if entanglement is increased or decreased
I was wondering if there is a way to check if the amount of entanglement is increased or decreased after a quantum operation without calculating the actual value.
That is, it does not concern with the amount of entanglement (i.e., no need for…
KEN
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