arXiv subjects

Syed A. Jafar

Publications and source records attributed to Syed A. Jafar.

At least 19 recordsLinked to original sources

arXiv2026

Unlocking Exponential and Unbounded Robust Gains in Shannon Capacity of Classical Multiple Access Channels with Causal CSIT via Quantum Entanglement Assistance

Quantum entanglement assistance is known to improve the Shannon capacity of classical communication networks but the largest gains noted thus far are rather modest (less than 6%), motivating the question: are large capacity gains ever possible? It is shown in this work that in the presence of causal channel state information at the transmitters (CSIT), quantum entanglement assistance provides a multiplicative capacity advantage that grows exponentially with the number of users K for certain classical K-user multiple access channels with fixed size (binary) alphabet for inputs, outputs and states. Similarly, in the presence of causal channel state information at the transmitters, quantum entanglement assistance is shown to provide a multiplicative capacity advantage that is unbounded as the size of the state alphabet grows, while the number of users (K=3) and the input and output alphabet (binary) are held fixed. Even with only a few users and small alphabet sizes, substantial multiplicative gains in capacity are found, e.g., with binary inputs, outputs and states, multiplicative gains by factors exceeding 21 and 88 are noted with K=5 and K=7 users, respectively. The gains are robust in the sense that they persist even with noisy quantum resources, e.g., an exponential (in K) capacity advantage from quantum entanglement assistance remains available even if each entangled qubit independently depolarizes completely with probability $\approx$ 30%. The gains are based on quantum entanglement assistance provided only to the transmitters.

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arXiv2026

The Capacity Region of the Multiple Access Channel with Non-Signaling Assistance

The capacity region of the $K$-sender discrete memoryless multiple access channel (MAC) is fully characterized when non-signaling (NS) assistance is available to all $K$ transmitters and the receiver. It is shown to have the same form as the classical capacity region of the MAC, except that the input distribution is allowed to be arbitrarily dependent across the senders. In particular, the NS-assisted capacity region matches the natural generalization to $K$ senders of an outer bound that was previously established by Fawzi and Fermé for $K=2$ senders. Additionally, we provide examples of $K$-sender MACs where the multiplicative gain in capacity from NS-assistance is arbitrarily close to $K$. Combined with an upper bound from prior work, this establishes $K$ as the extremal value of the multiplicative gain from NS-assistance across all $K$-sender MAC settings.

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arXiv2026

Wireless Linear Computation Broadcast

A linear computation broadcast (LCBC) problem comprises $K$ users (receivers) and a transmitter. The users wish to compute various (vector) linear functions of a common dataset, and possess in advance heterogeneous side information corresponding to various other linear computations. The goal for the broadcast transmitter, who knows the dataset and all desired and side-information functions, is to satisfy all demands as efficiently as possible. Prior work has explored the information-theoretic capacity of LCBC for zero-error finite-field computation over an ideal (noiseless) broadcast channel (BC). This paper develops a wireless LCBC (WLCBC) framework for the Gaussian MIMO BC with noisy receiver-side information under a transmit power constraint and arbitrary antenna configurations. In the WLCBC setting, a Gaussian source is linearly precoded for broadcast; each user requests a linear function of the source and forms an estimate by linearly combining its channel observation with its noisy side information. Assuming perfect channel state information, we cast the centralized joint linear transceiver design as a weighted sum-MSE minimization problem and propose an efficient alternating optimization algorithm. For a fixed precoder, the optimal decoders are the linear minimum mean-square error (LMMSE) estimators. For fixed decoders, the precoder update reduces to a convex quadratically constrained quadratic program which leads to a semi-closed-form solution parameterized by a single dual variable. The resulting algorithm guarantees a monotonic decrease in the objective and convergence of the weighted sum-MSE (WSMSE) objective sequence. Simulations demonstrate pronounced robustness gains over natural baselines obtained from prior works.

