On the Capacity of Erasure-prone Quantum Storage with Erasure-prone Entanglement Assistance

• URL: http://arxiv.org/abs/2510.17781v1
• Date: Mon, 20 Oct 2025 17:40:21 GMT
• Title: On the Capacity of Erasure-prone Quantum Storage with Erasure-prone Entanglement Assistance
• Authors: Hua Sun, Syed A. Jafar,
• Abstract summary: The capacity for this setting is the maximum size of the quantum message.<n>The capacity remains open for an intermediate range of $lambda_B$ values when a strict majority of the $N$ storage nodes, and a strict non-zero minority of the $N_B$ EA nodes, are erased.
• Score: 14.164370730003691
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A quantum message is encoded into $N$ storage nodes (quantum systems $Q_1\dots Q_N$) with assistance from $N_B$ maximally entangled bi-partite quantum systems $A_1B_1, \dots, A_{N_B}B_{N_B}$, that are prepared in advance such that $B_1\dots B_{N_B}$ are stored separately as entanglement assistance (EA) nodes, while $A_1\dots A_{N_B}$ are made available to the encoder. Both the storage nodes and EA nodes are erasure-prone. The quantum message must be recoverable given any $K$ of the $N$ storage nodes along with any $K_B$ of the $N_B$ EA nodes. The capacity for this setting is the maximum size of the quantum message, given that the size of each EA node is $\lambda_B$. All node sizes are relative to the size of a storage node, which is normalized to unity. The exact capacity is characterized as a function of $N,K,N_B,K_B, \lambda_B$ in all cases, with one exception. The capacity remains open for an intermediate range of $\lambda_B$ values when a strict majority of the $N$ storage nodes, and a strict non-zero minority of the $N_B$ EA nodes, are erased. As a key stepping stone, an analogous classical storage (with shared-randomness assistance) problem is introduced. A set of constraints is identified for the classical problem, such that classical linear code constructions translate to quantum storage codes, and the converse bounds for the two settings utilize similar insights. In particular, the capacity characterizations for the classical and quantum settings are shown to be identical in all cases where the capacity is settled.

Related papers

• Breaking the Storage-Bandwidth Tradeoff in Distributed Storage with Quantum Entanglement [46.17112353277822]
  This work investigates the use of quantum resources in distributed storage systems.<n>In this setting, we fully characterize the fundamental tradeoff between storage and repair bandwidth.
  arXiv  Detail & Related papers  (2026-01-15T18:41:10Z)
• Entanglement Cost of Erasure Correction in Quantum MDS Codes [2.7195102129095003]
  We focus on distributed quantum storage based on quantum maximum distance separable (MDS) codes.<n>We show that the simple method of downloading the non-erased qudits and performing operations at a single node is optimal when the minimal number of non-erased nodes are accessed.<n>It remains to be seen what the entanglement cost will be when a non-minimal number of non-erased nodes are accessed.
  arXiv  Detail & Related papers  (2025-05-26T17:58:43Z)
• Information storage and transmission under Markovian noise [11.745324895296465]
  We study the information transmission capacities of quantum Markov semigroups $(Psit)_tin mathbbN$ acting on $d-dimensional quantum systems.<n>We show that, in the limit of $tto infty$, the capacities can be efficiently computed in terms of the structure of the peripheral space of $Psi$.<n>We also establish convergence bounds to show that the infinite-time capacities are reached after time $tgtrsim d2ln (d)$.
  arXiv  Detail & Related papers  (2025-04-14T17:27:43Z)
• Quantum State Preparation via Free Binary Decision Diagram [2.8759931537641785]
  We construct a quantum algorithm for QSP when the classical description of a quantum state is given by an FBDD with weighted edges.<n>We show that any quantum state represented by the weighted FBDD with $N$ nodes can be prepared by an $O(N)$-sized quantum circuit.<n>We also provide an example of an $n$-qubit state that can be represented by a weighted FBDD with $N=O(mathrmpoly(n))$ nodes.
  arXiv  Detail & Related papers  (2024-07-01T18:00:01Z)
• Nearly Optimal Circuit Size for Sparse Quantum State Preparation [0.0]
  A quantum state is said to be $d$-sparse if it has only $d$ non-zero amplitudes.<n>We prove for the first time a trade-off between the number of ancillary qubits and the circuit size.
  arXiv  Detail & Related papers  (2024-06-23T15:28:20Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Spacetime-Efficient Low-Depth Quantum State Preparation with Applications [93.56766264306764]
  We show that a novel deterministic method for preparing arbitrary quantum states requires fewer quantum resources than previous methods. We highlight several applications where this ability would be useful, including quantum machine learning, Hamiltonian simulation, and solving linear systems of equations.
  arXiv  Detail & Related papers  (2023-03-03T18:23:20Z)
• A lower bound on the space overhead of fault-tolerant quantum computation [51.723084600243716]
  The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation. We prove an exponential upper bound on the maximal length of fault-tolerant quantum computation with amplitude noise.
  arXiv  Detail & Related papers  (2022-01-31T22:19:49Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)
• Quantum Coupon Collector [62.58209964224025]
  We study how efficiently a $k$-element set $Ssubseteq[n]$ can be learned from a uniform superposition $|Srangle of its elements. We give tight bounds on the number of quantum samples needed for every $k$ and $n$, and we give efficient quantum learning algorithms.
  arXiv  Detail & Related papers  (2020-02-18T16:14:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.