Related papers: Quantum incompatibility of channels with general o…
In quantum theory, there exist sets of operations that cannot be performed simultaneously. These sets of operations are referred to as incompatible. While this definition of incompatibility extends to general probabilistic theories (GPTs),…
Two quantum channels are called compatible if they can be obtained as marginals from a single broadcasting channel; otherwise they are incompatible. We derive a characterization of the compatibility relation in terms of concatenation and…
Incompatible quantum channels cannot be jointly and exactly realized, meaning that any approximate joint realization inevitably entails a tradeoff in implementation accuracy. While this notion of channel incompatibility unifies fundamental…
A collection of quantum channels is called incompatible if they cannot be obtained as marginals from a single channel. No-cloning theorem is the most prominent instance of incompatibility of quantum channels. We show that every collection…
A unit-preserving and completely positive linear map, or a channel, $\Lambda \colon \mathcal{A} \to \mathcal{A}_{\mathrm{in}}$ between $C^\ast$-algebras $\mathcal{A}$ and $\mathcal{A}_{\mathrm{in}}$ is called entanglement-breaking (EB) if…
Quantum instruments describe outcome probability as well as state change induced by measurement of a quantum system. Incompatibility of two instruments, i. e. the impossibility to realize them simultaneously on a given quantum system,…
A quantum observable and a channel are considered compatible if they form parts of the same measurement device, otherwise they are incompatible. Constrains on compatibility between observables and channels can be quantified via relations…
In many a traditional physics textbook, a quantum measurement is defined as a projective measurement represented by a Hermitian operator. In quantum information theory, however, the concept of a measurement is dealt with in complete…
Incompatibility of quantum devices is a useful resource in various quantum information theoretical tasks, and it is at the heart of some fundamental features of quantum theory. While the incompatibility of measurements and quantum channels…
One of the basic distinctions between classical and quantum mechanics is the existence of fundamentally incompatible quantities. Such quantities are present on all levels of quantum objects: states, measurements, quantum channels, and even…
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…
Given a set of local dynamics, are they compatible with a global dynamics? We systematically formulate these questions as quantum channel marginal problems. These problems are strongly connected to the generalization of the no-signaling…
Every theory of information, including classical and quantum, can be studied in the framework of operational probabilistic theories--where the notion of test generalizes that of quantum instrument, namely a collection of quantum operations…
Given two quantum channels, we examine the task of determining whether they are compatible - meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting…
Quantum channels represent a broad spectrum of operations crucial to quantum information theory, encompassing everything from the transmission of quantum information to the manipulation of various resources. In the domain of states, the…
The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be…
Surprisingly often decoherence is due to classical fluctuations of ambient fields and may thus be described in terms of random unitary (RU) dynamics. However, there are decoherence channels where such a representation cannot exist. Based on…
Incompatibility of quantum devices is one of the cornerstones of quantum theory, and the incompatibility of quantum measurements and channels has been linked to quantum advantage in certain information theoretic tasks. In this work, we…
Quantum channels describe subsystem or open system evolution. Using the classical Koopman operator that evolves functions on phase space, 4 classical Koopman channels are identified that are analogs of the 4 possible quantum channels in a…
An important distinction in our understanding of capacities of classical versus quantum channels is marked by the following question: is there an algorithm which can compute (or even efficiently compute) the capacity? While there is…