Related papers: Sphere-Packing Bound for Symmetric Classical-Quant…
A classical coding across a block of logical qubits is presented. We characterize subgroups of the product stabilizer group on a block of logical qubits corresponding to dual codes of classical error correcting codes. We prove conditions on…
A sphere is a fundamental geometric object widely used in (computer aided) geometric design. It possesses rational parameterizations but no parametric polynomial parameterization exists. The present study provides an approach to the optimal…
We consider a setting where a stream of qubits is processed sequentially. We derive fundamental limits on the rate at which classical information can be transmitted using qubits that decohere as they wait to be processed. Specifically, we…
We prove that the classical capacity of an arbitrary quantum channel assisted by a free classical feedback channel is bounded from above by the maximum average output entropy of the quantum channel. As a consequence of this bound, we…
Bi-quadratic programming over unit spheres is a fundamental problem in quantum mechanics introduced by pioneer work of Einstein, Schr\"odinger, and others. It has been shown to be NP-hard; so it must be solve by efficient heuristic…
The study on the relationship between the spheres and voids in packing system suggests that the edge effect at the interface between the container and the particles is an important factor lowering the packing ratio. To pack spheres in a…
We study perfect codes in the sum-rank metric, a generalization of both the Hamming and rank metrics relevant in multishot network coding and space-time coding. A perfect code attains equality in the sphere-packing bound, corresponding to a…
The quantum channel capacity gives the ultimate limit for the rate at which quantum data can be reliably transmitted through a noisy quantum channel. Degradable quantum channels are among the few channels whose quantum capacities are known.…
We establish the classical capacity of optical quantum channels as a sharp transition between two regimes---one which is an error-free regime for communication rates below the capacity, and the other in which the probability of correctly…
How well can we approximate a quantum channel output state using a random codebook with a certain size? In this work, we study the quantum soft covering problem. Namely, we use a random codebook with codewords independently sampled from a…
We study the problem of decoding classical information encoded on quantum states at the output of a quantum channel, with particular focus on increasing the communication rates towards the maximum allowed by Quantum Mechanics. After a brief…
Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been…
We propose an iterative method for approximating the capacity of classical-quantum channels with a discrete input alphabet and a finite dimensional output, possibly under additional constraints on the input distribution. Based on duality of…
In our previous work, we presented a Blahut-Arimoto type algorithm for computing the discrete memoryless (DM) classical-quantum channel capacity. And the speed of convergence is analyzed. In this paper, we present numerical experiment to…
We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds…
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…
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…
This paper establishes the exact strong converse exponent of the soft covering problem in the classical setting. This exponent characterizes the slowest achievable convergence speed of the total variation to one when a code of rate below…
flip is an extremely simple and maximally local classical decoder which has been used to great effect in certain classes of classical codes. When applied to quantum codes there exist constant-weight errors (such as half of a stabiliser)…
We revisit the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $. A multiple packing is a set…