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arXiv2026

The Capacity Region of the Broadcast Channel with Non-Signaling Assistance

The capacity region of the $K$-user discrete memoryless broadcast channel is fully characterized when non-signaling (NS) assistance is available to the transmitter and all $K$ receivers. The NS-assisted capacity region is shown to coincide with Sato's region, i.e., the region defined by sum-rate bounds over all subsets of messages, where each bound corresponds to full cooperation among that subset of receivers under a worst-case joint channel law consistent with the marginal channels.

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arXiv2026

Non-signaling Assisted Capacity of a Classical Channel with Causal CSIT

The non-signaling (NS) assisted capacity of a classical discrete memoryless channel with causal channel state information at the transmitter (CSIT) is shown to be $C^{NS,ca}=\max_{P_{X|S}}I(X;Y\mid S)$, where $X, Y, S$ correspond to the input, output and state of the channel. Remarkably, this is the same as the capacity of the channel in the NS-assisted non-causal CSIT setting, $C^{NS,nc}=\max_{P_{X|S}}I(X;Y\mid S)$, which was previously established, and also matches the (either classical or with NS assistance) capacity of the channel where the state is available not only (either causally or non-causally) to the transmitter but also to the receiver. While the capacity remains unchanged, the optimal probability of error for fixed message size and blocklength, in the NS-assisted causal CSIT setting can be further improved if channel state is made available to the receiver. This is in contrast to corresponding NS-assisted non-causal CSIT setting where it was previously noted that the optimal probability of error cannot be further improved by providing the state to the receiver. As a separate result we prove that non-signaling assistance, feedback, and strictly causal CSIT (i.e., transmitter knows only past channel states but not the current or future states), each of which is individually already known to not increase capacity, also cannot increase capacity when they are collectively made available to the transmitter.

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arXiv2026

Optimal Average Success Probabilities of Binary $(n,n-1)$ and $(n,n-2)$ Quantum Random Access Codes via a Proof of the Corresponding Conjectured Bound

A binary $(n,m)$ quantum random access code (QRAC) compresses an $n$-bit classical string into an $m$-qubit quantum state, from which a decoder attempts to recover a randomly selected target bit. Of particular interest is the optimal average probability of success, $P^{Q,\mathrm{avg},\mathrm{opt}}_{n,m}$, which is numerically conjectured to satisfy the bound $P^{Q,\mathrm{avg},\mathrm{opt}}_{n,m}\leq \frac{1}{2}+\frac{1}{2}\sqrt{\frac{m}{n}}$. Recent constructions of $(n,n-1)$ QRACs by Suzuki and $(n,n-2)$ QRACs by Akibue et al. meet this bound exactly, raising the question of their strict optimality. In this work, we settle this question by proving the conjectured upper bound for $m\in\{n-1,n-2\}$, thereby precisely determining $P^{Q,\mathrm{avg},\mathrm{opt}}_{n,n-1}$ and $P^{Q,\mathrm{avg},\mathrm{opt}}_{n,n-2}$. The proof utilizes a translation recently studied by Lin and de Wolf from local to global reconstruction via pretty good measurement, along with dimensional and positive-semidefinite constraints on an induced channel.

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arXiv2026

Degrees of Freedom of Over-the-Air Computation over a MIMO Gaussian Network with Two Transmitters and Two Receivers

The fundamental limits of over-the-air computation (AirComp) are explored in a two-transmitter, two-receiver MIMO Gaussian network, where both receivers demand the same aggregation of source symbols originating at the two transmitters. An AirComp degrees of freedom (ACDoF) metric is defined, constrained by an asymptotic mean-squared error threshold. For a generic MIMO setting where the two transmitters are equipped with $M_1, M_2$ antennas, and the two receivers with $N_1, N_2$ antennas, the AirComp DoF value is shown to be almost surely equal to $\min\{M_1,M_2,N_1,N_2,(1/3)\max\{M_1+M_2,N_1+N_2\}\}$. For SISO settings results are extended beyond generic channels to arbitrary channel realizations. For finite signal-to-noise ratio(SNR) settings, an iterative alternating optimization algorithm is explored.

