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The amount of information transmissible through a communications channel is determined by the noise characteristics of the channel and by the quantities of available transmission resources. In classical information theory, the amount of…
We prove that a broad array of capacities of a quantum channel are continuous. That is, two channels that are close with respect to the diamond norm have correspondingly similar communication capabilities. We first show that the classical…
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…
We present a constructive example of violation of additivity of minimum output R\'enyi entropy for each p>2. The example is provided by antisymmetric subspace of a suitable dimension. We discuss possibility of extension of the result to go…
The notion of the Holevo capacity for arbitrarily constrained infinite dimensional quantum channels is introduced. It is shown that despite nonexistence of an optimal ensemble in this case it is possible to define the notion of the output…
We present an alternative framework for quantifying the coherence of quantum channels, which contains three conditions: the faithfulness, nonincreasing under sets of all the incoherent superchannels and the additivity. Based on the…
We reformulate the R\'enyi entanglement of purification as a constrained minimum output R\'enyi entropy problem. Equivalently, for $p>1$, this formulation can be expressed in terms of a constrained maximal output Schatten $p$-norm. More…
Recently, the projective robustness of quantum states has been introduced in [arXiv:2109.04481(2021)]. It shows that the projective robustness is a useful resource monotone and can comprehensively characterize capabilities and limitations…
We argue that a fundamental (conjectured) property of memoryless quantum channels, namely the strong superadditivity, is intimately related to the decreasing property of the quantum relative entropy. Using the latter we first give, for a…
One of the fundamental tasks in quantum information processing is to measure the quantum channels. Similar to measurements of quantum states, measurements of quantum channels are inherently stochastic, that is, quantum theory provides a…
The task of determining whether a given quantum channel has positive capacity to transmit quantum information is a fundamental open problem in quantum information theory. In general, the coherent information needs to be computed for an…
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…
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 study the asymptotic behavior of the output states of sequences of quantum channels. Under a natural assumption, we show that the output set converges to a compact convex set, clarifying and substantially generalizing results in [BCN13].…
Recent research has demonstrated significant achievable performance gains by exploiting circularity/non-circularity or propeness/improperness of complex-valued signals. In this paper, we investigate the influence of these properties on…
This was significantly extended from the previous article quant-ph/9705043,especially in an information theoretic aspect, by adding new results.
Let $\Phi$ be a trace-preserving, positivity-preserving (but not necessarily completely positive) linear map on the algebra of complex $2 \times 2$ matrices, and let $\Omega$ be any finite-dimensional completely positive map. For $p=2$ and…
The notion of potential output purity of a completely positive map is introduced as a generalization of the regularized output purity. An upper bound is derived for this quantity, and for several classes of maps (including CQ, QC and…
The capacity of a quantum channel for transmission of classical information depends in principle on whether product states or entangled states are used at the input, and whether product or entangled measurements are used at the output. We…
The capacity of quantum channel with product input states was formulated by the quantum coding theorem. However, whether entangled input states can enhance the quantum channel is still open. It turns out that this problem is reduced to…