Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2605.12455

Simultaneously Minimizing Storage and Bandwidth Under Exact Repair With Quantum Entanglement

Lei Hu, Mohamed Nomeir, Alptug Aytekin, Sennur Ulukus

cs.ITcs.NIeess.SPquant-phSubmitted May 12, 2026• Announced May 13, 2026• 0 citations
arXivHTMLPDF

Abstract

We study exact-regenerating codes for entanglement-assisted distributed storage systems. Consider an $(n,k,d,α,β_{\mathsf{q}},B)$ distributed system that stores a file of $B$ classical symbols across $n$ nodes with each node storing $α$ symbols. A data collector can recover the file by accessing any $k$ nodes. When a node fails, any $d$ surviving nodes share an entangled state, and each of them transmits a quantum system of $β_{\mathsf{q}}$ qudits to a newcomer. The newcomer then performs a measurement on the received quantum systems to generate its storage. Recent work [1] showed that, under functional repair where the regenerated content may differ from that of the failed node, there exists a unique optimal regenerating point that \emph{simultaneously minimizes both storage $α$ and repair bandwidth $d β_{\mathsf{q}}$} when $d \geq 2k-2$. In this paper, we show that, under \emph{exact repair}, where the newcomer reproduces exactly the same content as the failed node, this optimal point remains achievable. Our construction builds on the classical product-matrix framework and the Calderbank-Shor-Steane (CSS)-based stabilizer formalism.

Related papers

Breaking the Storage-Bandwidth Tradeoff in Distributed Storage with Quantum Entanglement

Lei Hu, Mohamed Nomeir, Alptug Aytekin +1 more

This work investigates the use of quantum resources in distributed storage systems. Consider an $(n,k,d)$ distributed storage system in which a file is stored across $n$ nodes such that any $k$ nodes suffice to reconstruct the file. When a node fails, any $d$ helper nodes transmit information to a newcomer to rebuild the system. In contrast to the classical repair, where helper nodes transmit classical bits, we allow them to send classical information over quantum channels to the newcomer. The newcomer then generates its storage by performing appropriate measurements on the received quantum states. In this setting, we fully characterize the fundamental tradeoff between storage and repair bandwidth (total communication cost). Compared to classical systems, the optimal storage--bandwidth tradeoff can be significantly improved with the enhancement of quantum entanglement shared only among the surviving nodes, particularly at the minimum-storage regenerating point. Remarkably, we show that when $d \geq 2k-2$, there exists an operating point at which \textit{both storage and repair bandwidth are simultaneously minimized}. This phenomenon breaks the tradeoff in the classical setting and reveals a fundamentally new regime enabled by quantum communication.

cs.ITCross-listedarXiv:2601.10676•IEEE International Symposium on Information Theory (ISIT)•Jan 16, 2026•0 citations

Quantum Entanglement Halves the Oblivious Update Bandwidth

Sagar Dubey

We consider $(n,k)$ MDS-coded distributed storage over $\mathbb{F}_q$ with per-node storage $α$ symbols. For the oblivious update problem, where a single message symbol changes and neither helpers nor the stale node know which, the classical lower bound is $αk \log_2 q$ bits. We prove that when the $k$ contacted helpers share prior quantum entanglement, the update bandwidth is $\lceil α/2 \rceil \cdot k \log_2 q$ bits-equivalent, a factor approaching 2 reduction. For $α= 2$, a $[[k, k-2]]_q$ CSS code achieves bandwidth $k \log_2 q$ with one qudit per helper. For general $α$, a $[[\lceil α/2 \rceil k, \lceil α/2 \rceil k - α]]_q$ CSS code achieves the bound with $\lceil α/2 \rceil$ qudits per helper. The matching converse uses the superdense coding bound: the stale node holds all transmitted qudits and hence the entangled partners, so each helper's channel supports at most $D^2$ distinguishable signals for dimension $D$. The result holds for all $(n,k)$ pairs with sufficiently large prime $q$.

quant-pharXiv:2605.19248•May 20, 2026•0 citations

Entanglement-assisted fault-tolerant encoding and decoding for qudit stabilizer codes

