arXiv subjects

Farhad Farokhi

Publications and source records attributed to Farhad Farokhi.

At least 19 recordsLinked to original sources

arXiv2026

An Information-Theoretic Principle for Optimal Quantum Encoding: Tight Frames and Equiangular Ensembles

Optimal encoding of classical data for quantum-assisted statistical inference is investigated from an information-theoretic perspective. We prove that the accuracy of any quantum-computing inference procedure is upper bounded by the maximal quantum leakage from the classical data through its quantum encoding, establishing leakage as a universal, task-agnostic quality measure for encoders. The optimal encoding strategy, i.e., an encoding strategy that maximizes the maximal quantum leakage, is proved to be attained by pure states. When there are enough qubits, basis encoding is proved to be universally optimal. However, when the dimension of the system is small, phase encoding is optimal. For the latter, the optimal encoding is not unique. That is, any tight frame, any ensemble whose average state is the maximally mixed state, is in fact optimal. Within tight frames, equiangular tight frames (ETFs) are distinguished as the uniquely symmetric optimal encodings, i.e., they saturate the Welch lower bound on pairwise overlaps. Prominent special cases are the qubit trine, the regular simplex, and symmetric informationally complete positive operator-valued measures (SIC-POVMs), for which the ETF structure and explicit codeword constructions are provided. Numerical examples are presented to validate the theoretical predictions.

quant-ph↗

arXiv2026

Coherence Rather Than Error Rate Governs Privacy in Multi-Tenant Quantum Computing

Multi-tenant computing enables providers of commercial cloud quantum processors to rent disjoint sectors of a device to independent users. Average gate error, which cloud quantum computing providers report, does not determine how much one tenant learns about another. We propose an information-theoretic notion of information leakage across co-tenancy boundaries stemming from quantum state distinguishability. We measure this leakage on commercially-available 156-qubit (IBM Kingston) and 20-qubit (IQM Garnet) devices. Boundaries with identical benchmarked error can offer significantly different amount of information leakage because standard reported measures of error are blind to coherent-versus-stochastic nature of the error while the proposed notion of information leakage is not. A uniform Pauli randomisation implemented over the victim's whole register is used as a defence mechanism to reduce the information leakage to zero. The defence theoretically does not incur a fidelity cost, but the experiments show a non-trivial degradation caused by accumulation of errors. We provide a specific call-for-action to the providers of quantum cloud computing to report information leakage in addition to standard error rates in their device datasheet to enable users to compute privacy and security risks prior to engagement with the device.

quant-ph↗

arXiv2026

Maximal quantum leakage: operational interpretation and quantum channel analysis

Maximal quantum leakage quantifies privacy against adversaries with arbitrary intentions. In this work, we prove that computing this leakage is equivalent to minimum-error quantum state discrimination with equal priors. This establishes a computable operational interpretation, addressing the previous difficulty in computing maximal quantum leakage. We further analyze the impact of collective measurements on multiple copies of a state, demonstrating that leakage increases monotonically with the number of copies, which leads to explicitly characterizing the maximal leakage in the asymptotic limit. Extending this framework to quantum channels, we develop an iterative algorithm for the jointly designing of input states and measurements. Numerical examples involving collective measurements and the maximal channel leakage demonstrate our theoretical findings.

quant-ph↗

arXiv2026

Perturbation Analysis of Maximal Quantum Leakage

Maximal quantum leakage (MQL) is a worst-case information leakage measure that quantifies an adversary's inference advantage gained from accessing quantum encoding of classical data with arbitrary measurements. While MQL admits an exact characterization for a given ensemble of quantum states, its robustness to implementation imperfections has not been systematically studied. In this paper, we analyze the sensitivity of maximal quantum leakage under perturbations of the quantum encoding. We establish a continuity bound in terms of the trace distance between ideal and perturbed quantum states, and show, via an example, that this bound is attainable. We further derive fidelity-based and relative-entropy-based sufficient conditions for bounding the variation of maximal quantum leakage, and illustrate numerically that these conditions can be loose.

quant-ph↗

arXiv2026

Precision and Privacy in Distributed Quantum Sensing: A Quantum Fisher Information Duality

