arXiv subjects

Jihao Fan

Publications and source records attributed to Jihao Fan.

13 recordsLinked to original sources

arXiv2025

The Capacity of Collusion-Resilient Decentralized Secure Aggregation with Groupwise Keys

This paper investigates the information-theoretic decentralized secure aggregation (DSA) problem under practical groupwise secret keys and collusion resilience. In DSA, $K$ users are interconnected through error-free broadcast channels. Each user holds a private input and aims to compute the sum of all other users' inputs, while satisfying the security constraint that no user, even when colluding with up to $T$ other users, can infer any information about the inputs beyond the recovered sum. To ensure security, users are equipped with secret keys to mask their inputs. Motivated by recent advances in efficient group-based key generation protocols, we consider the symmetric groupwise key setting, where every subset of $G$ users shares a group key that is independent of all other group keys. The problem is challenging because the recovery and security constraints must hold simultaneously for all users, and the structural constraints on the secret keys limit the flexibility of key correlations. We characterize the optimal rate region consisting of all achievable pairs of per-user broadcast communication rate and groupwise key rate. In particular, we show that DSA with groupwise keys is infeasible when $G=1$ or $G\ge K-T$. Otherwise, when $2\le G<K-T$, to securely compute one symbol of the desired sum, each user must broadcast at least one symbol, and each group key must contain at least $(K-T-2)/\binom{K-T-1}{G}$ independent symbols. Our results establish the fundamental limits of DSA with groupwise keys and provide design insights for communication- and key-efficient secure aggregation in decentralized learning systems.

cs.IT↗

arXiv2025

Graph-Theoretic Characterization of Noise Capacity of Conditional Disclosure of Secrets

In the Conditional Disclosure of Secrets (CDS) problem, Alice and Bob hold inputs $x\in \mathcal{X}$ and $y\in \mathcal{Y}$ and share a secret. Let $f:\mathcal{X}\times\mathcal{Y}\to\{0,1\}$ be a function such that the secret is revealed to a third party, Carol, if and only if $f(x,y)=1$. To protect the secret when $f(x,y)=0$, Alice and Bob share a common noise variable unknown to Carol. We study the \emph{noise capacity} of CDS, defined as the maximum number of secret bits that can be securely revealed per noise bit. We first derive necessary and sufficient conditions on $f$, represented by a CDS graph, for the extremal case where the noise capacity equals $1$. We then develop converse bounds on the noise rate for all linear schemes: $\frac{(\rho-1)(d-1)}{\rho d-1}$ if $\rho$ is finite, and $\frac{d-1}{d}$ if $\rho$ is infinite, where $\rho$ is the covering parameter of the CDS graph and $d$ is the number of unqualified edges in an unqualified path. Under maximal communication efficiency (message size equals secret size), we refine these bounds by analyzing qualified components and their connections. Achievability is shown for CDS instances with cyclic qualified edges and a single unqualified path. This graph-theoretic framework links noise efficiency limits to the unqualified path distance and covering parameter, providing a systematic method to analyze CDS under arbitrary graph topologies.

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arXiv2025

Hierarchical Secure Aggregation with Heterogeneous Security Constraints and Arbitrary User Collusion

In hierarchical secure aggregation (HSA), a server communicates with clustered users through an intermediate layer of relays to compute the sum of users' inputs under two security requirements -- server security and relay security. Server security requires that the server learns nothing beyond the desired sum even when colluding with a subset of users, while relay security requires that each relay remains oblivious to the users' inputs under collusion. Existing work on HSA enforces homogeneous security where \tit{all} inputs must be protected against \tit{any} subset of potential colluding users with sizes up to a predefined threshold. Such a \homo formulation cannot capture scenarios with \tit{\het} \secty \reqs where \diff users may demand various levels of protection. In this paper, we study hierarchical secure aggregation (HSA) with heterogeneous security requirements and arbitrary user collusion. Specifically, we consider scenarios where the inputs of certain groups of users must remain information-theoretically secure against inference by the server or any relay, even if the server or any relay colludes with an arbitrary subset of other users. Under server security, the server learns nothing about these protected inputs beyond the prescribed aggregate sum, despite any such collusion. Under relay security, each relay similarly obtains no information about the protected inputs under the same collusion model. We characterize the optimal communication rates achievable across all layers for all parameter regimes. Furthermore, we study the minimum source keys required at the users to ensure security. For this source key requirement, we provide tight characterizations in two broad regimes determined by the security and collusion constraints, and establish a general information-theoretic lower bound together with a bounded-gap achievable scheme for the remaining regime.

