Related papers: A Blahut-Arimoto Type Algorithm for Computing Clas…
We give a technique to reduce the error probability of quantum algorithms that determine whether its input has a specified property of interest. The standard process of reducing this error is statistical processing of the results of…
Using quantum algorithms, we obtain, for accuracy $\epsilon>0$ and confidence $1-\delta,0<\delta<1,$ a new sample complexity upper bound of $O((\mbox{log}(\frac{1}{\delta}))/\epsilon)$ as $\epsilon,\delta\rightarrow 0$ for a general…
This paper provides new insight into the classical problem of determining both the capacity of the discrete-time channel with uniform output quantization and the capacity achieving input distribution. It builds on earlier work by Gallager…
We consider some classical and quantum approximate optimization algorithms with bounded depth. First, we define a class of "local" classical optimization algorithms and show that a single step version of these algorithms can achieve the…
We derive a new Sequential-Monte-Carlo-based algorithm to estimate the capacity of two-dimensional channel models. The focus is on computing the noiseless capacity of the 2-D one-infinity run-length limited constrained channel, but the…
Quantum channel discrimination has been studied from an information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of unknown channel accesses. In this paper, we…
Quantum queue-channels arise naturally in the context of buffering in quantum networks, wherein the noise suffered by the quantum states depends on the time spent waiting in the buffer. It has been shown that the upper-bound on the…
The set of Multi-level Amplitude Damping (MAD) quantum channels is introduced as a generalization of the standard qubit Amplitude Damping Channel to quantum systems of finite dimension $d$. In the special case of $d=3$, by exploiting…
We study the one-shot zero-error classical capacity of a quantum channel assisted by quantum no-signalling correlations, and the reverse problem of exact simulation of a prescribed channel by a noiseless classical one. Quantum no-signalling…
The capacity of a channel can usually be characterized as a maximization of certain entropic quantities. From a practical point of view it is of primary interest to not only compute the capacity value, but also to find the corresponding…
We investigate the capacity of three symmetric quantum states in three real dimensions to carry classical information. Several such capacities have already been defined, depending on what operations are allowed in the sending and receiving…
Standard quantum amplitude estimation algorithms provide quadratic speedup to Monte-Carlo simulations but require a circuit depth that scales as inverse of the estimation error. In view of the shallow depth in near-term devices, the…
Transmission of classical information using quantum objects such as polarized photons is studied. The classical (Shannon) channel capacity and its relation to quantum (von Neumann) channel capacity is investigated for various receiver…
We study the quantum umlaut information, a correlation measure defined for bipartite quantum states $\rho_{AB}$ as a reversed variant of the quantum mutual information: $U(A;B)_\rho = \min_{\sigma_B} D(\rho_A\otimes \sigma_B\|\rho_{AB})$ in…
We study information transmission over a fully correlated amplitude damping channel acting on two qubits. We derive the single-shot classical channel capacity and show that entanglement is needed to achieve the channel best performance. We…
Matrix scaling and matrix balancing are two basic linear-algebraic problems with a wide variety of applications, such as approximating the permanent, and pre-conditioning linear systems to make them more numerically stable. We study the…
We study commitment scheme for classical-quantum channels. To accomplish this we define various notions of commitment capacity for these channels and prove matching upper and lower bound on it in terms of the conditional entropy. Our…
Arnoldi method and conjugate gradient method are important classical iteration methods in solving linear systems and estimating eigenvalues. Their efficiency often affected by the high dimension of the space, where quantum computer can play…
The zero-error classical capacity of a quantum channel is the asymptotic rate at which it can be used to send classical bits perfectly, so that they can be decoded with zero probability of error. We show that there exist pairs of quantum…
We calculate the quantum capacity of an amplitude-damping channel with time correlated Markov noise, for two channel uses. Our results show that memory of the channel increases it's ability to transmit quantum information significantly. We…