Aug 2026· 2 citations· ⚡ 1 influential· 41 references
Computer ScienceMathematicsPhysics
Abstract
In this work, we define entanglement-assisted quantum locally recoverable codes with availability, in which any set of up to $\delta-1$ erased qudits can be recovered from any one of $t$ local recovery sets, each of size at most $r+\delta-1$, with the recovery sets intersecting exactly in the erased coordinates, where $r$ is a (small) positive integer. We show that shared entanglement permits $t>1$, meaning that multiple local recovery sets can be available for the same set of up to $\delta-1$ erasures. We establish a Singleton-like bound for this family of codes and present random constructions based on classical linear codes with Vandermonde parity-check matrices. We also provide explicit constructions of entanglement-assisted quantum locally recoverable codes with availability from several classical code families and their folded versions, including Tamo-Barg codes, fiber-product codes, and algebraic-geometry codes such as one-point Hermitian and Suzuki codes.
Quantum $(r,\delta)$-locally recoverable codes are quantum error-correcting codes capable of correcting $\delta-1$ qudit erasures within one subset of qudits of cardinality at most $r+\delta-1$. In this paper, we introduce the more general framework of entanglement-assisted quantum $(r,\delta)$-locally recoverable code...
Carlos Galindo, F. Hernando, Helena Martín-Cruz et al.· 0 citations
A quantum $(r,\rho)$-locally recoverable code ($(r,\rho)$-qLRC) is a quantum code in which every qudit can be recovered from at most $r+\rho-1$ other qudits, even after $\rho-1$ additional erasures inside the recovery set. The bounds currently known for this class, namely the Singleton-like and the GG Singleton-like bo...
Quantum locally recoverable codes (qLRCs), introduced recently by Golowich and Guruswami, allow any single-qudit erasure to be recovered from a small set of other qudits. Most known constructions require a large alphabet. We systematically investigate qLRCs obtained, via the CSS construction, from classical constacycli...
Locally recoverable codes (LRCs) combine global error correction with the ability to repair a small number of erased coordinates by accessing only a limited number of other coordinates. Motivated by their quantum counterparts, we construct several families of optimal cyclic $(r,\delta)$-LRCs that are Euclidean or Hermi...
We study classical string commitment over quantum channels with limited preshared entanglement. For noninteractive protocols, we determine the commitment capacity of a class of channels with input dimension $d$ that, at each use, sample a pair of classical random variables $(F,Z)$, apply one of the $d^2$ Heisenberg--We...
We develop a family of semi-device-independent (SDI) entanglement-assisted prepare-measure (PM) communication games involving two parties, within the n→l random-access code (RAC) framework where the sender Alice holds a n-bit string and communicates l<n bits or qubits to the receiver Bob. In contrast to the standard qu...
Rajdeep Paul, Prabuddha Roy, A. Pan· New Journal of Physics· 0 citations
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