Related papers: Two definitions of the Gell-Mann channels - a comp…
There are contextual sets of multiple qubits whose commutation is parametrized thanks to the coset geometry $\mathcal{G}$ of a subgroup $H$ of the two-generator free group $G=\left\langle x,y\right\rangle$. One defines geometric…
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…
The goal of this paper is to define a notion of non-commutative Gelfand duality. Using techniques from derived algebraic geometry, we show that the category of rings is anti-equivalent to a subcategory of pre-ringed sites, inspired by…
A formal correspondence between the q-distribution obtained from the Tsallis entropy and non-maxwellian distributions obtained from the Boltzmann-Gibbs entropy is afforded.
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),…
We define syntax and semantics of quantum circuits, allowing measurement gates and classical channels. We define circuit-based quantum algorithms and prove that, semantically, any such algorithm is equivalent to a single measurement that…
Entanglement is a key issue in the quantum physics which gives rise to resources for achieving tasks that are not possible within the realm of classical physics. Quantum entanglement varies with the evolution of the quantum systems. It is…
Compatibility conditions of quantum channels featuring symmetry through covariance are studied. Compatibility here means the possibility of obtaining two or more channels through partial trace out of a broadcasting channel. We see that…
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…
Quantum discord, as a measure of all quantum correlations, has been proposed as the key resource in certain quantum communication tasks and quantum computational models without containing much entanglement. Daki\'{c}, Vedral, and Brukner…
The notions of time in the theories of Newton and Einstein are reviewed so that the difficulty which impedes the unification of quantum mechanics (QM) and general relativity (GR) is clarified. It is seen that GR by itself contains an…
Two partial orderings among communication channels, namely, `being degradable into' and `being less noisy than,' are reconsidered in the light of recent results about statistical comparisons of quantum channels. Though our analysis covers…
Space and time are crucial twins in physics. In quantum mechanics, spatial correlations already reveal nonclassical features, such as entanglement, and have bred many quantum technologies. However, the nature of quantum temporal…
Supermaps between quantum channels (completely positive trace-preserving (CPTP) maps of matrix algebras) were introduced in [Chiribella et al., EPL 83(3) (2008)]. In this work we generalise to supermaps between channels of any type; by…
This paper continues the study of stochastic maps, or channels, which break entanglement. We give a detailed description of entanglement-breaking qubit channels, and show that such maps are precisely the convex hull of those known as…
An expression is derived characterizing the set of admissible rate pairs for simultaneous transmission of classical and quantum information over a given quantum channel, generalizing both the classical and quantum capacities of the channel.…
The traditional formalism of non-relativistic quantum theory allows the state of a quantum system to extend across space, but only restricts it to a single instant in time, leading to distinction between theoretical treatments of spatial…
We define and study the properties of channels which are analogous to unital qubit channels in several ways. A full treatment can be given only when the dimension d is a prime power, in which case each of the (d+1) mutually unbiased bases…
The classification of qubit channels is known since 2002. However, that of rebit channels has never been studied so far, maybe because of the scarcity of concrete rebit examples. In this paper we point out that the strategy used to classify…
Equivariant $\Gamma$-spaces model equivariant infinite loop spaces. In this article, we show that there exists a connective Quillen equivalence between the category of equivariant $\Gamma$-spaces and the category of orthogonal spectra.