Abhi Kumar Sharma, Shayan Srinivasa Garani

We propose fault-tolerant quantum encoders for Calderbank-Shor-Steane (CSS) and non-CSS codes over qudits by utilizing $g$-partite maximally entangled states. The qudits are grouped into $g$ contiguous blocks such that entangled states are shared across the blocks, and multiqudit gates are applied locally to restrict the error propagation within each block. We also propose a transversal fault-tolerant block decoder to decode the blocks individually and recover the complete encoded quantum information. The optimum value of $g$ to obtain an improvement in the probability of error propagation of the proposed encoders against non-fault-tolerant schemes is analytically determined for application in the encoding circuit. The proposed fault-tolerant scheme with entanglement assistance scales linearly with the number of $g$-partite entangled states and overcomes the limitations of diminishing coding rates for higher levels of concatenation within the concatenated coding scheme. We validate the proposed ideas by constructing fault-tolerant encoding circuits for the non-CSS ${[[5,1,3]]}_{3}$ code and the ${[[7,1,3]]}_{3}$ CSS code through illustrative examples. We reduced the probability of error propagation from 0.248 to 0.212 for the ${[[5,1,3]]}_{3}$ code and from 0.207 to 0.174 for the ${[[7,1,3]]}_{3}$ code. For example, over ${[[100,70]]}_{2}$ quantum code without any fault tolerance, using three-partite entangled pairs, one can get two orders of improvement (1e-2) in the probability of error propagation compared to the non-fault-tolerant encoder by encoding over 190 physical qubits with the same number of stabilizers.

Physical Review A•Dec 31, 2024•2 citations

On the Capacity of Erasure-Prone Quantum Storage With Erasure-Prone Entanglement Assistance

Hua Yan Sun, Syed A. Jafar

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 $λ_B$. 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 $N,K,N_B,K_B, λ_B$ in all cases, with one exception. The capacity remains open for an intermediate range of $λ_B$ 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.

arXiv:2510.17781•IEEE Transactions on Information Theory•Aug 18, 2026•0 citations

Entanglement-Assisted Coding for Arbitrary Linear Computations Over a Quantum MAC

Lei Hu, Mohamed W. Nomeir, Alptug Aytekin +3 more

We study a linear computation problem over a quantum multiple access channel (LC-QMAC), where S servers share an entangled state and separately store classical data streams W1,⋯,WSover a finite field ${\mathbb{F}_d}$. A user aims to compute K linear combinations of these data streams, represented as $Y = {{\mathbf{V}}_1}{W_1} + {{\mathbf{V}}_2}{W_2} + \cdot s + {{\mathbf{V}}_S}{W_S} \in \mathbb{F}_d^{K \times 1}$. To this end, each server encodes its classical information into its local quantum subsystem and transmits it to the user, who retrieves the desired computations via quantum measurements. In this work, we propose an achievable scheme for LC-QMAC based on the stabilizer formalism and the ideas from entanglement-assisted quantum error–correcting codes (EAQECC). Specifically, given any linear computation matrix, we construct a self-orthogonal matrix that can be implemented using the stabilizer formalism. Also, we apply precoding matrices to minimize the number of auxiliary qudits required. Our scheme achieves more computations per qudit, i.e., a higher computation rate, compared to the best-known methods in the literature, and attains the capacity in certain cases.

arXiv:2501.16296•IEEE Information Theory Workshop (ITW)•Sep 29, 2025•2 citations

Asymmetric Entanglement-Assisted Quantum Locally Recoverable Codes

Vijay Kumar, Ramakrishna Bandi

Locally recoverable codes (LRCs) permit reconstruction of a lost coordinate from a small subset of the remaining coordinates, a property that is a fundamental coding technique for distributed storage and, more recently, for fault-tolerant quantum memories and distributed storage systems. Existing constructions of quantum locally recoverable codes (qLRCs) and their entanglement-assisted generalizations (EA-qLRCs) impose a single locality parameter $r$ governing recovery from both bit-flip ($X$-type) and phase-flip ($Z$-type) errors, even though physical noise is rarely symmetric between the two. We introduce entanglement-assisted quantum locally recoverable codes (EA-qLRC) with \emph{asymmetric locality} $\{r_X,r_Z\}$, in which $X$-type and $Z$-type errors are corrected from recovery sets of size at most $r_X+1$ and $r_Z+1$, respectively. We extend a stabilizer sufficient condition for this property and, in particular, the CSS framework, where asymmetric locality corresponds to separate locality conditions on the two classical codes $\mathcal C_1$ and $\mathcal C_2$ underlying the construction. From this characterization we derive Singleton-, Griesmer-, Plotkin-, sphere-packing-, and Cadambe\textendash Mazumdar-like bounds for CSS-type asymmetric EA-qLRCs (AEA-qLRCs) built from Proposition~\ref{CSS-EA-qLRC-Asym}, and we characterize exactly when a pure CSS-type AEA-qLRC built from a pair of classical LRCs attains the Singleton-like bound with equality.

