Related papers: Quantum Sphere-Packing Bounds with Polynomial Pref…
We improve the previously best known upper bounds on the sizes of $\theta$-spherical codes for every $\theta<\theta^*\approx 62.997^{\circ}$ at least by a factor of $0.4325$, in sufficiently high dimensions. Furthermore, for sphere packing…
We study linear codes over Gaussian integers equipped with the Mannheim distance. We develop Mannheim-metric analogues of several classical bounds. We derive an explicit formula for the volume of Mannheim balls, which yields a sphere…
We systematically study the fundamental competition between quantum error correction (QEC) and continuous symmetries, two key notions in quantum information and physics, in a quantitative manner. Three meaningful measures of approximate…
Quantum entanglement can be used in a communication scheme to establish a correlation between successive channel inputs that is impossible by classical means. It is known that the classical capacity of quantum channels can be enhanced by…
Quantum coherence is a fundamental aspect of quantum physics and plays a central role in quantum information science. This essential property of the quantum states could be fragile under the influence of the quantum operations. The extent…
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…
We consider communication scenarios with multiple senders and a single receiver. Focusing on communication tasks where the distinguishability or anti-distinguishability of the sender's input is bounded, we show that quantum strategies…
We derive fundamental lower bounds on the performance of optical metrology and communication systems in a Bayesian framework. The derivation uses classical rate-distortion theory in conjunction with bounds on the capacity to transmit…
We apply the generalized sphere-packing bound to two classes of subblock-constrained codes. A la Fazeli et al. (2015), we made use of automorphism to significantly reduce the number of variables in the associated linear programming problem.…
In this work, we show that the sample complexity required in quantum learning theory within a general parametric framework, is fundamentally governed by the inverse Fisher information matrix. More specifically, we derive upper and lower…
In [1], it is shown that the simultaneous identification capacity region for the discrete, memoryless, classical-quantum multiple access channel is equal to the transmission capacity region for codes using a deterministic encoding scheme.…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…
We derive lower bounds on the maximal rates for multiple packings in high-dimensional Euclidean spaces. Multiple packing is a natural generalization of the sphere packing problem. For any $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $, a multiple…
One of the main limitations of variational quantum algorithms is the classical optimization of the highly dimensional non-convex variational parameter landscape. To simplify this optimization, we can reduce the search space using problem…
Polar codes are the first capacity achieving and efficiently implementable codes for classical communication. Recently they have also been generalized to communication over classical-quantum and quantum channels. In this work we present our…
We study the performance of Decoded Quantum Interferometry (DQI) on typical instances of MAX-$k$-XOR-SAT when the transpose of the constraint matrix is drawn from a standard ensemble of LDPC parity check matrices. We prove that if the…
Identifying the precise moment when a quantum channel undergoes a change is a fundamental problem in quantum information theory. We study how accurately one can determine the time at which a channel transitions to another. We investigate…
We propose a quantum soft-covering problem for a given general quantum channel and one of its output states, which consists in finding the minimum rank of an input state needed to approximate the given channel output. We then prove a…
We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm…
We propose constructive approaches for the optimization of binary classical communication over a general noisy qubit quantum channel, for both the error probability and the classical capacity functionals. After showing that the optimal…