Related papers: Axiomatic Approach to Quantum Superchannels
Determining capacities of quantum channels is a fundamental question in quantum information theory. Despite having rigorous coding theorems quantifying the flow of information across quantum channels, their capacities are poorly understood…
We investigate the set of quantum channels acting on a single qubit. We provide an alternative, compact generalization of the Fujiwara-Algoet conditions for complete positivity to non-unital qubit channels, which we then use to characterize…
Unital quantum channels, defined by their property of leaving the maximally mixed state invariant, form an important class of quantum operations. A distinguished subset of these channels can be represented as a probabilistic mixture of…
Recently the theory of communication developed by Shannon has been extended to the quantum realm by exploiting the rules of quantum theory. This latter stems on complex vector spaces. However complex (as well as real) numbers are just…
As the rapidly evolving field of machine learning continues to produce incredibly useful tools and models, the potential for quantum computing to provide speed up for machine learning algorithms is becoming increasingly desirable. In…
Quantum memories can be regarded as quantum channels that transmit information through time without moving it through space. Aiming at a reliable storage of information we may thus not only encode at the beginning and decode at the end, but…
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…
Axiomatic approach to measurement theory is developed. All the possible statistical properties of apparatuses measuring an observable with nondegenerate spectrum allowed in standard quantum mechanics are characterized.
We study completely positive and trace-preserving equivariant maps between operators on irreducible representations of $\mathrm{SU}(2)$. We find asymptotic approximations of channels in the limit of large output representation and we…
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…
To address Quantum Artificial Neural Networks as quantum dynamical computing systems, a formalization of quantum artificial neural networks as dynamical systems is developed, expanding the concept of unitary map to the neural computation…
A quantum channel is a mapping which sends density matrices to density matrices. The estimation of quantum channels is of great importance to the field of quantum information. In this thesis two topics related to estimation of quantum…
The propagation of waves through transmission eigenchannels in complex media is emerging as a new frontier of condensed matter and wave physics. A crucial step towards constructing a complete theory of eigenchannels is to demonstrate their…
We study the super dense coding capacity in the presence of quantum channels with correlated noise. We investigate both the cases of unitary and non-unitary encoding. Pauli channels for arbitrary dimensions are treated explicitly. The super…
Quantum simulation is one of the central discipline to demonstrate the power of quantum computing. In recent years, the theoretical framework of quantum superchannels has been developed and applied widely as the extension of quantum…
The quantum capacity of a quantum channel is always smaller than the capacity of the channel for private communication. However, both quantities are given by the infinite regularization of respectively the coherent and the private…
A linear map $L$ from ${\mathbb C}^{n \times n}$ into ${\mathbb C}^{n \times n}$ is called a quantum channel if it is completely positive and trace preserving. The set ${\cal L}_n$ of all such quantum channels is known to be a compact…
The quantum channel-state duality permits the characterization of a quantum process through a quantum state, referred to as a Choi state. This characteristic serves as the impetus for the quantum computing paradigm that utilizes Choi states…
The more than thirty years old issue of the (classical) information capacity of quantum communication channels was dramatically clarified during the last years, when a number of direct quantum coding theorems was discovered. The present…
At its core, Quantum Mechanics is a theory developed to describe fundamental observations in the spectroscopy of solids and gases. Despite these practical roots, however, quantum theory is infamous for being highly counterintuitive, largely…