Related papers: Multiplicativity of completely bounded p-norms imp…

Let $p$ be a prime, let $S$ be a non-empty subset of $\mathbb{F}_p$ and let $0<\epsilon\leq 1$. We show that there exists a constant $C=C(p, \epsilon)$ such that for every positive integer $k$, whenever $\phi_1, \dots, \phi_k:…

The entropy of a quantum operation, defined as the von Neumann entropy of the corresponding Choi-Jamio{\l}kowski state, characterizes the coupling of the principal system with the environment. For any quantum channel $\Phi$ acting on a…

We show that for the standard map family, for all values of the parameter, except one, the mapping has positive topological entropy. The main tool is the following result. Let $S$ be a compact connected orientable surface and $f:S…

We investigate the possibility of dividing quantum channels into concatenations of other channels, thereby studying the semigroup structure of the set of completely-positive trace-preserving maps. We show the existence of 'indivisible'…

This paper is motivated by the problem of error control in network coding when errors are introduced in a random fashion (rather than chosen by an adversary). An additive-multiplicative matrix channel is considered as a model for random…

We show that a positive linear map preserves local continuity (convergence) of the entropy if and only if it preserves finiteness of the entropy, i.e. transforms operators with finite entropy to operators with finite entropy. The last…

Some new examples of quantum channels for which the infimum of the output entropy is additive under taking a tensor product of channels are given.

For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on…

Using limit linear series and a result controlling degeneration from separable maps to inseparable maps, we give a formula for the number of self-maps of the projective line with ramification to order e_i at general points P_i, in the case…

Quantum ergodicity asserts that almost all infinite sequences of eigenstates of a quantized ergodic system are equidistributed in the phase space. On the other hand, there are might exist exceptional sequences which converge to different…

Quantum channels, also called quantum operations, are linear, trace preserving and completely positive transformations in the space of quantum states. Such operations describe discrete time evolution of an open quantum system interacting…

Hastings disproved additivity conjecture for minimum output entropy by using random unitary channels. In this note, we employ his approach to show that minimum output $p-$R\'{e}nyi entropy is non-additive for $p\in(0,p_0)\cup(1-p_0,1)$…

We study binary discrimination of idempotent quantum channels. When the two channels share a common full-rank invariant state, we show that a simple image inclusion condition completely determines the asymptotic behavior: when it holds, a…

Let $\mathcal{P}_G$ be the family of all topologically mixing, but not exact self-maps of a topological graph $G$. It is proved that the infimum of topological entropies of maps from $\mathcal{P}_G$ is bounded from below by $(\log 3/…

Completely positive trace-preserving maps $S$, also known as quantum channels, arise in quantum physics as a description of how the density operator $\rho$ of a system changes in a given time interval, allowing not only for unitary…

Let $\Gamma \curvearrowright \Omega$ be a measure-preserving action and $\mathcal{L} \Gamma \hookrightarrow L^\infty(\Omega) \rtimes \Gamma$ the natural inclusion of the group von Neumann algebra into the crossed product. When $\mu(\Omega)…

We give a simple and conceptual proof of the fact that random unitary channels yield violation of the Minimum Output Entropy additivity. The proof relies on strong convergence of random unitary matrices and Haagerup's inequality.

We investigate models of nonlinear quantum computation based on deterministic positive trace-preserving (PTP) channels and evolution equations. The models are defined in any finite Hilbert space, but the main results are for dimension $N \!…

We derive the monotonicity of the quantum relative entropy by an elementary operational argument based on Stein's lemma in quantum hypothesis testing. For the latter we present an elementary and short proof that requires the law of large…

It is conjectured that the Holevo capacity of a product channel \Omega \otimes \Phi is achieved when product states are used as input. Amosov, Holevo and Werner have also conjectured that the maximal p-norm of a product channel is achieved…