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arXiv2025

Entanglement-Assisted Concatenated Quantum Codes: Parameters and Asymptotic Performance

Entanglement-assisted concatenated quantum codes (EACQCs) are constructed by concatenating two entanglement-assisted quantum error-correcting codes (EAQECCs). By selecting the inner and outer component codes carefully, it is able to construct state-of-the-art EACQCs with parameters better than previous quantum codes. In this work, we use almost maximum-distance-separable (MDS) codes and $\hbar$-MDS codes as the outer codes to construct EACQCs. Because the range of code length of almost MDS and $\hbar$-MDS codes is much more free than that of the commonly used MDS codes. We derive several families of new EACQCs with parameters better than the previously best known EAQECCs and standard quantum error-correcting codes (QECCs) of the same length and net transmissions. Moreover, we demonstrate that EACQCs are with maximal entanglement if both the inner and outer component codes are with maximal entanglement. As a result, we construct three new maximal-entanglement EACQCs which have optimal parameters. In addition, we present several new maximal-entanglement EACQCs whose minimum distance is only one less than the minimum distance of the optimal codes. In particular, we propose two new families of asymptotically good maximal-entanglement EACQCs with explicit constructions by using entanglement-assisted quantum algebraic geometry codes as the outer codes. At last, we prove that EACQCs can attain the quantum Gilbert-Varshamov bound for EAQECCs asymptotically.

quant-ph↗

arXiv2025

Characterizing the Burst Error Correction Ability of Quantum Cyclic Codes

Quantum burst error correction codes (QBECCs) are of great importance to deal with the memory effect in quantum channels. As the most important family of QBECCs, quantum cyclic codes (QCCs) play a vital role in the correction of burst errors. In this work, we characterize the burst error correction ability of QCCs constructed from the Calderbank-Shor-Steane (CSS) and the Hermitian constructions. We determine the burst error correction limit of QCCs and quantum Reed-Solomon codes with algorithms in polynomial-time complexities. As a result, lots of QBECCs saturating the quantum Reiger bound are obtained. We show that quantum Reed-Solomon codes have better burst error correction abilities than the previous results. At last, we give the quantum error-trapping decoder (QETD) of QCCs for decoding burst errors. The decoder runs in linear time and can decode both degenerate and nondegenerate burst errors. What's more, the numerical results show that QETD can decode much more degenerate burst errors than the nondegenerate ones.

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arXiv2023

A quantum system control method based on enhanced reinforcement learning

Traditional quantum system control methods often face different constraints, and are easy to cause both leakage and stochastic control errors under the condition of limited resources. Reinforcement learning has been proved as an efficient way to complete the quantum system control task. To learn a satisfactory control strategy under the condition of limited resources, a quantum system control method based on enhanced reinforcement learning (QSC-ERL) is proposed. The states and actions in reinforcement learning are mapped to quantum states and control operations in quantum systems. By using new enhanced neural networks, reinforcement learning can quickly achieve the maximization of long-term cumulative rewards, and a quantum state can be evolved accurately from an initial state to a target state. According to the number of candidate unitary operations, the three-switch control is used for simulation experiments. Compared with other methods, the QSC-ERL achieves close to 1 fidelity learning control of quantum systems, and takes fewer episodes to quantum state evolution under the condition of limited resources.

