Related papers: Minimum output entropy of Gaussian channels
Quantum Gaussian channels play a key role in quantum information theory. In particular, the attenuation and amplification channels are useful to describe noise and decoherence effects on continuous variables systems. They are directly…
We prove that whenever the coherent information of a one-mode Gaussian channel is non-zero its supremum is achieved for the infinite input power. This is a well established fact for the zero added classical noise, whereas the nonzero case…
While the channel capacity reflects a theoretical upper bound on the achievable information transmission rate in the limit of infinitely many bits, it does not characterise the information transfer of a given encoding routine with finitely…
We prove the quantum conditional Entropy Power Inequality for quantum additive noise channels. This inequality lower bounds the quantum conditional entropy of the output of an additive noise channel in terms of the quantum conditional…
We present explicit quantum channels with strictly sub-additive minimum output R\'enyi entropy for all $p>1$, improving upon prior constructions which handled $p>2$. Our example is provided by explicit constructions of linear subspaces with…
For information transmission a discrete time channel with independent additive Gaussian noise is used. There is also feedback channel with independent additive Gaussian noise, and the transmitter observes without delay all outputs of the…
Entropy comparison inequalities are obtained for the differential entropy $h(X+Y)$ of the sum of two independent random vectors $X,Y$, when one is replaced by a Gaussian. For identically distributed random vectors $X,Y$, these are closely…
The full solution of the optimization problem giving the Gaussian capacity of the single-mode fiducial Gaussian quantum channel is provided. Since it was shown that the Gaussian capacity of an arbitrary (phase-sensitive or insensitive)…
Quantum channels can be activated by a kind of channels whose quantum capacity is zero. This activation effect might be useful to overcome noise of channels by attaching other channels which can enhance the capacity of a given channel. In…
We present a constructive example of violation of additivity of minimum output R\'enyi entropy for each p>2. The example is provided by antisymmetric subspace of a suitable dimension. We discuss possibility of extension of the result to go…
The channel output entropy of a transmitted sequence is the entropy of the possible channel outputs and similarly the channel input entropy of a received sequence is the entropy of all possible transmitted sequences. The goal of this work…
Hastings recently provided a proof of the existence of channels which violate the additivity conjecture for minimal output entropy. In this paper we present an expanded version of Hastings' proof. In addition to a careful elucidation of the…
Optical channels, such as fibers or free-space links, are ubiquitous in today's telecommunication networks. They rely on the electromagnetic field associated with photons to carry information from one point to another in space. As a result,…
This paper first focuses on deriving an alternative approach for proving an extremal entropy inequality (EEI), originally presented in [11]. The proposed approach does not rely on the channel enhancement technique, and has the advantage…
We show that the uniform distribution minimizes entropy among all one-dimensional symmetric log-concave distributions with fixed variance, as well as various generalizations of this fact to R\'enyi entropies of orders less than 1 and with…
We study the input-entropy-constrained Gaussian channel capacity problem in the asymptotic high signal-to-noise ratio (SNR) regime. We show that the capacity-achieving distribution as SNR goes to infinity is given by a discrete Gaussian…
We determine the minimum Wehrl entropy among the quantum states with a given von Neumann entropy, and prove that it is achieved by thermal Gaussian states. This result determines the relation between the von Neumann and the Wehrl entropies.…
A longstanding open problem in quantum information theory is to find the classical capacity of an optical communication link, modeled as a Gaussian bosonic channel. It has been conjectured that this capacity is achieved by a random coding…
One of most important issues in quantum information theory concerns transmission of information through noisy quantum channels. We discuss few channel characteristics expressed by means of generalized entropies. Such characteristics can…
We show that under a certain condition of local commutativity the minimum von-Neumann entropy output of a quantum channel is locally additive. We also show that local minima of the 2-norm entropy functions are closed under tensor products…