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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 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 present quantum fidelity benchmarks for continuous-variable (CV) quantum devices to outperform quantum channels which can transmit at most $k$-dimensional coherences for positive integers $k$. We determine an upper bound of an average…
With the control of ever more complex quantum systems becoming a reality, new scenarios are emerging where generalizations of the most foundational aspects of statistical quantum mechanics are imperative. In such experimental scenarios the…
The capacity of a channel is known to be equivalent to the highest rate at which it can generate entanglement. Analogous to entanglement, the notion of a causality measure characterises the temporal aspect of quantum correlations. Despite…
Coherent superposition is a key feature of quantum mechanics that underlies the advantage of quantum technologies over their classical counterparts. Recently, coherence has been recast as a resource theory in an attempt to identify and…
The reliability of quantum channels for transmitting information is of profound importance from the perspective of quantum information. This naturally leads to the question as how well a quantum state is preserved when subjected to a…
We investigate the coherence of quantum channels and establish a resource theory for quantifying the coherence of quantum channels via Choi matrix. To this aim, we define the incoherent channels and incoherent superchannels. This theory…
We associate to every quantum channel $T$ acting on a Hilbert space $\mathcal{H}$ a pair of Hamiltonian operators over the symmetric subspace of $\mathcal{H}^{\otimes 2}$. The expectation values of these Hamiltonians over symmetric product…
Inevitably, assessing the overall performance of a quantum computer must rely on characterizing some of its elementary constituents and, from this information, formulate a broader statement concerning more complex constructions thereof.…
We introduce the concepts of cohering and de-cohering power of quantum channels. Using the axiomatic definition of coherence measure, we show that the optimizations required for calculations of these measures can be restricted to pure input…
We obtain continuity bounds for basic information characteristics of quantum channels depending on their input dimension (if it is finite) and on the input energy bound (if the input dimension is infinite). We pay a special attention to the…
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…
The goal of quantum channel discrimination and estimation is to determine the identity of an unknown channel from a discrete or continuous set, respectively. The query complexity of these tasks is equal to the minimum number of times one…
Quantum coherence is a fundamental aspect of quantum physics and plays a central role in quantum information science. This essential property of the quantum states could be fragile under the influence of the quantum operations. The extent…
As a toy model for the capacity problem in quantum information theory we investigate finite and asymptotic regularizations of the maximum pure-state input-output fidelity $F(\cal N$) of a general quantum channel $\cal N$. We show that the…
Sharing entanglement across quantum interconnects is fundamental for quantum information processing. We discuss a practical setting where this interconnect, modeled by a quantum channel, is used once with the aim of sharing high fidelity…
Fundamental limits on communication rates over quantum channels are given by mathematical expressions involving entropic formulas. Often, it is unclear if these expressions are computable. This thesis describes contributions to the study of…
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…
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…