We establish a quantum Fisher information (QFI) duality for distributed quantum sensor networks with local phase encoding. For any $N$-qubit probe state, where $N$ denotes the number of sensors, $F_Q(\boldsymbol{w}^\top \boldsymbolθ) + F_Q(\boldsymbol{v}^\top \boldsymbolθ) \leq N$ for all unit orthogonal sensing directions $\boldsymbol{w}$ and $\boldsymbol{v}$, with equality for all equatorial states when $N=2$ and for Greenberger--Horne--Zeilinger (GHZ) states when $N\geq 2$. Heisenberg-limited precision for direction $\boldsymbol{w}$, $F_Q(\boldsymbol{w}^\top \boldsymbolθ)=N$, saturates the bound and simultaneously forces zero QFI for all other independent directions. This can be interpreted as the condition for parameter privacy in distributed quantum sensing: attaining Heisenberg-limited precision for the sensing target renders all alternative privacy-intrusive estimations impossible.

quant-ph↗

arXiv2025

Generalized collective quantum tomography: algorithm design, optimization, and validation

Quantum tomography is a fundamental technique for characterizing, benchmarking, and verifying quantum states and devices. It plays a crucial role in advancing quantum technologies and deepening our understanding of quantum mechanics. Collective quantum state tomography, which estimates an unknown state \r{ho} through joint measurements on multiple copies $ρ\otimes\cdots\otimesρ$ of the unknown state, offers superior information extraction efficiency. Here we extend this framework to a generalized setting where the target becomes $S_1\otimes\cdots\otimes S_n$, with each $S_i$ representing identical or distinct quantum states, detectors, or processes from the same category. We formulate these tasks as optimization problems and develop three algorithms for collective quantum state, detector and process tomography, respectively, each accompanied by an analytical characterization of the computational complexity and mean squared error (MSE) scaling. Furthermore, we develop optimal solutions of these optimization problems using sum of squares (SOS) techniques with semi-algebraic constraints. The effectiveness of our proposed methods is demonstrated through numerical examples. Additionally, we experimentally demonstrate the algorithms using two-copy collective measurements, where entangled measurements directly provide information about the state purity. Compared to existing methods, our algorithms achieve lower MSEs and approach the collective MSE bound by effectively leveraging purity information.

quant-ph↗

arXiv2025

$α$-leakage Interpretation of Rényi Capacity

For $\tilde{f}(t) = \exp(\frac{α-1}αt)$, this paper shows that the Sibson mutual information is an $α$-leakage averaged over the adversary's $\tilde{f}$-mean relative information gain (on the secret) at elementary event of channel output $Y$ as well as the joint occurrence of elementary channel input $X$ and output $Y$. This interpretation is used to derive a sufficient condition that achieves a $δ$-approximation of $ε$-upper bounded $α$-leakage. A $Y$-elementary $α$-leakage is proposed, extending the existing pointwise maximal leakage to the overall Rényi order range $α\in [0,\infty)$. Maximizing this $Y$-elementary leakage over all attributes $U$ of channel input $X$ gives the Rényi divergence. Further, the Rényi capacity is interpreted as the maximal $\tilde{f}$-mean information leakage over both the adversary's malicious inference decision and the channel input $X$ (represents the adversary's prior belief). This suggests an alternating max-max implementation of the existing generalized Blahut-Arimoto method.

cs.IT↗

arXiv2025

Two-timescale EXTRA for Distributed Smooth Non-convex Optimization

In this paper, we study distributed optimization with smooth non-convex local objectives. We propose a novel variant of the well-known EXact firsT-ordeR Algorithm (EXTRA), called Two-timescale EXTRA, by introducing two distinct step-sizes. Leveraging the two-timescale strategy, we construct a Lyapunov function and establish the sub-linear convergence of Two-timescale EXTRA to a consensual first-order stationary point. Additionally, we introduce an off-line sequential method for algorithm parameter selection, and the numerical results support the theoretical guarantees.

math.OC↗

arXiv2025

Privacy-Preserving State Estimation with Crowd Sensors: An Information-Theoretic Respective

Privacy-preserving state estimation for linear time-invariant dynamical systems with crowd sensors is considered. At any time step, the estimator has access to measurements from a randomly selected sensor from a pool of sensors with pre-specified models and noise profiles. A Luenberger-like observer is used to fuse the measurements with the underlying model of the system to recursively generate the state estimates. An additive privacy-preserving noise is used to constrain information leakage. Information leakage is measured via mutual information between the identity of the sensors and the state estimate conditioned on the actual state of the system. This captures an omnipotent adversary that not only can access state estimates but can also gather direct high-quality state measurements. Any prescribed level of information leakage is shown to be achievable by appropriately selecting the variance of the privacy-preserving noise. Therefore, privacy-utility trade-off can be fine-tuned.

