arXiv subjects

Graeme Smith

Publications and source records attributed to Graeme Smith.

At least 19 recordsLinked to original sources

arXiv2026

Private Correlations Certify Sensing Capability

We show that private correlations in a bipartite quantum state constitute a metrological resource for distributed sensing assisted by a possibly noisy channel from one party to the other. We begin with an example with distillable secret key but poor locally accessible sensing performance and show that an assisting channel substantially improves its performance. We then prove a general theorem showing that positive private information in the encoding basis certifies a quantitative lower bound on the locally accessible sensing capability after assistance. We further show that classical correlations alone provide no analogous guarantee, whereas, in the absence of the assisting subsystem, the privacy-based guarantee reduces to an entanglement-based one. Finally, in a channel formulation, we show that a channel with positive private information allows nonzero locally accessible sensitivity when paired with a suitable assisting channel.

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arXiv2026

Distributed Monogamy of Entanglement limits Quantum Channel Simulation

Entanglement is monogamous: if it is shared among more than two parties, the entanglement between any pair cannot be very strong. For an integer $k\geq 2$, $k$-extendibility of a state $\rho_{AB}$ quantifies this as the number of copies of $B$ that can be simulated by the state's environment. We introduce fractional extendibility, which gives a finer characterization of the quantum correlation that is leaked to the environment, and prove that it is invariant under tensor products and monotonic under local processing. We also establish the distributed monogamy of entanglement: for any state on $AB_1B_2\dots B_n$, the maximum average probability of extracting an EPR pair from a random subset of $k \leq n/2$ systems among the $B_i$'s is the fraction $k/n$. With these tools we resolve a conjecture posed by Matthew Hastings: any quantum erasure channel with erasure probability at least $\frac{1}{2}$ cannot simulate a less noisy erasure channel, even with asymptotically many uses of the noisier channel.

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arXiv2026

Information flow security on persistent memory

Persistent memory is a recently proposed memory paradigm that delivers many system-wide benefits, including improved runtime efficiency and the ability of programs to recover from power outages and system crashes. While recent research has investigated techniques for proving functional correctness of programs running on related architectures, this is not the case for the orthogonal concept of information flow security. In this paper, we provide an information flow logic for an unstructured language (i.e., with gotos rather than loops) modelling a simple assembly language. We apply this logic to x86 assembly using a notion of reordering interference freedom (rif) to reason about potential out-of-order propagation of instructions to memory. We then show how this same notion of rif can be used to similarly reason about information flow on persistent memory.

cs.LO↗

arXiv2026

No-Go Theorem for Gaussian Quantum Repeaters from Fractional Extendibility

Photon loss in optical channels fundamentally limits long-range reliable quantum communication. A standard approach to overcoming this limitation is the use of quantum repeater nodes, which typically perform experimentally demanding non-Gaussian operations. However, whether Gaussian repeater protocols can enhance quantum communication rates over bosonic attenuation channels has remained open. In this work, we prove a no-go theorem for Gaussian quantum repeaters in a quantum network. Specifically, we show that any repeater chain composed of Gaussian operations, homodyne measurements, and arbitrary classical communication cannot enhance the quantum capacity of a pure-loss attenuation channel beyond that achievable by direct transmission. Our proof introduces a generalisation of $k$-extendibility to a notion of fractional extendibility for Gaussian states and establishes some of its useful properties, thereby providing a powerful framework for analysing Gaussian quantum networks.

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arXiv2026

Enhanced quantum capacity thresholds from symmetry

The quantum capacity captures the value of a quantum channel for transmitting quantum information, establishing the fundamental limits on quantum communication. In spite of its central role in quantum information theory, the quantum capacity of most channels is unknown, with wide gaps between the best upper and lower bounds. Even deciding whether a channel has nonzero capacity -- finding its capacity threshold -- is difficult. In this paper we report significant increases in the capacity thresholds of two prototypical noise models: the depolarizing channel and Pauli channels. In the case of the depolarizing channel, this is the first improvement in 18 years, giving a bigger increase beyond the hashing bound than all previous improvements combined. Our starting point is the representation theoretic framework recently proposed by Bhalerao and Leditzky (2025) to compute coherent information for special permutation invariant states. We generalize their framework to the full symmetric subspace, which allow us to optimize coherent information over rank two states in that space. A representation theoretic calculation shows that exponentially many Kraus operators of the channel annihilate the symmetric space, corresponding to a massive decrease in environment entropy for states on the symmetric space compared to the maximally mixed state. This explains the enhanced coherent information as a manifestation of degeneracy for the resulting codes.

