Related papers: Potential output purity of completely positive map…
Here, we study the capacity of a quantum channel, assuming linear optical encoding, as a function of available photons and optical modes. First, we observe that substantial improvement is made possible by not restricting ourselves to a…
We define here a new kind of quantum channel capacity by extending the concept of zero-error capacity for a noisy quantum channel. The necessary requirement for which a quantum channel has zero-error capacity greater than zero is given.…
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…
Quantum channels describe the most general dynamics of open quantum systems. A quantum channel, as a linear map on vectorized quantum states, can be represented by a single matrix, whose spectrum is called the channel spectrum. Here we…
In this paper, Monge-Kantorovich problem is considered in the infinite dimension on an abstract Wiener space $(W, H,\mu)$, where $H$ is Cameron-Martin space and $\mu$ is the Gaussian measure. We study the regularity of optimal transport…
A linear map between matrix spaces is positive if it maps positive semidefinite matrices to positive semidefinite ones, and is called completely positive if all its ampliations are positive. In this article quantitative bounds on the…
A set of exactly solvable one-dimensional quantum mechanical potentials is described. It is defined by a finite-difference-differential equation generating in the limiting cases the Rosen-Morse, harmonic, and P\"oschl-Teller potentials.…
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…
Non-classical joint measurements can hugely improve the efficiency with which certain figures of merit of quantum systems are measured. We use such a measurement to determine a particular figure of merit, the purity, for a polarization…
An E_0-semigroup is called q-pure if it is a CP-flow and its set of flow subordinates is totally ordered by subordination. The range rank of a positive boundary weight map is the dimension of the range of its dual map. Let K be a separable…
Potentialism is the view that objects are successively generated in an incompletable process. A strict version of the view adds that truths are successively determined. Strict potentialism can be analyzed using two modalities: one for the…
We introduce Partially Coherent Direct Sum (PCDS) quantum channels, as a generalization of the already known Direct Sum quantum channels. We derive necessary and sufficient conditions to identify the subset of those maps which are…
Holevo, Schumacher, and Westmoreland's coding theorem guarantees the existence of codes that are capacity-achieving for the task of sending classical data over a channel with classical inputs and quantum outputs. Although they demonstrated…
Given a large number N of copies of a qubit state of which we wish to estimate its purity, we prove that separable-measurement protocols can be as efficient as the optimal joint-measurement one if classical communication is used. This shows…
Polarization phenomenon over any finite field $\mathbb{F}_{q}$ with size $q$ being a power of a prime is considered. This problem is a generalization of the original proposal of channel polarization by Arikan for the binary field, as well…
Basing on states and channels isomorphism we point out that semidefinite programming can be used as a quick test for nonzero one-way quantum channel capacity. This can be achieved by search of symmetric extensions of states isomorphic to a…
An infinite family of exactly-solvable and integrable potentials on a plane is introduced. It is shown that all already known rational potentials with the above properties allowing separation of variables in polar coordinates are particular…
In a recent paper, Buscemi and al. defined a notion of clean positive operator valued measures (POVMs). We here characterize which POVMs are clean in some class that we call quasi-qubit POVMs, namely POVMs whose elements are all rank-one or…
Optimization methods aimed at estimating the capacities of a general Gaussian channel are developed. Specifically evaluation of classical capacity as maximum of the Holevo information is pursued over all possible Gaussian encodings for the…
Parties connected to independent sources through a network can generate correlations among themselves. Notably, the space of feasible correlations for a given network, depends on the physical nature of the sources and the measurements…