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Ashwin Nayak

Publications and source records attributed to Ashwin Nayak.

At least 19 recordsLinked to original sources
arXiv2026

An exponential separation between entanglement-assisted and unassisted one-way quantum communication

A longstanding question in quantum communication complexity is whether some task can be accomplished with a small amount of communication in the presence of entanglement, yet require much more quantum communication in the absence of entanglement. Separations of this nature were previously known for relational problems and, in the simultaneous message passing model, for partial functions. But it has remained unresolved whether any such separation exists for a total Boolean function. We resolve this question with an exponential separation in the one-way setting: we exhibit a family of total Boolean functions $f_n\colon \{0,1\}^n \times \{0,1\}^n \to \{0,1\}$ that can be computed with $O(\log n)$ bits of one-way classical communication given prior entanglement, but that require $Ω(n^{1/3})$ qubits of one-way quantum communication without entanglement. Our function is a special case of the subgroup membership problem, first studied in the communication setting by Aaronson, Le Gall, Russell, and Tani.

quant-ph↗
arXiv2026

Optimal Low-Rank Quantum State Tomography with Bounded-Sample Joint Measurements

We determine the optimal sample complexity of low-rank quantum state tomography when each measurement may act jointly on at most $t$ samples. For sufficiently small $\varepsilon$, estimating an unknown state on $\mathbb{C}^d$ of rank at most $r$ to trace norm error $\varepsilon$ with constant success probability requires, and is achievable with, $$ Θ\left( \frac{dr}{\varepsilon^2} \max\left\{1,\frac r{\sqrt t}\right\} \right)$$ samples. The lower bound allows the protocol to choose each joint measurement adaptively using all previous classical outcomes; the matching upper bound is nonadaptive. Thus joint measurements on at most $t$ samples improve the complexity of algorithms making single-sample measurements by at most a factor $\sqrt t$. Further, measuring order $r^2$ samples jointly is necessary and sufficient to attain the unrestricted collective rate. For the lower bound, we vary the support of a state with fixed uniform spectrum and bound the Fisher information trace of every joint measurement on $t$ samples. The adaptive Fisher chain rule and the van Trees inequality then give the trace norm lower bound. For the upper bound, we construct and analyze a nonadaptive tomography protocol based on a Gaussian joint measurement. An explicit second moment identity and a conditional Gaussian law outside the state's support give a rank-dependent error analysis, yielding the matching rate.

quant-ph↗
arXiv2026

PhysicianBench: Evaluating LLM Agents in Real-World EHR Environments

We introduce PhysicianBench, a benchmark for evaluating LLM agents on physician tasks grounded in real clinical setting within electronic health record (EHR) environments. Existing medical agent benchmarks primarily focus on static knowledge recall, single-step atomic actions, or action intent without verifiable execution against the environment. As a result, they fail to capture the long-horizon, composite workflows that characterize real clinical systems. PhysicianBench comprises 100 long-horizon tasks adapted from real consultation cases between primary care and subspecialty physicians, with each task independently reviewed by a separate panel of physicians. Tasks are instantiated in an EHR environment with real patient records and accessed through the same standard APIs used by commercial EHR vendors. Tasks span 21 specialties (e.g., cardiology, endocrinology, oncology, psychiatry) and diverse workflow types (e.g., diagnosis interpretation, medication prescribing, treatment planning), requiring an average of 27 tool calls per task. Solving each task requires retrieving data across encounters, reasoning over heterogeneous clinical information, executing consequential clinical actions, and producing clinical documentation. Each task is decomposed into structured checkpoints (670 in total across the benchmark) capturing distinct stages of completion graded by task-specific scripts with execution-grounded verification. Across 13 proprietary and open-source LLM agents, the best-performing model achieves only 46% success rate (pass@1), while open-source models reach at most 19%, revealing a substantial gap between current agent capabilities and the demands of real-world clinical workflows. PhysicianBench provides a realistic and execution-grounded benchmark for measuring progress toward autonomous clinical agents.

