Related papers: Continuous-Variable Quantum MacWilliams Identities
The properties of quantum mechanics with a discrete phase space are studied. The minimum uncertainty states are found, and these states become the Gaussian wave packets in the continuum limit. With a suitably chosen Hamiltonian that gives…
A quantum code is a subspace of a Hilbert space of a physical system chosen to be correctable against a given class of errors, where information can be encoded. Ideally, the quantum code lies within the ground space of the physical system.…
We develop a duality theory of locally recoverable codes (LRCs) and apply it to establish a series of new bounds on their parameters. We introduce and study a refined notion of weight distribution that captures the code's locality. Using a…
This work develops new foundations for the theory of linear codes over local Artinian commutative rings. We use algebraic invariants such as the socle, type, length, and minimal number of generators to measure the size of codes. We prove a…
We investigate quantum error correction using continuous parity measurements to correct bit-flip errors with the three-qubit code. Continuous monitoring of errors brings the benefit of a continuous stream of information, which facilitates…
The quantum analogues of classical variable-length codes are indeterminate-length quantum codes, in which codewords may exist in superpositions of different lengths. This paper explores some of their properties. The length observable for…
Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These…
This paper investigates the relationship between the rank weight distribution of a linear code and that of its dual code. The main result of this paper is that, similar to the MacWilliams identity for the Hamming metric, the rank weight…
We consider energy-constrained infinite-dimensional quantum channels from a given system (satisfying a certain condition) to any other systems. We show that dealing with basic capacities of these channels we may assume (accepting…
Continuous-time quantum walks (CTQWs) provide a valuable model for quantum transport, universal quantum computation and quantum spatial search, among others. Recently, the empowering role of new degrees of freedom in the Hamiltonian…
Bosonic codes offer noise resilience for quantum information processing. Good performance often comes at a price of complex decoding schemes, limiting their practicality. Here, we propose using a Gottesman-Kitaev-Preskill (GKP) code to…
Stable quantum computation requires noisy results to remain bounded even in the presence of noise fluctuations. Yet non-stationary noise processes lead to drift in the varying characteristics of a quantum device that can greatly influence…
We investigate multi-mode GKP (Gottesman--Kitaev--Preskill) quantum error-correcting codes from a geometric perspective. First, we construct their moduli space as a quotient of groups and exhibit it as a fiber bundle over the moduli space…
The two-way capacities of quantum channels determine the ultimate entanglement and secret-key distribution rates achievable by two distant parties that are connected by a noisy transmission line, in absence of quantum repeaters. Since…
A generalization of the stabilizer code construction presented by Gottesman is described, which allows for the construction of quantum error-correcting codes for continuous-variable systems. This formalism describes all continuous-variable…
A hybrid code can simultaneously encode classical and quantum information into quantum digits such that the information is protected against errors when transmitted through a quantum channel. It is shown that a hybrid code has the…
Continuous-variable quantum key distribution (CV-QKD) enables two remote parties to establish information-theoretically secure keys and offers high practical feasibility due to its compatibility with mature coherent optical communication…
Many of the classic problems of coding theory are highly symmetric, which makes it easy to derive sphere-packing upper bounds and sphere-covering lower bounds on the size of codes. We discuss the generalizations of sphere-packing and…
Bounds on linear codes play a central role in coding theory, as they capture the fundamental trade-off between error-correction capability (minimum distance) and information rate (dimension relative to length). Classical results…
The sphere packing problem asks for the greatest density of a packing of congruent balls in Euclidean space. The current best upper bound in all sufficiently high dimensions is due to Kabatiansky and Levenshtein in 1978. We revisit their…