Related papers: On diagonal quantum channels
One of the most challenging open problems in quantum information theory is to clarify and quantify how entanglement behaves when part of an entangled state is sent through a quantum channel. Of central importance in the description of a…
The study of quantum channels is the fundamental field and promises wide range of applications, because any physical process can be represented as a quantum channel transforming an initial state into a final state. Inspired by the method…
Degradable quantum channels are among the only channels whose quantum and private classical capacities are known. As such, determining the structure of these channels is a pressing open question in quantum information theory. We give a…
The fragile nature of quantum information makes it practically impossible to completely isolate a quantum state from noise under quantum channel transmissions. Quantum networks are complex systems formed by the interconnection of quantum…
Several techniques of generating random quantum channels, which act on the set of $d$-dimensional quantum states, are investigated. We present three approaches to the problem of sampling of quantum channels and show under which conditions…
A completely depolarising quantum channel always outputs a fully mixed state and thus cannot transmit any information. In a recent Letter [D. Ebler et al., Phys. Rev. Lett. 120, 120502 (2018)], it was however shown that if a quantum state…
Quantum channels, which are completely positive and trace preserving mappings, can alter the dimension of a system; e.g., a quantum channel from a qubit to a qutrit. We study the convex set properties of dimension-altering quantum channels,…
This work presents a differentiable geometric parameterization of quantum channels in Kraus representation, which can be efficiently probed to find an unknown quantum channel. We explore its feasibility in finding the quasi inverse…
It is proved that every doubly stochastic quantum channel that is properly averaged with the completely depolarizing channel can be written as a convex combination of unitary channels. As a consequence, we find that the collection of…
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…
We present a complete characterization of diagonal unitary covariant (DU-covariant) superchannels, i.e. higher-order transformations transforming quantum channels into themselves. Necessary and sufficient conditions for complete positivity…
We address the question of the existence of quantum channels that are divisible in two quantum channels but not in three or, more generally, channels divisible in $n$ but not in $n+1$ parts. We show that for the qubit those channels…
Channel-state duality is a central result in quantum information science. It refers to the correspondence between a dynamical process (quantum channel) and a static quantum state in an enlarged Hilbert space. Since the corresponding dual…
We study the problem of approximating a quantum channel by one with as few Kraus operators as possible (in the sense that, for any input state, the output states of the two channels should be close to one another). Our main result is that…
The group symmetries inherent in quantum channels often make them tractable and applicable to various problems in quantum information theory. In this paper, we introduce natural probability distributions for covariant quantum channels.…
In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and…
Operator-sum representations of quantum channels can be obtained by applying the channel to one subsystem of a maximally entangled state and deploying the channel-state isomorphism. However, for continuous-variable systems, such schemes…
We consider a quantum channel acting on an infinite dimensional von Neumann algebra of operators on a separable Hilbert space. When there exists an invariant normal faithful state, the cyclic properties of such channels are investigated…
Quantum process tomography, the standard procedure to characterize any quantum channel in nature, is affected by a circular argument: in order to characterize the channel, the tomographic preparation and measurement need in turn to be…
Let $K$ be a convex subset of the state space of a finite dimensional $C^*$-algebra. We study the properties of channels on $K$, which are defined as affine maps from $K$ into the state space of another algebra, extending to completely…