cs.AI↗
arXiv2026

Quaternionic Perfect Sequences and Hadamard Matrices

A finite sequence of numbers is perfect if it has zero periodic autocorrelation after a nontrivial cyclic shift. In this work, we study quaternionic perfect sequences having a one-to-one correspondence with the binary sequences arising in Williamson's construction of quaternion-type Hadamard matrices. Using this correspondence, we devise an enumeration algorithm that is significantly faster than previously used algorithms and does not require the sequences to be symmetric. We implement our algorithm and use it to enumerate all circulant and possibly non-symmetric Williamson-type matrices of orders up to 21; previously, the largest order exhaustively enumerated was 13. We prove that when the blocks of a quaternion-type Hadamard matrix are circulant, the blocks are necessarily pairwise amicable. This dramatically improves the filtering power of our algorithm: in order 20, the number of block pairs needing consideration is reduced by a factor of over 25,000. We use our results to construct quaternionic Hadamard matrices of interest in quantum communication and prove they are not equivalent to those constructed by other means. We also study the properties of quaternionic Hadamard matrices analytically, and demonstrate the feasibility of characterizing quaternionic Hadamard matrices with a fixed pattern of entries. These results indicate a richer set of properties and suggest an abundance of quaternionic Hadamard matrices for sufficiently large orders.

math.CO↗
arXiv2025

Lower Bounds for Learning Quantum States with Single-Copy Measurements

We study the problems of quantum tomography and shadow tomography using measurements performed on individual, identical copies of an unknown $d$-dimensional state. We first revisit a known lower bound due to Haah et al. (2017) on quantum tomography with accuracy $ε$ in trace distance, when the measurements choices are independent of previously observed outcomes (i.e., they are nonadaptive). We give a succinct proof of this result. This leads to stronger lower bounds when the learner uses measurements with a constant number of outcomes. In particular, this rigorously establishes the optimality of the folklore ``Pauli tomography" algorithm in terms of its sample complexity. We also derive novel bounds of $Ω(r^2 d/ε^2)$ and $Ω(r^2 d^2/ε^2)$ for learning rank $r$ states using arbitrary and constant-outcome measurements, respectively, in the nonadaptive case. In addition to the sample complexity, a resource of practical significance for learning quantum states is the number of different measurements used by an algorithm. We extend our lower bounds to the case where the learner performs possibly adaptive measurements from a fixed set of $\exp(O(d))$ measurements. This implies in particular that adaptivity does not give us any advantage using single-copy measurements that are efficiently implementable. We also obtain a similar bound in the case where the goal is to predict the expectation values of a given sequence of observables, a task known as shadow tomography. Finally, in the case of adaptive, single-copy measurements implementable with polynomial-size circuits, we prove that a straightforward strategy based on computing sample means of the given observables is optimal.

quant-ph↗
arXiv2025

MedHELM: Holistic Evaluation of Large Language Models for Medical Tasks

While large language models (LLMs) achieve near-perfect scores on medical licensing exams, these evaluations inadequately reflect the complexity and diversity of real-world clinical practice. We introduce MedHELM, an extensible evaluation framework for assessing LLM performance for medical tasks with three key contributions. First, a clinician-validated taxonomy spanning 5 categories, 22 subcategories, and 121 tasks developed with 29 clinicians. Second, a comprehensive benchmark suite comprising 35 benchmarks (17 existing, 18 newly formulated) providing complete coverage of all categories and subcategories in the taxonomy. Third, a systematic comparison of LLMs with improved evaluation methods (using an LLM-jury) and a cost-performance analysis. Evaluation of 9 frontier LLMs, using the 35 benchmarks, revealed significant performance variation. Advanced reasoning models (DeepSeek R1: 66% win-rate; o3-mini: 64% win-rate) demonstrated superior performance, though Claude 3.5 Sonnet achieved comparable results at 40% lower estimated computational cost. On a normalized accuracy scale (0-1), most models performed strongly in Clinical Note Generation (0.73-0.85) and Patient Communication & Education (0.78-0.83), moderately in Medical Research Assistance (0.65-0.75), and generally lower in Clinical Decision Support (0.56-0.72) and Administration & Workflow (0.53-0.63). Our LLM-jury evaluation method achieved good agreement with clinician ratings (ICC = 0.47), surpassing both average clinician-clinician agreement (ICC = 0.43) and automated baselines including ROUGE-L (0.36) and BERTScore-F1 (0.44). Claude 3.5 Sonnet achieved comparable performance to top models at lower estimated cost. These findings highlight the importance of real-world, task-specific evaluation for medical use of LLMs and provides an open source framework to enable this.