cs.ET↗

arXiv2022

Entanglement-assisted concatenated quantum codes

Entanglement-assisted concatenated quantum codes (EACQCs), constructed by concatenating two quantum codes, are proposed. These EACQCs show several advantages over the standard concatenated quantum codes (CQCs). Several families of EACQCs that, unlike standard CQCs, can beat the nondegenerate Hamming bound for entanglement-assisted quantum error correction codes (EAQECCs) are derived. Further, a number of EACQCs with better parameters than the best known standard quantum error correction codes (QECCs) and EAQECCs are also derived. In particular, several catalytic EACQCs with better parameters than the best known QECCs of the same length and net transmission are constructed. Furthermore, each catalytic EACQC consumes only one or two ebits. It is also shown that EACQCs make entanglement-assisted quantum communication possible even if the ebits are noisy. Finally, it is shown that EACQCs can outperform CQCs in entanglement fidelity over depolarizing channels if the ebits are less noisy than the qubits. Moreover, the threshold error probability of EACQCs is larger than that of CQCs when the error probability of ebits is sufficiently lower than that of qubits. Therefore EACQCs are not only competitive in quantum communication but also applicable in fault-tolerant quantum computation.

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arXiv2021

Partially Concatenated Calderbank-Shor-Steane Codes Achieving the Quantum Gilbert-Varshamov Bound Asymptotically

In this paper, we utilize a concatenation scheme to construct new families of quantum error correction codes achieving the quantum Gilbert-Varshamov (GV) bound asymptotically. We concatenate alternant codes with any linear code achieving the classical GV bound to construct Calderbank-Shor-Steane (CSS) codes. We show that the concatenated code can achieve the quantum GV bound asymptotically and can approach the Hashing bound for asymmetric Pauli channels. By combing Steane's enlargement construction of CSS codes, we derive a family of enlarged stabilizer codes achieving the quantum GV bound for enlarged CSS codes asymptotically. As applications, we derive two families of fast encodable and decodable CSS codes with parameters $\mathscr{Q}_1=[[N,\Omega(\sqrt{N}),\Omega( \sqrt{N})]],$ and $\mathscr{Q}_2=[[N,\Omega(N/\log N),\Omega(N/\log N)/\Omega(\log N)]].$ We show that $\mathscr{Q}_1$ can be encoded very efficiently by circuits of size $O(N)$ and depth $O(\sqrt{N})$. For an input error syndrome, $\mathscr{Q}_1$ can correct any adversarial error of weight up to half the minimum distance bound in $O(N)$ time. $\mathscr{Q}_1$ can also be decoded in parallel in $O(\sqrt{N})$ time by using $O(\sqrt{N})$ classical processors. For an input error syndrome, we proved that $\mathscr{Q}_2$ can correct a linear number of ${X}$-errors with high probability and an almost linear number of ${Z}$-errors in $O(N )$ time. Moreover, $\mathscr{Q}_2$ can be decoded in parallel in $O(\log(N))$ time by using $O(N)$ classical processors.

quant-ph↗

arXiv2020

Asymmetric Quantum Concatenated and Tensor Product Codes with Large Z-Distances

In this paper, we present a new construction of asymmetric quantum codes (AQCs) by combining classical concatenated codes (CCs) with tensor product codes (TPCs), called asymmetric quantum concatenated and tensor product codes (AQCTPCs) which have the following three advantages. First, only the outer codes in AQCTPCs need to satisfy the orthogonal constraint in quantum codes, and any classical linear code can be used for the inner, which makes AQCTPCs very easy to construct. Second, most AQCTPCs are highly degenerate, which means they can correct many more errors than their classical TPC counterparts. Consequently, we construct several families of AQCs with better parameters than known results in the literature. Third, AQCTPCs can be efficiently decoded although they are degenerate, provided that the inner and outer codes are efficiently decodable. In particular, we significantly reduce the inner decoding complexity of TPCs from $\Omega(n_2a^{n_1})(a>1)$ to $O(n_2)$ by considering error degeneracy, where $n_1$ and $n_2$ are the block length of the inner code and the outer code, respectively. Furthermore, we generalize our concatenation scheme by using the generalized CCs and TPCs correspondingly.

