Related papers: Potential output purity of completely positive map…
We consider generalizations of depolarizing channels to maps in which the identity channel is replaced by a convex combinations of unitary conjugations. We show that one can construct unital channels of this type for which the input which…
A problem in quantum information theory that has received considerable attention in recent years is the question of multiplicativity of the so-called maximal output purity (MOP) of a quantum channel. This quantity is defined as the maximum…
We introduce potential capacities of quantum channels in an operational way and provide upper bounds for these quantities, which quantify the ultimate limit of usefulness of a channel for a given task in the best possible context.…
Purification is a process in which decoherence is partially reversed by using several input systems which have been subject to the same noise. The purity of the outputs generally increases with the number of input systems, and decreases…
In this work we examine quantum states which have non-negative amplitudes (in a fixed basis) and the channels which preserve them. These states include the ground states of stoquastic Hamiltonians and they are of interest since they avoid…
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…
We present a method for the determination of the completely positive (CP) map describing a physical device based on random preparation of the input states, random measurements at the output, and maximum-likelihood principle. In the…
A conjecture arising naturally in the investigation of additivity of classical information capacity of quantum channels states that the maximal purity of outputs from a quantum channel, as measured by the p-norm, should be multiplicative…
We explore complementarity between output and environment of a quantum channel (or, more generally, CP map), making an observation that the output purity characteristics for complementary CP maps coincide. Hence, validity of the…
We analyze the quantum capacity of a unital quantum channel, using ideas from the proof of near-optimality of Petz recovery map [Barnum and Knill 2000] and give an upper bound on the quantum capacity in terms of regularized output $2$-norm…
Let $\Phi$ be a trace-preserving, positivity-preserving (but not necessarily completely positive) linear map on the algebra of complex $2 \times 2$ matrices, and let $\Omega$ be any finite-dimensional completely positive map. For $p=2$ and…
The quantum capacity of a memoryless channel is often used as a single figure of merit to characterize its ability to transmit quantum information coherently. The capacity determines the maximal rate at which we can code reliably over…
The qubit depolarizing channel with noise parameter $\eta$ transmits an input qubit perfectly with probability $1-\eta$, and outputs the completely mixed state with probability $\eta$. We show that its complementary channel has positive…
Degradable quantum channels are an important class of completely positive trace-preserving maps. Among other properties, they offer a single-letter formula for the quantum and the private classical capacity and are characterized by the fact…
Evaluating the channel capacity is one of many key problems in information theory. In this work we derive rather-mild sufficient conditions under which the capacity is finite and achievable. These conditions are derived for generic,…
Quantum supermaps are a higher-order generalization of quantum maps, taking quantum maps to quantum maps. It is known that any completely positive, trace non-increasing (CPTNI) map can be performed as part of a quantum measurement. By…
A pair of quantum channels are said to be incompatible if they cannot be realized as marginals of a single channel. This paper addresses the general structure of the incompatibility of completely positive channels with a fixed quantum input…
Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum…
A generalized channel is a completely positive map that preserves trace on a given subspace. We find conditions under which a generalized channel with respect to a positively generated subspace J is an extreme point in the set of all such…
One of the fundamental tasks in quantum information processing is to measure the quantum channels. Similar to measurements of quantum states, measurements of quantum channels are inherently stochastic, that is, quantum theory provides a…