Related papers: On the minimum number of unitaries needed to descr…

A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output $p$-norm can be…

We analyze the quantum capacity of a unital quantum channel, using ideas from the proof of near-optimality of Petz recovery map [Barnum and Knill 2000] and give an upper bound on the quantum capacity in terms of regularized output $2$-norm…

We describe here, for the first time, a lower bound on the total number of fundamental constants required for a mathematical description of our physical universe to be complete. The answer is shown to be one. The formal arithmetized…

We present novel bounds on the capacity of the independent and identically distributed binary deletion channel. Four upper bounds are obtained by providing the transmitter and the receiver with genie-aided information on suitably-defined…

For minimum-error channel discrimination tasks that involve only unitary channels, we show that sequential strategies may outperform the parallel ones. Additionally, we show that general strategies that involve indefinite causal order are…

We consider the problem of universal decoding for arbitrary unknown channels in the random coding regime. For a given random coding distribution and a given class of metric decoders, we propose a generic universal decoder whose average…

Given a unitary operator in a finite dimensional complex Hilbert space, its unitary reduction to a subspace is defined. The application to quantum graphs is discussed. It is shown how the reduction allows to generate the scattering matrices…

In the problem of channel resolvability, where a given output probability distribution via a channel is approximated by transforming the uniform random numbers, characterizing the asymptotically minimum rate of the size of the random…

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…

This work contains two main contributions concerning the asymmetric broadcast channel. The first is an analysis of the exact random coding error exponents for both users, and the second is the derivation of universal decoders for both…

We consider the maximum coding rate achievable by uniformly-random codes for the deletion channel. We prove an upper bound that's within 0.1 of the best known lower bounds for all values of the deletion probability $d,$ and much closer for…

Classical capacity of unital qubit channels is well known, whereas that of nonunital qubit channels is not. We find lower and upper bounds on classical capacity of nonunital qubit channels by using a recently developed decomposition…

Estimating the unitarity of an unknown quantum channel $\mathcal{E}$ provides information on how much it is unitary, which is a basic and important problem in quantum device certification and benchmarking. Unitarity estimation can be…

We derive an upper bound for the time needed to implement a generic unitary transformation in a $d$ dimensional quantum system using $d$ control fields. We show that given the ability to control the diagonal elements of the Hamiltonian,…

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 introduce two additive invariants of output quantum channels. If the value of one these invariants is less than 1 then the logarithm of the inverse of its value is a positive lower bound for the regularized minimum entropy of an output…

We investigate the set of quantum channels acting on a single qubit. We provide an alternative, compact generalization of the Fujiwara-Algoet conditions for complete positivity to non-unital qubit channels, which we then use to characterize…

We investigate minimum output (R\'enyi) entropy of qubit channels and unital quantum channels. We obtain an exact formula for the minimum output entropy of qubit channels, and bounds for unital quantum channels. Interestingly, our bounds…

The quantum channel decomposition techniques, which contain the so-called probabilistic error cancellation and gate/wire cutting, are powerful approach for simulating a hard-to-implement (or an ideal) unitary operation by concurrently…

This paper presents an achievability bound that evaluates the exact probability of error of an ensemble of random codes that are decoded by a minimum distance decoder. Compared to the state-of-the-art which demands exponential computation…