cs.CL↗
arXiv2024

Proper vs Improper Quantum PAC learning

A basic question in the PAC model of learning is whether proper learning is harder than improper learning. In the classical case, there are examples of concept classes with VC dimension $d$ that have sample complexity $Ω\left(\frac dε\log\frac1ε\right)$ for proper learning with error $ε$, while the complexity for improper learning is O$\!\left(\frac dε\right)$. One such example arises from the Coupon Collector problem. Motivated by the efficiency of proper versus improper learning with quantum samples, Arunachalam, Belovs, Childs, Kothari, Rosmanis, and de Wolf (TQC 2020) studied an analogue, the Quantum Coupon Collector problem. Curiously, they discovered that for learning size $k$ subsets of $[n]$ the problem has sample complexity $Θ(k\log\min\{k,n-k+1\})$, in contrast with the complexity of $Θ(k\log k)$ for Coupon Collector. This effectively negates the possibility of a separation between the two modes of learning via the quantum problem, and Arunachalam et al.\ posed the possibility of such a separation as an open question. In this work, we first present an algorithm for the Quantum Coupon Collector problem with sample complexity that matches the sharper lower bound of $(1-o_k(1))k\ln\min\{k,n-k+1\}$ shown recently by Bab Hadiashar, Nayak, and Sinha (IEEE TIT 2024), for the entire range of the parameter $k$. Next, we devise a variant of the problem, the Quantum Padded Coupon Collector. We prove that its sample complexity matches that of the classical Coupon Collector problem for both modes of learning, thereby exhibiting the same asymptotic separation between proper and improper quantum learning as mentioned above. The techniques we develop in the process can be directly applied to any form of padded quantum data. We hope that padding can more generally lift other forms of classical learning behaviour to the quantum setting.

quant-ph↗
arXiv2024

Optimal lower bounds for Quantum Learning via Information Theory

Although a concept class may be learnt more efficiently using quantum samples as compared with classical samples in certain scenarios, Arunachalam and de Wolf (JMLR, 2018) proved that quantum learners are asymptotically no more efficient than classical ones in the quantum PAC and Agnostic learning models. They established lower bounds on sample complexity via quantum state identification and Fourier analysis. In this paper, we derive optimal lower bounds for quantum sample complexity in both the PAC and agnostic models via an information-theoretic approach. The proofs are arguably simpler, and the same ideas can potentially be used to derive optimal bounds for other problems in quantum learning theory. We then turn to a quantum analogue of the Coupon Collector problem, a classic problem from probability theory also of importance in the study of PAC learning. Arunachalam, Belovs, Childs, Kothari, Rosmanis, and de Wolf (TQC, 2020) characterized the quantum sample complexity of this problem up to constant factors. First, we show that the information-theoretic approach mentioned above provably does not yield the optimal lower bound. As a by-product, we get a natural ensemble of pure states in arbitrarily high dimensions which are not easily (simultaneously) distinguishable, while the ensemble has close to maximal Holevo information. Second, we discover that the information-theoretic approach yields an asymptotically optimal bound for an approximation variant of the problem. Finally, we derive a sharper lower bound for the Quantum Coupon Collector problem, via the generalized Holevo-Curlander bounds on the distinguishability of an ensemble. All the aspects of the Quantum Coupon Collector problem we study rest on properties of the spectrum of the associated Gram matrix, which may be of independent interest.