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arXiv2026

Virtual Signaling of CSIT via Non-Signaling Assistance

Non-signaling correlations, which (strictly) include quantum correlations, provide a tractable path to explore the potential impact of quantum nonlocality on the capacity of classical communication networks. Motivated by a recent discovery that certain wireless network settings benefit significantly from non-signaling (NS) correlations, various generalizations are considered. First, it is shown that for a point to point discrete memoryless channel with a non-causal channel state information at the transmitter (CSIT), the NS-assisted Shannon capacity matches the classical (without NS assistance) capacity of the channel for the setting where the state is also made available to the receiver. The key insight is summarized as 'virtual signaling of CSIT via NS-assistance' and is supported by further results as follows. For a discrete memoryless 2-user broadcast channel (BC), the Shannon capacity region with NS-assistance available only between the transmitter and User 1, is found next. Consistent with the aforementioned key insight, the result matches the classical capacity region for the setting where the desired message of User 2 is made available in advance as side-information to User 1. The latter capacity region is known from a result of Kramer and Shamai. Next, for a semi-deterministic BC, the Shannon capacity region with full (tripartite) NS-assistance is shown to be the same as if only bipartite NS-assistance was available between the transmitter and the non-deterministic user. Bipartite NS-assistance between the transmitter and only the deterministic user, does not improve the capacity region relative to the corresponding classical setting. Finally, the analysis is extended to a K-user BC with full NS-assistance among all parties.

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arXiv2026

Quantum Entanglement Assistance Improves the Capacity and Activates the Zero-Error Capacity of Classical Channels with Causal CSIT

For classical point-to-point channels, it has been shown by Bennett et al. that quantum entanglement assistance cannot improve their capacity, and by Cubitt et al. that entanglement assistance cannot activate (increase from zero to non-zero) their zero-error capacity. In contrast, we show that for classical point-to-point channels with causal CSIT (channel state information at the transmitter), quantum entanglement assistance can in some cases improve their capacity, and in some cases activate their zero-error capacity.

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arXiv2025

Can Non-Signaling Assistance Increase the Degrees of Freedom of a Wireless Network?

An open question posed by Fawzi and Ferme [Transactions on Information Theory 2024], asks whether non-signaling (NS) assistance can increase the capacity of a broadcast channel (BC). We answer this question in the affirmative, by showing that for a certain K-receiver BC setting, called Coordinated Multipoint (CoMP) that arises naturally in wireless networks, NS-assistance provides multiplicative gains in capacity and degrees of freedom (DoF), even achieving K-fold improvements in some cases. Somewhat surprisingly, this is shown to be true even for 2-receiver broadcast channels that are semi-deterministic and/or degraded. In a CoMP BC, B single-antenna transmitters, supported by a backhaul that allows them to share data, act as one B-antenna transmitter, to send independent messages to K receivers, each equipped with a single receive antenna. A fixed and globally known connectivity matrix M, specifies for each transmit antenna, the subset of receivers that are connected to (have a non-zero channel coefficient to) that antenna. Besides the connectivity, there is no channel state information at the transmitter. The DoF region is fully characterized for a class of connectivity patterns associated with tree graphs. Sum-capacity with NS-assistance for arbitrary connectivity patterns is bounded below and above by the triangle number and the min-rank of the connectivity matrix, respectively. While translations to Gaussian settings are demonstrated, most of our results are presented under noise-free, finite-field (Fq) models. Converse proofs for classical DoF adapt the Aligned Images bounds to the finite field model. Converse bounds for NS-assisted capacity extend the same-marginals property to the BC with NS-assistance available to all parties. Even stronger (unbounded) gains are established for certain 'communication with side-information' settings, such as the fading dirty paper channel.

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arXiv2025

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

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.

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arXiv2025

On the Capacity of Distributed Quantum Storage

A distributed quantum storage code maps a quantum message to N storage nodes, of arbitrary specified sizes, such that the stored message is robust to an arbitrary specified set of erasure patterns. The sizes of the storage nodes, and erasure patterns may not be homogeneous. The capacity of distributed quantum storage is the maximum feasible size of the quantum message (relative to the sizes of the storage nodes), when the scaling of the size of the message and all storage nodes by the same scaling factor is allowed. Representing the decoding sets as hyperedges in a storage graph, the capacity is characterized for various graphs, including MDS graph, wheel graph, Fano graph, and intersection graph. The achievability is related via quantum CSS codes to a classical secure storage problem. Remarkably, our coding schemes utilize non-trivial alignment structures to ensure recovery and security in the corresponding classical secure storage problem, which leads to similarly non-trivial quantum codes. The converse is based on quantum information inequalities, e.g., strong sub-additivity and weak monotonicity of quantum entropy, tailored to the topology of the storage graphs.

