Related papers: Random covariant quantum channels
The data processing inequality is the most basic requirement for any meaningful measure of information. It essentially states that distinguishability measures between states decrease if we apply a quantum channel and is the centerpiece of…
The well-known duality relating entangled states and noisy quantum channels is expressed in terms of a channel ket, a pure state on a suitable tripartite system, which functions as a pre-probability allowing the calculation of statistical…
We investigate unitary operators acting on a tensor product space, with the property that the quantum channels they generate, via the Stinespring dilation theorem, are of a particular type, independently of the state of the ancilla system…
Just a few years after the inception of quantum mechanics, there has been a research program using the nonclassical values of some quasiprobability distributions to delineate the nonclassical aspects of quantum phenomena. In particular, in…
In this work we improve the quantum communication rates of various quantum channels of interest using permutation-invariant quantum codes. We focus in particular on parametrized families of quantum channels and aim to improve bounds on…
We develop the theory of quantum (a.k.a. noncommutative) relations and quantum (a.k.a. noncommutative) graphs in the finite-dimensional covariant setting, where all systems (finite-dimensional $C^*$-algebras) carry an action of a compact…
We study a class of quantum channels arising from the representation theory of compact quantum groups that we call Temperley-Lieb quantum channels. These channels simultaneously extend those introduced in [BC18], [AN14], and [LS14].…
Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements.…
We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the…
We analyze the ergodic properties of quantum channels that are covariant with respect to diagonal orthogonal transformations. We prove that the ergodic behaviour of a channel in this class is essentially governed by a classical stochastic…
Probabilistic quantum filtering is proposed to properly adapt sequential independent quantum channels in order to stop sudden death of entanglement. In the adaptation, the quantum filtering does not distill or purify more entanglement, it…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…
The classical randomization criterion is an important result of statistical decision theory. Recently, a quantum analogue has been proposed, giving equivalent conditions for two sets of quantum states, ensuring existence of a quantum…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
Using well known duality between quantum maps and states of composite systems we introduce the notion of Schmidt number of a quantum channel. It enables one to define classes of quantum channels which partially break quantum entanglement.…
Quantum channel, as the information transmitter, is an indispensable tool in quantum information theory. In this paper, we study a class of special quantum channels named the mixed-permutation channels. The properties of these channels are…
Shared entanglement is a resource available to parties communicating over a quantum channel, much akin to public coins in classical communication protocols. Whereas shared randomness does not help in the transmission of information, or…
Capacities of quantum channels and decoherence times both quantify the extent to which quantum information can withstand degradation by interactions with its environment. However, calculating capacities directly is known to be intractable…
The set of doubly-stochastic quantum channels and its subset of mixtures of unitaries are investigated. We provide a detailed analysis of their structure together with computable criteria for the separation of the two sets. When applied to…
We study relaxations of entanglement-assisted quantum channel coding and establish that non-signaling assistance and a natural semi-definite programming relaxation\, -- \,termed meta-converse\, -- \,are equivalent in terms of success…