quant-ph↗
arXiv2023

MedAlign: A Clinician-Generated Dataset for Instruction Following with Electronic Medical Records

The ability of large language models (LLMs) to follow natural language instructions with human-level fluency suggests many opportunities in healthcare to reduce administrative burden and improve quality of care. However, evaluating LLMs on realistic text generation tasks for healthcare remains challenging. Existing question answering datasets for electronic health record (EHR) data fail to capture the complexity of information needs and documentation burdens experienced by clinicians. To address these challenges, we introduce MedAlign, a benchmark dataset of 983 natural language instructions for EHR data. MedAlign is curated by 15 clinicians (7 specialities), includes clinician-written reference responses for 303 instructions, and provides 276 longitudinal EHRs for grounding instruction-response pairs. We used MedAlign to evaluate 6 general domain LLMs, having clinicians rank the accuracy and quality of each LLM response. We found high error rates, ranging from 35% (GPT-4) to 68% (MPT-7B-Instruct), and an 8.3% drop in accuracy moving from 32k to 2k context lengths for GPT-4. Finally, we report correlations between clinician rankings and automated natural language generation metrics as a way to rank LLMs without human review. We make MedAlign available under a research data use agreement to enable LLM evaluations on tasks aligned with clinician needs and preferences.

cs.CL↗
arXiv2023

Methods to Estimate Large Language Model Confidence

Large Language Models have difficulty communicating uncertainty, which is a significant obstacle to applying LLMs to complex medical tasks. This study evaluates methods to measure LLM confidence when suggesting a diagnosis for challenging clinical vignettes. GPT4 was asked a series of challenging case questions using Chain of Thought and Self Consistency prompting. Multiple methods were investigated to assess model confidence and evaluated on their ability to predict the models observed accuracy. The methods evaluated were Intrinsic Confidence, SC Agreement Frequency and CoT Response Length. SC Agreement Frequency correlated with observed accuracy, yielding a higher Area under the Receiver Operating Characteristic Curve compared to Intrinsic Confidence and CoT Length analysis. SC agreement is the most useful proxy for model confidence, especially for medical diagnosis. Model Intrinsic Confidence and CoT Response Length exhibit a weaker ability to differentiate between correct and incorrect answers, preventing them from being reliable and interpretable markers for model confidence. We conclude GPT4 has a limited ability to assess its own diagnostic accuracy. SC Agreement Frequency is the most useful method to measure GPT4 confidence.

cs.CL↗
arXiv2023

Mutually Unbiased Measurements, Hadamard Matrices, and Superdense Coding

Mutually unbiased bases (MUBs) are highly symmetric bases on complex Hilbert spaces, and the corresponding rank-1 projective measurements are ubiquitous in quantum information theory. In this work, we study a recently introduced generalization of MUBs called mutually unbiased measurements (MUMs). These measurements inherit the essential property of complementarity from MUBs, but the Hilbert space dimension is no longer required to match the number of outcomes. This operational complementarity property renders MUMs highly useful for device-independent quantum information processing. It has been shown that MUMs are strictly more general than MUBs. In this work we provide a complete proof of the characterization of MUMs that are direct sums of MUBs. We then proceed to construct new examples of MUMs that are not direct sums of MUBs. A crucial technical tool for these construction is a correspondence with quaternionic Hadamard matrices, which allows us to map known examples of such matrices to MUMs that are not direct sums of MUBs. Furthermore, we show that -- in stark contrast with MUBs -- the number of MUMs for a fixed outcome number is unbounded. Next, we focus on the use of MUMs in quantum communication. We demonstrate how any pair of MUMs with d outcomes defines a d-dimensional superdense coding protocol. Using MUMs that are not direct sums of MUBs, we disprove a recent conjecture due to Nayak and Yuen on the rigidity of superdense coding for infinitely many dimensions. The superdense coding protocols arising in the refutation reveal how shared entanglement may be used in a manner heretofore unknown.

