Related papers: A note on quantum expanders
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…
For a noisy quantum channel, a quantum error correcting code exists if and only if the joint higher rank numerical ranges associated with the error operators of the channel is non-empty. In this paper, geometric properties of the joint…
We define a class of "algebraic" random matrix channels for which one can generically compute the limiting Shannon transform using numerical techniques and often enumerate the low SNR series expansion coefficients in closed form. We…
Inevitably, assessing the overall performance of a quantum computer must rely on characterizing some of its elementary constituents and, from this information, formulate a broader statement concerning more complex constructions thereof.…
Degradable quantum channels are an important class of completely positive trace-preserving maps. Among other properties, they offer a single-letter formula for the quantum and the private classical capacity and are characterized by the fact…
Noise is usually regarded as the main obstacle to achieving a scalable quantum advantage, but recent evidence in quantum reservoir computing [L. Domingo, F. Borondo, and G. G. Carlo. Taking advantage of noise in quantum reservoir computing,…
In quantum chaos, the spectral statistics generally follows the predictions of Random Matrix Theory (RMT). A notable exception is given by scar states, that enhance probability density around unstable periodic orbits of the classical…
Compound channel models offer a simple and straightforward way of analyzing the stability of decoder design under model variations. With this work we provide a coding theorem for a large class of practically relevant compound channel…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
We present a pair of heuristic algorithms. The first is to generate a random regular graph of fixed size. The second is the introduction of the Metropolis Coupled Simulated Annealer (MCSA) for optimizing spectral gaps in fixed size regular…
Kernel methods augmented with random features give scalable algorithms for learning from big data. But it has been computationally hard to sample random features according to a probability distribution that is optimized for the data, so as…
The one-shot zero-error classical capacity of a quantum channel is the amount of classical information that can be transmitted with zero probability of error by a single use. Then the one-shot zero-error classical capacity equals to the…
A feasible quantum key distribution (QKD) network scheme has been proposed with the wavelength routing. An apparatus called "quantum router", which is made up of many wavelength division multiplexers, can route the quantum signals without…
We consider quantum systems with a chaotic classical limit that depend on an external parameter, and study correlations between the spectra at different parameter values. In particular, we consider the parametric spectral form factor…
By using the conjugate distribution technique of Cram\'er, we obtain some expansions of large deviation probabilities for martingales with differences satisfying the conditional Bernstein's condition. The expansions are of the same order as…
The use of quantum scissors, as candidates for non-deterministic amplifiers, in continuous-variable quantum key distribution systems is investigated. Such devices rely on single-photon sources for their operation and as such, they do not…
In this work we design a specific simulation tool for quantum channels which is based on the use of a control system. This allows us to simulate an average quantum channel which is expressed in terms of an ensemble of channels, even when…
While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds are not optimized to quantify the performance of quantum codes under the effect of arbitrary…
Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…
Quantum repeaters have promised efficient scaling of quantum networks for over two decades. Despite numerous platforms proclaiming functional repeaters, the realization of large-scale networks remains elusive, indicating that the resources…