Search Results

Consider a classical channel $N_{X\rightarrow Y}$ which takes every input alphabet $x\in X$ to output alphabet $y\in Y$ with probability $P(y|x)_{Y|X}$. It is stated in many papers that even if the se …

Consider Hilbert spaces $\mathcal{X}, \mathcal{Y}$. For any quantum channel $\mathcal{E}_{\mathcal{X}\rightarrow \mathcal{Y}}$, the bipartite Choi state $J(\mathcal{E}) \in L(\mathcal{Y}\otimes\mathca …

For a quantum channel $\mathcal{E}$, the Choi state is defined by the action of the channel on one half of an unnormalized maximally entangled state as below: $$J(\mathcal{E}) = (\mathcal{E}\otimes I) …

I am given fixed quantum states $\rho_X$ and $\sigma_Y$ and some function of the form $\text{Tr}(N_{X\rightarrow Y}(\rho_X)\sigma_Y)$. I would like to maximize this function over all completely positi …

Suppose I have a pair of bipartite states $\rho_{AR}$ and $\sigma_{BR}$. $R$ is a reference system that we do not have access to. It is clear that we cannot always have a channel $N_{A\rightarrow B}$ …

Consider a $d$-dimensional maximally entangled state $\vert\phi\rangle = \frac{1}{d}\sum_{i=1}^d\vert i\rangle_A\vert i\rangle_B$. Let $N_{A\rightarrow A'}$ be a quantum channel and consider $\rho_{A' …

Updated and edited question: Let $N_{\delta}:P(\mathcal{H}_A)\rightarrow P(\mathcal{H}_B)$ be a completely positive trace nonincreasing map from the set of positive semidefinite operators in $\mathca …

Let $H_A, H_B$ be Hilbert spaces and let a channel $N_{A\rightarrow B}$ be a CPTP map between them. If there exist that unitaries $U\in H_A$ and $U'\in H_B$ such that for all $\rho\in H_A$ $$N(U\rho U …

Suppose Alice and Bob share $n$ copies of a noiseless quantum channel $I_{A\rightarrow B}$ which can be used to send quantum states and $H_A\cong H_B$ i.e. the input and output Hilbert spaces are the …

Let $\mathcal{E}_{A\rightarrow B}$ be a quantum channel and consider its $n-$fold tensor product $\mathcal{E}^{\otimes n}_{A^n\rightarrow B^n}$. Any isometry $V_{A\rightarrow BE}$ that satisfies $\tex …

This isn't strictly a quantum question but the idea of complementary channels is the following: Take any channel $N_{A\rightarrow B}$. Take it's Stinespring dilation (which is an isometry) $V_{A\right …

Given some joint state $\rho_{AB}$, one can find either the marginal state $\rho_A$ or the marginal state $\rho_B$ through a CPTP map. The proof being that partial tracing is indeed CPTP. Is a CPTP ma …

Given an arbitrary state $\rho_{AB}$, is it always possible to construct an extension $\rho_{ABC}$ such that $$Tr_B(\rho_{ABC}) := \rho_{AC} = \rho_{AB} := Tr_C(\rho_{ABC})$$ If yes, does there exist …

Let the stabilized channel fidelity between two channels $M_{A\rightarrow B}$ and $N_{A\rightarrow B}$ be defined as $$F(M,N) = \min\limits_{\vert\psi\rangle_{AR}} F\left((M\otimes I_R)\vert\psi\rangl …

I am interested in a quantum channel from $A^{\otimes n}$ to $B^{\otimes n}$ denoted as $N_{A^{\otimes n} \rightarrow B^{\otimes n}}(\cdot)$. Let $\pi(\cdot)$ be a permutation operation among the $n$ …