quant-ph↗
arXiv2023

One-shot quantum state redistribution and quantum Markov chains

We revisit the task of quantum state redistribution in the one-shot setting, and design a protocol for this task with communication cost in terms of a measure of distance from quantum Markov chains. More precisely, the distance is defined in terms of quantum max-relative entropy and quantum hypothesis testing entropy. Our result is the first to operationally connect quantum state redistribution and quantum Markov chains, and can be interpreted as an operational interpretation for a possible one-shot analogue of quantum conditional mutual information. The communication cost of our protocol is lower than all previously known ones and asymptotically achieves the well-known rate of quantum conditional mutual information. Thus, our work takes a step towards the important open question of near-optimal characterization of the one-shot quantum state redistribution.

quant-ph↗
arXiv2023

Diagnostic Reasoning Prompts Reveal the Potential for Large Language Model Interpretability in Medicine

One of the major barriers to using large language models (LLMs) in medicine is the perception they use uninterpretable methods to make clinical decisions that are inherently different from the cognitive processes of clinicians. In this manuscript we develop novel diagnostic reasoning prompts to study whether LLMs can perform clinical reasoning to accurately form a diagnosis. We find that GPT4 can be prompted to mimic the common clinical reasoning processes of clinicians without sacrificing diagnostic accuracy. This is significant because an LLM that can use clinical reasoning to provide an interpretable rationale offers physicians a means to evaluate whether LLMs can be trusted for patient care. Novel prompting methods have the potential to expose the black box of LLMs, bringing them one step closer to safe and effective use in medicine.

cs.CL↗
arXiv2023

Rigidity of superdense coding

The famous superdense coding protocol of Bennett and Wiesner demonstrates that it is possible to communicate two bits of classical information by sending only one qubit and using a shared EPR pair. Our first result is that an arbitrary protocol for achieving this task (where there are no assumptions on the sender's encoding operations or the dimension of the shared entangled state) is locally equivalent to the canonical Bennett-Wiesner protocol. In other words, the superdense coding task is rigid. In particular, we show that the sender and receiver only use additional entanglement (beyond the EPR pair) as a source of classical randomness. We also investigate several questions about higher-dimensional superdense coding, where the goal is to communicate one of $d^2$ possible messages by sending a $d$-dimensional quantum state, for general dimensions $d$. Unlike the $d=2$ case (i.e. sending a single qubit), there can be inequivalent superdense coding protocols for higher $d$. We present concrete constructions of inequivalent protocols, based on constructions of inequivalent orthogonal unitary bases for all $d > 2$. Finally, we analyze the performance of superdense coding protocols where the encoding operators are independently sampled from the Haar measure on the unitary group. Our analysis involves bounding the distinguishability of random maximally entangled states, which may be of independent interest.

quant-ph↗
arXiv2022

Augmented Index and Quantum Streaming Algorithms for DYCK(2)

We show how two recently developed quantum information theoretic tools can be applied to obtain lower bounds on quantum information complexity. We also develop new tools with potential for broader applicability, and use them to establish a lower bound on the quantum information complexity for the Augmented Index function on an easy distribution. This approach allows us to handle superpositions rather than distributions over inputs, the main technical challenge faced previously. By providing a quantum generalization of the argument of Jain and Nayak [IEEE TIT'14], we leverage this to obtain a lower bound on the space complexity of multi-pass, unidirectional quantum streaming algorithms for the DYCK(2) language.