quant-pharXiv:2610.23889•Sep 29, 2026•0 citations
We study exact-regenerating codes for entanglement-assisted distributed storage systems. Consider an (n,k,d,α,βq,B)(n,k,d,α,β_{\mathsf{q}},B)(n,k,d,α,βq​,B) distributed system that stores a file of BBB classical symbols across nnn nodes with each node storing ααα symbols. A data collector can recover the file by accessing any kkk nodes. When a node fails, any ddd surviving nodes share an entangled state, and each of them transmits a quantum system of βqβ_{\mathsf{q}}βq​ qudits to a newcomer. The newcomer then performs a measurement on the received quantum systems to generate its storage. Recent work [1] showed that, under functional repair where the regenerated content may differ from that of the failed node, there exists a unique optimal regenerating point that \emph{simultaneously minimizes both storage ααα and repair bandwidth dβqd β_{\mathsf{q}}dβq​} when d≥2k−2d \geq 2k-2d≥2k−2. In this paper, we show that, under \emph{exact repair}, where the newcomer reproduces exactly the same content as the failed node, this optimal point remains achievable. Our construction builds on the classical product-matrix framework and the Calderbank-Shor-Steane (CSS)-based stabilizer formalism.
This work investigates the use of quantum resources in distributed storage systems. Consider an (n,k,d)(n,k,d)(n,k,d) distributed storage system in which a file is stored across nnn nodes such that any kkk nodes suffice to reconstruct the file. When a node fails, any ddd helper nodes transmit information to a newcomer to rebuild the system. In contrast to the classical repair, where helper nodes transmit classical bits, we allow them to send classical information over quantum channels to the newcomer. The newcomer then generates its storage by performing appropriate measurements on the received quantum states. In this setting, we fully characterize the fundamental tradeoff between storage and repair bandwidth (total communication cost). Compared to classical systems, the optimal storage--bandwidth tradeoff can be significantly improved with the enhancement of quantum entanglement shared only among the surviving nodes, particularly at the minimum-storage regenerating point. Remarkably, we show that when d≥2k−2d \geq 2k-2d≥2k−2, there exists an operating point at which \textit{both storage and repair bandwidth are simultaneously minimized}. This phenomenon breaks the tradeoff in the classical setting and reveals a fundamentally new regime enabled by quantum communication.
We consider (n,k)(n,k)(n,k) MDS-coded distributed storage over Fq\mathbb{F}_qFq​ with per-node storage ααα symbols. For the oblivious update problem, where a single message symbol changes and neither helpers nor the stale node know which, the classical lower bound is αklog⁡2qαk \log_2 qαklog2​q bits. We prove that when the kkk contacted helpers share prior quantum entanglement, the update bandwidth is ⌈α/2⌉⋅klog⁡2q\lceil α/2 \rceil \cdot k \log_2 q⌈α/2⌉⋅klog2​q bits-equivalent, a factor approaching 2 reduction. For α=2α= 2α=2, a [[k,k−2]]q[[k, k-2]]_q[[k,k−2]]q​ CSS code achieves bandwidth klog⁡2qk \log_2 qklog2​q with one qudit per helper. For general ααα, a [[⌈α/2⌉k,⌈α/2⌉k−α]]q[[\lceil α/2 \rceil k, \lceil α/2 \rceil k - α]]_q[[⌈α/2⌉k,⌈α/2⌉k−α]]q​ CSS code achieves the bound with ⌈α/2⌉\lceil α/2 \rceil⌈α/2⌉ qudits per helper. The matching converse uses the superdense coding bound: the stale node holds all transmitted qudits and hence the entangled partners, so each helper's channel supports at most D2D^2D2 distinguishable signals for dimension DDD. The result holds for all (n,k)(n,k)(n,k) pairs with sufficiently large prime qqq.
We propose fault-tolerant quantum encoders for Calderbank-Shor-Steane (CSS) and non-CSS codes over qudits by utilizing ggg-partite maximally entangled states. The qudits are grouped into ggg contiguous blocks such that entangled states are shared across the blocks, and multiqudit gates are applied locally to restrict the error propagation within each block. We also propose a transversal fault-tolerant block decoder to decode the blocks individually and recover the complete encoded quantum information. The optimum value of ggg to obtain an improvement in the probability of error propagation of the proposed encoders against non-fault-tolerant schemes is analytically determined for application in the encoding circuit. The proposed fault-tolerant scheme with entanglement assistance scales linearly with the number of ggg-partite entangled states and overcomes the limitations of diminishing coding rates for higher levels of concatenation within