Related papers: Axiomatic Approach to Quantum Superchannels
Divisibility of dynamical maps turns out to be a fundamental notion in characterising Markovianity of quantum evolution, although the decision problem for divisibility itself is computationally intractable. In this work, we propose the…
In this survey article we give basic introduction to the theory of quantum families of maps. We begin with a general look at non-commutative (or "quantum") topology. Then we formulate all our results in this language. Existence of quantum…
Quantum connections are defined by parallel transport operators acting on a Hilbert space. They transport tangent operators along paths in parameter space. The metric tensor of a Riemannian manifold is replaced by an inner product of pairs…
We investigate attractor quantum neural networks (aQNNs) within the framework of coherence theory. We show that: i) aQNNs are associated to non-coherence-generating quantum channels; ii) the depth of the network is given by the decohering…
Entropic quantifiers of states lie at the cornerstone of the quantum information theory. While a quantum state can be abstracted as a device that only has outputs, the most general quantum device is a quantum channel that also has inputs.…
The quantum capacity of a quantum channel captures its capability for noiseless quantum communication. It lies at the heart of quantum information theory. Unfortunately, our poor understanding of nonadditivity of coherent information makes…
Quantum machine learning has shown promise for high-dimensional data analysis, yet many existing approaches rely on linear unitary operations and shared trainable parameters across outputs. These constraints limit expressivity 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…
In a topological space, a family of continuous mappings is called universal if its action, in at least one element of the space, is dense. If the mappings are unitary or trace-preserving completely positive, the notion of universality is…
We define the binding entanglement channel as the quantum channel through which quantum information cannot be reliably transmitted, but which can be used to share bound entanglement. We provide a characterization of such class of channels.…
Quantum capacity, as the ultimate transmission rate of quantum communication, is characterized by regularized coherent information. In this work, we reformulate approximations of the quantum capacity by operator space norms and give both…
Classification, the computational process of categorizing an input into pre-existing classes, is now a cornerstone in modern computation in the era of machine learning. Here we propose a new type of quantum classifier, based on quantum…
The more than thirty years old issue of the information capacity of quantum communication channels was dramatically clarified during the last period, when a number of direct quantum coding theorems was discovered. To considerable extent…
Quantum Cellular Automata are unitary maps that preserve locality and respect causality. We identify them, in any dimension, with simple tensor networks (PEPU) whose bond dimension does not grow with the system size. As a result, they…
Diagrammatic representation and manipulation of tensor networks has proven to be a useful tool in mathematics, physics, and computer science. Here we present several important and mostly well-known theorems regarding the dualities between…
If a quantum channel or process cannot be described by any measure-and-prepare scheme, we may say the channel is in \textit{quantum domain} (QD) since it can transmit quantum correlations. The concept of QD clarifies the role of quantum…
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…
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 find a connection between the existence of a factorization of a quantum channel and the existence of low-rank solutions to certain linear matrix equations. Using this, we show that if a quantum channel is factorized by a direct integral…
Classification of states of quantum channels of information transfer is built on the basis of unreducible representations of qubit state space group of symmetry and properties of density matrix spectrum. It is shown that pure disentangled…