quant-ph↗
arXiv2022

Deterministic Algorithms for the Hidden Subgroup Problem

We present deterministic algorithms for the Hidden Subgroup Problem. The first algorithm, for abelian groups, achieves the same asymptotic worst-case query complexity as the optimal randomized algorithm, namely O($\sqrt{ n}\,$), where $n$ is the order of the group. The analogous algorithm for non-abelian groups comes within a $\sqrt{ \log n}$ factor of the optimal randomized query complexity. The best known randomized algorithm for the Hidden Subgroup Problem has expected query complexity that is sensitive to the input, namely O($\sqrt{ n/m}\,$), where $m$ is the order of the hidden subgroup. In the first version of this article (arXiv:2104.14436v1 [cs.DS]), we asked if there is a deterministic algorithm whose query complexity has a similar dependence on the order of the hidden subgroup. Prompted by this question, Ye and Li (arXiv:2110.00827v1 [cs.DS]) present deterministic algorithms for abelian groups which solve the problem with O($\sqrt{ n/m }\,$ ) queries, and find the hidden subgroup with O($\sqrt{ n (\log m) / m} + \log m$) queries. Moreover, they exhibit instances which show that in general, the deterministic query complexity of the problem may be o($\sqrt{ n/m } \,$), and that of finding the entire subgroup may also be o($\sqrt{ n/m } \,$) or even $ω(\sqrt{ n/m } \,)$. We present a different deterministic algorithm for the Hidden Subgroup Problem that also has query complexity O($\sqrt{ n/m }\,$) for abelian groups. The algorithm is arguably simpler. Moreover, it works for non-abelian groups, and has query complexity O($\sqrt{ (n/m) \log (n/m) }\,$) for a large class of instances, such as those over supersolvable groups. We build on this to design deterministic algorithms to find the hidden subgroup for all abelian and some non-abelian instances, at the cost of a $\log m$ multiplicative factor increase in the query complexity.

cs.DS↗
arXiv2022

Quantum Distributed Complexity of Set Disjointness on a Line

Set Disjointness on a Line is a variant of the Set Disjointness problem in a distributed computing scenario with $d+1$ processors arranged on a path of length $d$. It was introduced by Le Gall and Magniez (PODC 2018) for proving lower bounds on the quantum distributed complexity of computing the diameter of an arbitrary network in the CONGEST model. However, they were only able to provide a lower bound when the local memory used by the processors on the intermediate vertices of the path consists of O$( \log n)$ qubits for $n$-bit inputs. We prove an unconditional lower bound of $\widetildeΩ\big(\sqrt[3]{n d^2}+\sqrt{n} \, \big)$ rounds for Set Disjointness on a Line with $d + 1$ processors. The result gives us a new lower bound of $\widetildeΩ \big( \sqrt[3]{nδ^2}+\sqrt{n} \, \big)$ on the number of rounds required for computing the diameter $δ$ of any $n$-node network with quantum messages of size O$(\log n)$ in the CONGEST model. We draw a connection between the distributed computing scenario above and a new model of query complexity. The information-theoretic technique we use for deriving the round lower bound for Set Disjointness on a Line also applies to the number of rounds in this query model. We provide an algorithm for Set Disjointness in this query model with round complexity that matches the round lower bound stated above, up to a polylogarithmic factor. This presents a barrier for obtaining a better round lower bound for Set Disjointness on the Line. At the same time, it hints at the possibility of better communication protocols for the problem.

quant-ph↗
arXiv2020

On the Entanglement Cost of One-Shot Compression

We revisit the task of visible compression of an ensemble of quantum states with entanglement assistance in the one-shot setting. The protocols achieving the best compression use many more qubits of shared entanglement than the number of qubits in the states in the ensemble. Other compression protocols, with potentially larger communication cost, have entanglement cost bounded by the number of qubits in the given states. This motivates the question as to whether entanglement is truly necessary for compression, and if so, how much of it is needed. Motivated by questions in communication complexity, we lift certain restrictions that are placed on compression protocols in tasks such as state-splitting and channel simulation. We show that an ensemble of the form designed by Jain, Radhakrishnan, and Sen (ICALP'03) saturates the known bounds on the sum of communication and entanglement costs, even with the relaxed compression protocols we study. The ensemble and the associated one-way communication protocol have several remarkable properties. The ensemble is incompressible by more than a constant number of qubits without shared entanglement, even when constant error is allowed. Moreover, in the presence of shared entanglement, the communication cost of compression can be arbitrarily smaller than the entanglement cost. The quantum information cost of the protocol can thus be arbitrarily smaller than the cost of compression without shared entanglement. The ensemble can also be used to show the impossibility of reducing, via compression, the shared entanglement used in two-party protocols for computing Boolean functions.

quant-ph↗