cs.IT↗

arXiv2018

Construction and Performance of Quantum Burst Error Correction Codes for Correlated Errors

In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat such error patterns in the quantum regime. Our contributions are as follows. Firstly, we derive an upper bound for the correctable burst errors of QBECCs, the quantum Reiger bound (QRB). This bound generalizes the quantum Singleton bound for standard quantum error correction codes (QECCs). Secondly, we propose two constructions of QBECCs: one by heuristic computer search and the other by concatenating two quantum tensor product codes (QTPCs). We obtain several new QBECCs with better parameters than existing codes with the same coding length. Moreover, some of the constructed codes can saturate the quantum Reiger bounds. Finally, we perform numerical experiments for our constructed codes over Markovian correlated depolarizing quantum memory channels, and show that QBECCs indeed outperform standard QECCs in this scenario.

cs.IT↗

arXiv2017

On Quantum Tensor Product Codes

We present a general framework for the construction of quantum tensor product codes (QTPC). In a classical tensor product code (TPC), its parity check matrix is con- structed via the tensor product of parity check matrices of the two component codes. We show that by adding some constraints on the component codes, several classes of dual-containing TPCs can be obtained. By selecting different types of component codes, the proposed method enables the construction of a large family of QTPCs and they can provide a wide variety of quantum error control abilities. In particular, if one of the component codes is selected as a burst-error-correction code, then QTPCs have quantum multiple-burst-error-correction abilities, provided these bursts fall in distinct subblocks. Compared with concatenated quantum codes (CQC), the component code selections of QTPCs are much more exible than those of CQCs since only one of the component codes of QTPCs needs to satisfy the dual-containing restriction. We show that it is possible to construct QTPCs with parameters better than other classes of quantum error-correction codes (QECC), e.g., CQCs and quantum BCH codes. Many QTPCs are obtained with parameters better than previously known quantum codes available in the literature. Several classes of QTPCs that can correct multiple quantum bursts of errors are constructed based on reversible cyclic codes and maximum-distance-separable (MDS) codes.

quant-ph↗

arXiv2016

Constructions of q-ary entanglement-assisted quantum MDS codes with minimum distance greater than q + 1

The entanglement-assisted stabilizer formalism provides a useful framework for constructing quantum error-correcting codes (QECC), which can transform arbitrary classical linear codes into entanglement-assisted quantum error correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this paper, we construct five classes of entanglement-assisted quantum MDS (EAQMDS) codes based on classical MDS codes by exploiting one or more pre-shared maximally entangled states. We show that these EAQMDS codes have much larger minimum distance than the standard quantum MDS (QMDS) codes of the same length, and three classes of these EAQMDS codes consume only one pair of maximally entangled states.

quant-ph↗

arXiv2014

Constructions of Pure Asymmetric Quantum Alternant Codes Based on Subclasses of Alternant Codes

In this paper, we construct asymmetric quantum error-correcting codes(AQCs) based on subclasses of Alternant codes. Firstly, We propose a new subclass of Alternant codes which can attain the classical Gilbert-Varshamov bound to construct AQCs. It is shown that when $d_x=2$, $Z$-parts of the AQCs can attain the classical Gilbert-Varshamov bound. Then we construct AQCs based on a famous subclass of Alternant codes called Goppa codes. As an illustrative example, we get three $[[55,6,19/4]],[[55,10,19/3]],[[55,15,19/2]]$ AQCs from the well known $[55,16,19]$ binary Goppa code. At last, we get asymptotically good binary expansions of asymmetric quantum GRS codes, which are quantum generalizations of Retter's classical results. All the AQCs constructed in this paper are pure.

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