Linked Questions

As was already asked about in this phys.SE question many years ago—which, sadly, got closed and never received an answer—is there a collection of counterexamples in quantum information theory, "...

In addition to the Kraus operator and Choi matrix, the Pauli transfer matrix (PTM) is another useful representation of a quantum map, its matrix entries are $(R)_{ij}=\frac{1}{d}tr\{P_i\Lambda(P_j)\}$,...

Obviously, positive semi-definite operators always admit a positive trace as ${\rm tr}(A)=\|A\|_1\geq 0$ whenever $A\geq 0$. This motivates the following "lifted" question: Given any ...

I am working on a project and I expect to have expressions of a bunch of quantum channels of interest. The quantum channels will be in matrix form. For example for a 2 qubit system, the quantum ...

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) ...

Let $\mathcal{X} \in {\rm CP}(\mathcal{H}, \mathcal{K})$ and unital (completely positive and unital maps). Let $\mathcal{Y} \in {\rm CPT}(\mathcal{H}, \mathcal{K})$ (completely positive and trace ...

Recalling the spectral radius $r(T):=\max_{\lambda\in\sigma(T)}|\lambda|$ of a linear map $T$ (where $\sigma(T)$ refers to the spectrum of $T$), it is known that every quantum channel $\Phi:\mathbb C^{...

Let $\rho, \sigma$ be two states of a qubit, and let $U$ be the $CX_{12}$-gate (control on 1st qubit, target on 2nd qubit). Prove that, for an arbitrary CPTP Map $\mathcal{E}$, $$ \|\mathcal{E}(\rho - ...

When asking whether every channel is covariant with respect to some non-trivial unitary channel I mean the following: Does there for every CPTP map $\Phi:\mathbb C^{n\times n}\to\mathbb C^{n\times n}$...

I was wondering if anyone knows about any good resources on representing unital/quantum channels by using rotations/pauli matrices. It is mentioned in Nielsen&Chuang on p774, but i feel it is ...