cs.CR↗

arXiv2025

Using Gaussian Mixtures to Model Evolving Multi-Modal Beliefs Across Social Media

We use Gaussian mixtures to model formation and evolution of multi-modal beliefs and opinion uncertainty across social networks. In this model, opinions evolve by Bayesian belief update when incorporating exogenous factors (signals from outside sources, e.g., news articles) and by non-Bayesian mixing dynamics when incorporating endogenous factors (interactions across social media). The modeling enables capturing the richness of behavior observed in multi-modal opinion dynamics while maintaining interpretability and simplicity of scalar models. We present preliminary results on opinion formation and uncertainty to investigate the effect of stubborn individuals (as social influencers). This leads to a notion of centrality based on the ease with which an individual can disrupt the flow of information across the social network.

eess.SY↗

arXiv2025

A DPI-PAC-Bayesian Framework for Generalization Bounds

We develop a unified Data Processing Inequality PAC-Bayesian framework -- abbreviated DPI-PAC-Bayesian -- for deriving generalization error bounds in the supervised learning setting. By embedding the Data Processing Inequality (DPI) into the change-of-measure technique, we obtain explicit bounds on the binary Kullback-Leibler generalization gap for both Rényi divergence and any $f$-divergence measured between a data-independent prior distribution and an algorithm-dependent posterior distribution. We present three bounds derived under our framework using Rényi, Hellinger $p$ and Chi-Squared divergences. Additionally, our framework also demonstrates a close connection with other well-known bounds. When the prior distribution is chosen to be uniform, our bounds recover the classical Occam's Razor bound and, crucially, eliminate the extraneous $\log(2\sqrt{n})/n$ slack present in the PAC-Bayes bound, thereby achieving tighter results. The framework thus bridges data-processing and PAC-Bayesian perspectives, providing a flexible, information-theoretic tool to construct generalization guarantees.

cs.IT↗

arXiv2025

Sample Complexity Bounds for Scalar Parameter Estimation Under Quantum Differential Privacy

This paper presents tight upper and lower bounds for minimum number of samples (copies of a quantum state) required to attain a prescribed accuracy (measured by error variance) for scalar parameters estimation using unbiased estimators under quantum local differential privacy for qubits. Particularly, the best-case (optimal) scenario is considered by minimizing the sample complexity over all differentially-private channels; the worst-case channels can be arbitrarily uninformative and render the problem ill-defined. In the small privacy budget $ε$ regime, i.e., $ε\ll 1$, the sample complexity scales as $Θ(ε^{-2})$. This bound matches that of classical parameter estimation under local differential privacy. The lower bound however loosens in the large privacy budget regime, i.e., $ε\gg 1$. The upper bound for the minimum number of samples is generalized to qudits (with dimension $d$) resulting in sample complexity of $O(dε^{-2})$.

quant-ph↗

arXiv2025

Discerning media bias within a network of political allies: an analytic condition for disruption by partisans

An individual's opinion concerning political bias in the media is shaped by exogenous factors (independent analysis of media outputs) and endogenous factors (social activity, e.g. peer pressure by political allies and opponents in a network). Previous numerical studies show, that persuadable agents in allies-only networks are disrupted from asymptotically learning the intrinsic bias of a media organization, when the network is populated by one or more obdurate agents (partisans), who are not persuadable themselves but exert peer pressure on other agents. Some persuadable agents asymptotically learn a false bias, while others vacillate indefinitely between a false bias and the true bias, a phenomenon called turbulent nonconvergence which also emerges in opponents-only and mixed networks without partisans. Here we derive an analytic instability condition, which demarcates turbulent nonconvergence from asymptotic learning as a function of key network properties, for an idealized model of media bias featuring a biased coin. The condition is verified with Monte Carlo simulations as a function of network size, sparsity, and partisan fraction. It is derived in a probabilistic framework, where an agent's opinion is uncertain and is described by a probability density function, which is multimodal in general, generalizing previous studies which assume that an agent's opinion is certain (i.e. described by one number). The results and their social implications are interpreted briefly in terms of the social science theory of structural balance.