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arXiv2025

On the Capacity of Vector Linear Computation over a Noiseless Quantum Multiple Access Channel with Entangled Transmitters

Network function computation is an active topic in network coding, with much recent progress for linear (over a finite field) computations over broadcast (LCBC) and multiple access (LCMAC) channels. Over a quantum multiple access channel (QMAC) with quantum-entanglement shared among transmitters, the linear computation problem (LC-QMAC) is non-trivial even when the channel is noiseless, because of the challenge of optimally exploiting transmit-side entanglement through distributed coding. Given an arbitrary linear function of data streams defined in a finite field $\mathbb{F}_d$, the LC-QMAC problem seeks the optimal communication cost (minimum number of qudits that need to be sent by the transmitters to the receiver, per computation instance) over a noise-free QMAC, when the independent input data streams originate at the corresponding transmitters, who share quantum entanglement in advance. As our main result, we fully solve this problem for $K=3$ transmitters ($K\geq 4$ settings remain open). Coding schemes based on the $N$-sum box protocol (along with time-sharing and batch-processing) are shown to be information theoretically optimal in all cases.

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arXiv2025

Quantum $X$-Secure $T$-Private Information Retrieval From MDS Coded Storage With Unresponsive and Byzantine Servers

A communication-efficient protocol is introduced over a many-to-one quantum network for Q-E-B-MDS-X-TPIR, i.e., quantum private information retrieval with MDS-$X$-secure storage and $T$-private queries. The protocol is resilient to any set of up to $E$ unresponsive servers (erased servers or stragglers) and any set of up to $B$ Byzantine servers. The underlying coding scheme incorporates an enhanced version of a Cross Subspace Alignment (CSA) code, namely a Modified CSA (MCSA) code, into the framework of CSS codes. The error-correcting capabilities of CSS codes are leveraged to encode the dimensions that carry desired computation results from the MCSA code into the error space of the CSS code, while the undesired interference terms are aligned into the stabilized code space. The challenge is to do this efficiently while also correcting quantum erasures and Byzantine errors. The protocol achieves superdense coding gain over comparable classical baselines for Q-E-B-MDS-X-TPIR, recovers as special cases the state of art results for various other quantum PIR settings previously studied in the literature, and paves the way for applications in quantum coded distributed computation, where CSA code structures are important for communication efficiency, while security and resilience to stragglers and Byzantine servers are critical.

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arXiv2025

On the Capacity of Secure $K$-user Product Computation over a Quantum MAC

Inspired by recent work by Christensen and Popovski on secure $2$-user product computation for finite-fields of prime-order over a quantum multiple access channel, the generalization to $K$ users and arbitrary finite fields is explored. Asymptotically optimal (capacity-achieving for large alphabet) schemes are proposed. Additionally, the capacity of modulo-$d$ ($d\geq 2$) secure $K$-sum computation is shown to be $2/K$ computations/qudit, generalizing a result of Nishimura and Kawachi beyond binary, and improving upon it for odd $K$.

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arXiv2025

Blind Interference Alignment for MapReduce: Exploiting Side-information with Reconfigurable Antennas

