Related papers: On strong superadditivity for a class of quantum c…
Given an arbitrary quantum state ($\sigma$), we obtain an explicit construction of a state $\rho^*_\varepsilon(\sigma)$ (resp. $\rho_{*,\varepsilon}(\sigma)$) which has the maximum (resp. minimum) entropy among all states which lie in a…
We consider energy-constrained infinite-dimensional quantum channels from a given system (satisfying a certain condition) to any other systems. We show that dealing with basic capacities of these channels we may assume (accepting…
We introduce an axiomatic approach for channel divergences and channel relative entropies that is based on three information-theoretic axioms of monotonicity under superchannels (i.e. generalized data processing inequality), additivity…
In the study of d-dimensional quantum channels $(d \geq 2)$, an assumption which is not very restrictive, and which has a natural physical interpretation, is that the corresponding Kraus operators form a representation of a Lie algebra.…
Superadditivity effects in the classical capacity of discrete multi-access channels (MACs) and continuous variable (CV) Gaussian MACs are analysed. New examples of the manifestation of superadditivity in the discrete case are provided…
Let $\left(\Omega,\Sigma,p\right)$ be a probability measure space and let $X:\Omega\to{\mathbb{R}}^k$ be a (vector valued) random variable. We suppose that the probability $p_X$ induced by $X$ is absolutely continuous with respect to the…
A problem in quantum information theory that has received considerable attention in recent years is the question of multiplicativity of the so-called maximal output purity (MOP) of a quantum channel. This quantity is defined as the maximum…
In this article, we investigate the additivity phenomenon in the dynamic capacity of a quantum channel for trading classical communication, quantum communication and entanglement. Understanding such additivity property is important if we…
In a recent paper it was shown that all the Hilbert space formulas for quantum probabilities can be realized as functions of geometric properties of the associated projective space, but those functions were expressed using the structures of…
We study encodings that give the best known thresholds for the non-zero capacity of quantum channels, i.e., the upper bound for correctable noise, using an entropic approach to calculation of the threshold values. Our results show that…
The complete positivity vs positivity correspondence in the Choi-Jamio{\l}kowski-Kraus-Sudarshan quantum channel-state isomorphism depends on the choice of basis. Instead of the "canonical" basis, if we use, e.g., the Pauli spin matrices…
We give an elementary self-contained proof that the minimal entropy output of arbitrary products of channels $\rho \mapsto \frac{1}{d-1}(1-\rho^T)$ is additive.
Effective information transmission is a central element in quantum information protocols, but the quest for optimal efficiency in channels with symmetrical characteristics remains a prominent challenge in quantum information science. In…
Let $\Phi$ be a trace-preserving, positivity-preserving (but not necessarily completely positive) linear map on the algebra of complex $2 \times 2$ matrices, and let $\Omega$ be any finite-dimensional completely positive map. For $p=2$ and…
When classical information is sent through a quantum channel of nonorthogonal states, there is a possibility that transmittable classical information exceeds a channel capacity in a single use of the initial channel by extending it into…
Data-processing inequalities capture the phenomenon that two probability distributions can only become less distinguishable under any common post-processing. For more fine-grained inequalities, one turns to strong data-processing inequality…
A special class of quantum channels, named subspace local (SL), are defined and investigated. The proposed definition of subspace locality of quantum channels is an attempt to answer the question of what kind of restriction should be put on…
Understanding quantum channels and the strange behavior of their capacities is a key objective of quantum information theory. Here we study a remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic…
We begin by deriving bounds for the entanglement of a spin with an (adjacent and non-adjacent) interval of spins in an arbitrary pure Finitely Correlated States (FCS). The bounds we derive become exact in the case where one considers the…
In this paper we give several equivalent formulations of the additivity conjecture for constrained channels, which formally is substantially stronger than the unconstrained additivity. To this end a characteristic property of the optimal…