physics.soc-ph↗

arXiv2024

Optimal Universal Quantum Encoding for Statistical Inference

Optimal encoding of classical data for statistical inference using quantum computing is investigated. A universal encoder is sought that is optimal for a wide array of statistical inference tasks. Accuracy of any statistical inference is shown to be upper bounded by a term that is proportional to maximal quantum leakage from the classical data, i.e., the input to the inference model, through its quantum encoding. This demonstrates that the maximal quantum leakage is a universal measure of the quality of the encoding strategy for statistical inference as it only depends on the quantum encoding of the data and not the inference task itself. The optimal universal encoding strategy, i.e., the encoding strategy that maximizes the maximal quantum leakage, is proved to be attained by pure states. When there are enough qubits, basis encoding is proved to be universally optimal. An iterative method for numerically computing the optimal universal encoding strategy is presented.

quant-ph↗

arXiv2024

Measuring Quantum Information Leakage Under Detection Threat

Gentle quantum leakage is proposed as a measure of information leakage to arbitrary eavesdroppers that aim to avoid detection. Gentle (also sometimes referred to as weak or non-demolition) measurements are used to encode the desire of the eavesdropper to evade detection. The gentle quantum leakage meets important axioms proposed for measures of information leakage including positivity, independence, and unitary invariance. Global depolarizing noise, an important family of physical noise in quantum devices, is shown to reduce gentle quantum leakage (and hence can be used as a mechanism to ensure privacy or security). A lower bound for the gentle quantum leakage based on asymmetric approximate cloning is presented. This lower bound relates information leakage to mutual incompatibility of quantum states. A numerical example, based on the encoding in the celebrated BB84 quantum key distribution algorithm, is used to demonstrate the results.

quant-ph↗

arXiv2024

Barycentric and Pairwise Renyi Quantum Leakage

Barycentric and pairwise quantum Renyi leakages are proposed as two measures of information leakage for privacy and security analysis in quantum computing and communication systems. These quantities both require minimal assumptions on the eavesdropper, i.e., they do not make any assumptions on the eavesdropper's attack strategy or the statistical prior on the secret or private classical data encoded in the quantum system. They also satisfy important properties of positivity, independence, post-processing inequality, and unitary invariance. The barycentric quantum Renyi leakage can be computed by solving a semi-definite program and the pairwise quantum Renyi leakage possesses an explicit formula. The barycentric and pairwise quantum Renyi leakages form upper bounds on the maximal quantum leakage, the sandwiched quantum $α$-mutual information, the accessible information, and the Holevo's information. Furthermore, differentially-private quantum channels are shown to bound these measures of information leakage. Global and local depolarizing channels, that are common models of noise in quantum computing and communication, restrict private or secure information leakage. Finally, a privacy-utility trade-off formula in quantum machine learning using variational circuits is developed. The privacy guarantees can only be strengthened, i.e., information leakage can only be reduced, if the performance degradation grows larger and vice versa.

quant-ph↗

arXiv2024

Maximal Information Leakage from Quantum Encoding of Classical Data

A new measure of information leakage for quantum encoding of classical data is defined. An adversary can access a single copy of the state of a quantum system that encodes some classical data and is interested in correctly guessing a general randomized or deterministic function of the data (e.g., a specific feature or attribute of the data in quantum machine learning) that is unknown to the security analyst. The resulting measure of information leakage, referred to as maximal quantum leakage, is the multiplicative increase of the probability of correctly guessing any function of the classical data upon observing measurements of the quantum state. Maximal quantum leakage is shown to satisfy post-processing inequality (i.e., applying a quantum channel reduces information leakage) and independence property (i.e., leakage is zero if the quantum state is independent of the classical data), which are fundamental properties required for privacy and security analysis. It also bounds accessible information. Effects of global and local depolarizing noise models on the maximal quantum leakage are established.

quant-ph↗

arXiv2023

Distributionally-Robust Optimization with Noisy Data for Discrete Uncertainties Using Total Variation Distance

Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost over ambiguity sets, i.e., sets of distributions that are sufficiently compatible with the observed data. In this paper, the ambiguity sets capture the set of probability distributions whose convolution with the noise distribution remains within a ball centered at the empirical noisy distribution of data samples parameterized by the total variation distance. Using the prescribed ambiguity set, the solutions of the distributionally-robust optimizations converge to the solutions of the original stochastic programs when the numbers of the data samples grow to infinity. Therefore, the proposed distributionally-robust optimization problems are asymptotically consistent. This is proved under the assumption that the distribution of the noise is uniformly diagonally dominant. More importantly, the distributionally-robust optimization problems can be cast as tractable convex optimization problems and are therefore amenable to large-scale stochastic problems.

math.OC↗