the concatenated coding scheme. We validate the proposed ideas by constructing fault-tolerant encoding circuits for the non-CSS [[5,1,3]]3{[[5,1,3]]}_{3}[[5,1,3]]3​ code and the [[7,1,3]]3{[[7,1,3]]}_{3}[[7,1,3]]3​ CSS code through illustrative examples. We reduced the probability of error propagation from 0.248 to 0.212 for the [[5,1,3]]3{[[5,1,3]]}_{3}[[5,1,3]]3​ code and from 0.207 to 0.174 for the [[7,1,3]]3{[[7,1,3]]}_{3}[[7,1,3]]3​ code. For example, over [[100,70]]2{[[100,70]]}_{2}[[100,70]]2​ quantum code without any fault tolerance, using three-partite entangled pairs, one can get two orders of improvement (1e-2) in the probability of error propagation compared to the non-fault-tolerant encoder by encoding over 190 physical qubits with the same number of stabilizers.
A quantum message is encoded into NNN storage nodes (quantum systems Q1…QNQ_1\dots Q_NQ1​…QN​) with assistance from NBN_BNB​ maximally entangled bi-partite quantum systems A1B1,…,ANBBNBA_1B_1, \dots, A_{N_B}B_{N_B}A1​B1​,…,ANB​​BNB​​, that are prepared in advance such that B1…BNBB_1\dots B_{N_B}B1​…BNB​​ are stored separately as entanglement assistance (EA) nodes, while A1…ANBA_1\dots A_{N_B}A1​…ANB​​ are made available to the encoder. Both the storage nodes and EA nodes are erasure-prone. The quantum message must be recoverable given any KKK of the NNN storage nodes along with any KBK_BKB​ of the NBN_BNB​ EA nodes. The capacity for this setting is the maximum size of the quantum message, given that the size of each EA node is λBλ_BλB​. 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,NB,KB,λBN,K,N_B,K_B, λ_BN,K,NB​,KB​,λB​ in all cases, with one exception. The capacity remains open for an intermediate range of λBλ_BλB​ values when a strict majority of the NNN storage nodes, and a strict non-zero minority of the NBN_BNB​ 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.
We study a linear computation problem over a quantum multiple access channel (LC-QMAC), where S servers share an entangled state and separately store classical data streams W1,⋯,WSover a finite field Fd{\mathbb{F}_d}Fd​. A user aims to compute K linear combinations of these data streams, represented as Y=V1W1+V2W2+⋅s+VSWS∈FdK×1Y = {{\mathbf{V}}_1}{W_1} + {{\mathbf{V}}_2}{W_2} + \cdot s + {{\mathbf{V}}_S}{W_S} \in \mathbb{F}_d^{K \times 1}Y=V1​W1​+V2​W2​+⋅s+VS​WS​∈FdK×1​. To this end, each server encodes its classical information into its local quantum subsystem and transmits it to the user, who retrieves the desired computations via quantum measurements. In this work, we propose an achievable scheme for LC-QMAC based on the stabilizer formalism and the ideas from entanglement-assisted quantum error–correcting codes (EAQECC). Specifically, given any linear computation matrix, we construct a self-orthogonal matrix that can be implemented using the stabilizer formalism. Also, we apply precoding matrices to minimize the number of auxiliary qudits required. Our scheme achieves more computations per qudit, i.e., a higher computation rate, compared to the best-known methods in the literature, and attains the capacity in certain cases.
Locally recoverable codes (LRCs) permit reconstruction of a lost coordinate from a small subset of the remaining coordinates, a property that is a fundamental coding technique for distributed storage and, more recently, for fault-tolerant quantum memories and distributed storage systems. Existing constructions of quantum locally recoverable codes (qLRCs) and their entanglement-assisted generalizations (EA-qLRCs) impose a single locality parameter rrr governing recovery from both bit-flip (XXX-type) and phase-flip (ZZZ-type) errors, even though physical noise is rarely symmetric between the two. We introduce entanglement-assisted quantum locally recoverable codes (EA-qLRC) with \emph{asymmetric locality} {rX,rZ}\{r_X,r_Z\}{rX​,rZ​}, in which XXX-type and ZZZ-type errors are corrected from recovery sets of size at most rX+1r_X+1rX​+1 and rZ+1r_Z+1rZ​+1, respectively. We extend a stabilizer sufficient condition for this property and, in particular, the CSS framework, where asymmetric locality corresponds to separate locality conditions on the two classical codes C1\mathcal C_1C1​ and C2\mathcal C_2C2​ underlying the construction. From this characterization we derive Singleton-, Griesmer-, Plotkin-, sphere-packing-, and Cadambe\textendash Mazumdar-like bounds for CSS-type asymmetric EA-qLRCs (AEA-qLRCs) built from Proposition~\ref{CSS-EA-qLRC-Asym}, and we characterize exactly when a pure CSS-type AEA-qLRC built from a pair of classical LRCs attains the Singleton-like bound with equality.