Related papers: A universal set of qubit quantum channels
No quantum circuit can turn a completely unknown unitary gate into its coherently controlled version. Yet, coherent control of unknown gates has been realised in experiments, making use of a different type of initial resources. Here, we…
Several techniques of generating random quantum channels, which act on the set of $d$-dimensional quantum states, are investigated. We present three approaches to the problem of sampling of quantum channels and show under which conditions…
The study of quantum channels is the fundamental field and promises wide range of applications, because any physical process can be represented as a quantum channel transforming an initial state into a final state. Inspired by the method…
Two quantum channels are called compatible if they can be obtained as marginals from a single broadcasting channel; otherwise they are incompatible. We derive a characterization of the compatibility relation in terms of concatenation and…
State transformations in quantum mechanics are described by completely positive maps which are constructed from quantum channels. We call a finest sharp quantum channel a context. The result of a measurement depends on the context under…
We introduce a class of quantum channels with correlations acting on pairs of qubits, where the correlation takes the form of a shift operator onto a maximally entangled state. We optimise the output purity and show that below a certain…
To decide whether a quantum channel is degradable is relatively easy: one has to find at least one example of a degrading quantum channel. But in general, no conclusive criterion exists to show the opposite. Using elementary methods we…
We address the problem of optimally approximating the action of a desired and unavailable quantum channel $\Phi $ having at our disposal a single use of a given set of other channels $\{\Psi_i \}$. The problem is recast to look for the…
For a quantum channel (completely positive, trace-preserving map), we prove a generalization to the infinite dimensional case of a result by Baumgartner and Narnhofer. This result is, in a probabilistic language, a decomposition of a…
We introduce the concept of quasi-inverse of quantum and classical channels, prove general properties of these inverses and determine them for a large class of channels acting in an arbitrary finite dimension. Therefore we extend the…
We consider energy-constrained infinite-dimensional quantum channels from a given system (satisfying a certain condition) to any other systems. We show that dealing with basic capacities of these channels we may assume (accepting…
We analyze quantum communication properties of phase-covariant channels depending on their degree of non-unitality. In particular, we derive analytical formulas for minimal and maximal channel fidelity on pure states and maximal output…
We study quantum causal inference in a set-up proposed by Ried et al. [Nat. Phys. 11, 414 (2015)] in which a common-cause scenario can be mixed with a cause-effect scenario, and for which it was found that quantum mechanics can bring an…
In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi-Jamio{\l}kowski state. The second one is based on the relative entropy…
We analyze qubit channels by exploiting the possibility of representing two-level quantum systems in terms of characteristic functions. To do so, we use functions of non-commuting variables (Grassmann variables), defined in terms of…
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…
We present and investigate a new class of quantum channels, what we call `universal collective rotation channels', that includes the well-known class of collective rotation channels as a special case. The fixed point set and noise commutant…
A canonical form for unital qubit channels under local unitary transforms is obtained. In particular, it is shown that the eigenvalues of the Choi matrix of a unital quantum channel form a complete set of invariants of the canonical form.…
We determine the capacity of compound classical-quantum channels. As a consequence we obtain the capacity formula for the averaged classical-quantum channels. The capacity result for compound channels demonstrates, as in the classical…
We first consider various methods for the indirect implementation of unitary gates. We apply these methods to rederive the universality of 4-qubit measurements based on a scheme much simpler than Nielsen's original construction…