Related papers: On equalities in two entropic inequalities

Many important properties of quantum channels are quantified by means of entropic functionals. Characteristics of such a kind are closely related to different representations of a quantum channel. In the Jamio{\l}kowski-Choi representation,…

The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this work, we provide a family of…

In this paper, we consider the minimal entropy of qubit states transmitted through two uses of a noisy quantum channel, which is modeled by the action of a completely positive trace-preserving (or stochastic) map. We provide strong support…

Determining the ultimate classical information carrying capacity of electromagnetic waves requires quantum-mechanical analysis to properly account for the bosonic nature of these waves. Recent work has established capacity theorems for…

The Holevo bound is a bound on the mutual information for a given quantum encoding. In 1996 Schumacher, Westmoreland and Wootters [Schumacher, Westmoreland and Wootters, Phys. Rev. Lett. 76, 3452 (1996)] derived a bound which reduces to the…

We provide lower and upper bounds on the information transmission capacity of one single use of a classical-quantum channel. The lower bound is expressed in terms of the Hoeffding capacity, that we define similarly to the Holevo capacity,…

We determine the p->q norms of the Gaussian one-mode quantum-limited attenuator and amplifier and prove that they are achieved by Gaussian states, extending to noncommutative probability the seminal theorem "Gaussian kernels have only…

We determine both the quantum and the private capacities of low-noise quantum channels to leading orders in the channel's distance to the perfect channel. It has been an open problem for more than 20 years to determine the capacities of…

We obtain continuity bounds for basic information characteristics of quantum channels depending on their input dimension (if it is finite) and on the input energy bound (if the input dimension is infinite). We pay a special attention to the…

The entropy H_T(rho) of a state rho with respect to a channel T and the Holevo capacity of the channel require the solution of difficult variational problems. For a class of 1-qubit channels, which contains all the extremal ones, the…

We characterise Gaussian quantum channels that are Gaussian incompatibility breaking, that is, transform every set of Gaussian measurements into a set obtainable from a joint Gaussian observable via Gaussian postprocessing. Such channels…

Quantum capacity quantifies the amount of quantum information that can be transmitted by a quantum channel with an arbitrary small probability of error. Mathematically, the quantum capacity is given by an asymptotic formula involving the…

The sum-rate capacity of the parallel Gaussian interference channel is shown to be achieved by independent transmission across sub-channels and treating interference as noise in each sub-channel if the channel coefficients and power…

This paper presents self-contained proofs of the strong subadditivity inequality for quantum entropy and some related inequalities for the quantum relative entropy, most notably its convexity and its monotonicity under stochastic maps.…

This paper considers a Gaussian broadcast channel with two unmatched degraded components, three particular messages, and a common message that is intended for all three receivers. It is shown that for this channel superposition coding and…

While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the…

We investigate decoherence induced by a quantum channel in terms of minimal output entropy and of map entropy. The latter is the von Neumann entropy of the Jamiolkowski state of the channel. Both quantities admit q-Renyi versions. We prove…

By carrying out appropriate continuous quantum measurements with a family of projection operators, a unitary channel can be approximated in an arbitrary precision in the trace norm sense. In particular, the quantum Zeno effect is described…

We discuss the entropic criterion for separability of compound quantum systems for general non-additive entropic forms based on arbitrary concave functions $f$. For any separable state, the generalized entropy of the whole system is shown…

We introduce a new incompatibility criterion for quantum channels, based on the notion of (quantum) Fisher information. Our construction is based on a similar criterion for quantum measurements put forward by H.~Zhu. We then study the power…