In order to explore how blind interference alignment (BIA) schemes may take advantage of side-information in computation tasks, we study the degrees of freedom (DoF) of a $K$ user wireless network setting that arises in full-duplex wireless MapReduce applications. In this setting the receivers are assumed to have reconfigurable antennas and channel knowledge, while the transmitters have neither, i.e., the transmitters lack channel knowledge and are only equipped with conventional antennas. The central ingredient of the problem formulation is the message structure arising out of the Shuffle phase of MapReduce, whereby each transmitter has a subset of messages that need to be delivered to various receivers, and each receiver has a subset of messages available to it in advance as side-information. We approach this problem by decomposing it into distinctive stages that help identify key ingredients of the overall solution. The novel elements that emerge from the first stage, called broadcast with groupcast messages, include an outer maximum distance separable (MDS) code structure at the transmitter, and an algorithm for iteratively determining groupcast-optimal reconfigurable antenna switching patterns at the receiver to achieve intra-message (among the symbols of the same message) alignment. The next stage, called unicast with side-information, reveals optimal inter-message (among symbols of different messages) alignment patterns to exploit side-information, and by a relabeling of messages, connects to the desired MapReduce setting.

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arXiv2025

On the Generic Capacity of $K$-User Symmetric Linear Computation Broadcast

Linear computation broadcast (LCBC) refers to a setting with $d$ dimensional data stored at a central server, where $K$ users, each with some prior linear side-information, wish to retrieve various linear combinations of the data. For each computation instance, the data is represented as a $d$-dimensional vector with elements in a finite field $\mathbb{F}_{p^n}$ where $p^n$ is a power of a prime. The computation is to be performed many times, and the goal is to determine the minimum amount of information per computation instance that must be broadcast to satisfy all the users. The reciprocal of the optimal broadcast cost is the capacity of LCBC. The capacity is known for up to $K=3$ users. Since LCBC includes index coding as a special case, large $K$ settings of LCBC are at least as hard as the index coding problem. Instead of the general setting (all instances), by focusing on the generic setting (almost all instances) this work shows that the generic capacity of the symmetric LCBC (where every user has $m'$ dimensions of side-information and $m$ dimensions of demand) for large number of users ($K>d$ suffices) is $C_g=1/Δ_g$, where $Δ_g=\min\left\{\max\{0,d-m'\}, \frac{dm}{m+m'}\right\}$, is the broadcast cost that is both achievable and unbeatable asymptotically almost surely for large $n$, among all LCBC instances with the given parameters $p,K,d,m,m'$. Relative to baseline schemes of random coding or separate transmissions, $C_g$ shows an extremal gain by a factor of $K$ as a function of number of users, and by a factor of $\approx d/4$ as a function of data dimensions, when optimized over remaining parameters. For arbitrary number of users, the generic capacity of the symmetric LCBC is characterized within a factor of $2$.

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arXiv2025

Capacity of Summation over a Symmetric Quantum Erasure MAC with Partially Replicated Inputs

The optimal quantum communication cost of computing a classical sum of distributed sources is studied over a quantum erasure multiple access channel (QEMAC). K classical messages comprised of finite-field symbols are distributed across $S$ servers, who also share quantum entanglement in advance. Each server $s\in[S]$ manipulates its quantum subsystem $\mathcal{Q}_s$ according to its own available classical messages and sends $\mathcal{Q}_s$ to the receiver who then computes the sum of the messages based on a joint quantum measurement. The download cost from Server $s\in [S]$ is the logarithm of the dimension of $\mathcal{Q}_s$. The rate $R$ is defined as the number of instances of the sum computed at the receiver, divided by the total download cost from all the servers. The main focus is on the symmetric setting with $K= {S \choose α} $ messages where each message is replicated among a unique subset of $α$ servers, and the answers from any $β$ servers may be erased. If no entanglement is initially available to the receiver, then we show that the capacity (maximal rate) is precisely $C= \max\left\{ \min \left\{ \frac{2(α-β)}{S}, \frac{S-2β}{S} \right\}, \frac{α-β}{S} \right\}$. The capacity with arbitrary levels of prior entanglement $(Δ_0)$ between the $S$ data-servers and the receiver is also characterized, by including an auxiliary server (Server $0$) that has no classical data, so that the communication cost from Server $0$ is a proxy for the amount of receiver-side entanglement that is available in advance. The challenge on the converse side resides in the optimal application of the weak monotonicity property, while the achievability combines ideas from classical network coding and treating qudits as classical dits, as well as new constructions based on the $N$-sum box abstraction that rely on absolutely maximally entangled quantum states.

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