Related papers: Duality between quantum channels and super-channel…
Quantum coherence quantifies the amount of superposition in a quantum system, and is the reason and resource behind several phenomena and technologies. It depends on the natural basis in which the quantum state of the system is expressed,…
We construct implementations of the PR-box using quantum and classical channels as state spaces. In both cases our constructions are very similar and they share the same idea taken from general probabilistic theories and the square state…
We describe a categorical model of MALL (Multiplicative Additive Linear Logic) inspired by the Heisenberg-Schr\"odinger duality of finite-dimensional quantum theory. Proofs of formulas with positive logical polarity correspond to CPTP…
We show that the basic dynamical rules of quantum physics can be derived from its static properties and the condition that superluminal communication is forbidden. More precisely, the fact that the dynamics has to be described by linear…
We address various aspects of a widely used tool in quantum information theory: the Choi-Jamiolkowski isomorphism [A. Jamiolkowski, Rep. Math. Phys., 3, 275 (1972)]. We review different versions of the isomorphism, their properties and…
Positivity or the stronger notion of complete positivity, and contextuality are central properties of quantum dynamics. In this work, we demonstrate that a physical unitary-universe dilation model could be employed to characterize the…
We formulate a relation between quantum-mechanical coherent states and complex-differentiable structures on the classical phase space ${\cal C}$ of a finite number of degrees of freedom. Locally-defined coherent states parametrised by the…
Using the known possibility to associate the completely positive maps with density matrices and recent results on expressing the density matrices with sets of classical probability distributions of dichotomic random variables we construct…
For many completely positive maps repeated compositions will eventually become entanglement breaking. To quantify this behaviour we develop a technique based on the Schmidt number: If a completely positive map breaks the entanglement with…
In quantum Shannon theory, the way information is encoded and decoded takes advantage of the laws of quantum mechanics, while the way communication channels are interlinked is assumed to be classical. In this Letter we relax the assumption…
We describe the structure of all bijective maps on the cone of positive definite operators acting on a finite and at least two-dimensional complex Hilbert space which preserve the quantum $\chi_\alpha^2$-divergence for some $\alpha \in…
The quantum capacity of bosonic Gaussian quantum channels can be non-additive in a particularly striking way: a pair of such optical-fiber type channels can individually have zero quantum capacity but super-activate each other such that the…
In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi-Jamio{\l}kowski state. The second one is based on the relative entropy…
We prove that any perfect quantum strategy for the two-prover game encoding a constraint satisfaction problem (CSP) can be simulated via a perfect classical strategy with an extra classical communication channel, whose size depends only on…
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…
We study extensions of the mappings arising in usual channel-state duality to the case of Hilbert spaces with a direct sum structure. This setting arises in representations of algebras with centers, which are commonly associated with…
Quantum theory of the free Maxwell field in Minkowski space is constructed using a representation in which the self dual connection is diagonal. Quantum states are now holomorphic functionals of self dual connections and a decomposition of…
We formulate a general theory of wave-particle duality for many-body quantum states, which quantifies how wave- and particle-like properties balance each other. Much as in the well-understood single-particle case, which-way information --…
Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that…
Entanglement-assisted communication over a random-parameter quantum channel with either causal or non-causal channel side information (CSI) at the encoder is considered. This describes a scenario where the quantum channel depends on the…