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arXiv2026

Single-letter one-way distillable entanglement for non-degradable states

The one-way distillable entanglement is a central operational measure of bipartite entanglement, quantifying the optimal rate at which maximally entangled pairs can be extracted by one-way LOCC. Despite its importance, it is notoriously hard to compute, since it is defined by a regularized optimization over many copies and adaptive one-way protocols. At present, single-letter formulas are only known for (conjugate) degradable and PPT states. More generally, it has remained unclear when one-way distillable entanglement can still be additive beyond degradability and PPT settings, and how such additivity relates to additivity questions of quantum capacity of channels. In this paper, we address this gap by identifying three explicit families of non-degradable and non-PPT states whose one-way distillable entanglement is nevertheless single-letter. First, we introduce two weakened degradability-type conditions--regularized less-noisy and informationally degradable--and prove that each guarantees additivity and hence a single-letter formula. Second, we show a stability result for orthogonally flagged mixtures: when one component has orthogonal support on Alice's system and zero one-way distillable entanglement, the mixture remains single-letter, even though degradability is typically lost under such mixing. Finally, we propose a generalized spin-alignment principle for entropy minimization in tensor-product settings, which we establish in several key cases, including a complete R\'enyi-2 result. As an application, we obtain additivity results for generalized direct-sum channels and their corresponding Choi states.

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arXiv2026

On Error Thresholds for Pauli Channels: Some answers with many more questions

This paper focuses on error thresholds for Pauli channels. We numerically compute lower bounds for the thresholds using the analytic framework of coset weight enumerators pioneered by DiVincenzo, Shor and Smolin in 1998. In particular, we study potential non-additivity of a variety of small stabilizer codes and their concatenations, and report several new concatenated stabilizer codes of small length that show significant non-additivity. We also give a closed form expression of coset weight enumerators of concatenated phase and bit flip repetition codes. Using insights from this formalism, we estimate the threshold for concatenated repetition codes of large lengths. Finally, for several concatenations of small stabilizer codes we optimize for channels which lead to maximal non-additivity at the hashing point of the corresponding channel. We supplement these results with a discussion on the performance of various stabilizer codes from the perspective of the non-additivity and threshold problem. We report both positive and negative results, and highlight some counterintuitive observations, to support subsequent work on lower bounds for error thresholds.

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arXiv2026

Generating Rely-Guarantee Conditions with the Conditional-Writes Domain

Abstract interpretation has been shown to be a promising technique for the thread-modular verification of concurrent programs. Central to this is the generation of interferences, in the form of rely-guarantee conditions, conforming to a user-chosen structure. In this work, we introduce one such structure called the conditional-writes domain, designed for programs where it suffices to establish only the conditions under which particular variables are written to by each thread. We formalise our analysis within a novel abstract interpretation framework that is highly modular and can be easily extended to capture other structures for rely-guarantee conditions. We formalise two versions of our approach and evaluate their implementations on a simple programming language.

cs.LO↗

arXiv2026

Simple broadband signal detection at the fundamental limit

Broadband detection of a weak oscillatory field with unknown carrier frequency underlies magnetometry, axion searches and gravitational-wave sensing. We show that the Grover-like integration-time lower bound for this task is a geometric corollary of an upper bound on the integrated quantum Fisher information and present an all-analog protocol with near-optimal scaling.

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arXiv2025

Quantum $f$-divergences and Their Local Behaviour: An Analysis via Relative Expansion Coefficients

Any reasonable measure of distinguishability of quantum states must satisfy a data processing inequality, that is, it must not increase under the action of a quantum channel. We can ask about the proportion of information lost or preserved and this leads us to study contraction and expansion coefficients respectively, which can be combined into a single \emph{relative expansion coefficient}. We focus on two prominent families: (i) standard quantum $f$ divergences and (ii) their local (second-order) behaviour, which induces a monotone Riemannian semi-norm (that is linked to the $\chi^2$ divergence). Building on prior work, we identify new families of $f$ for which the global ($f$ divergence) and local (Riemannian) relative expansion coefficients coincide for every pair of channels, and we clarify how exceptional such exact coincidences are. Beyond equality, we introduce an \emph{equivalence} framework that transfers qualitative properties such as strict positivity uniformly across different relative expansion coefficients. Leveraging the link between equality in the data processing inequality (DPI) and channel reversibility, we apply our framework of relative expansion coefficients to approximate recoverability of quantum information. Using our relative expansion results for primitive channels, we prove a reverse quantum Markov convergence theorem, converting positive expansion coefficients into quantitative lower bounds on the convergence rate.

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arXiv2025

Secure quantum ranging

Determining and verifying an object's position is a fundamental task with broad practical relevance. We propose a secure quantum ranging protocol that combines quantum ranging with quantum position verification (QPV). Our method achieves Heisenberg-limited precision in position estimation while simultaneously detecting potential cheaters. Two verifiers each send out a state that is entangled in frequency space within a single optical mode. An honest prover only needs to perform simple beam-splitter operations, whereas cheaters are allowed to use arbitrary linear optical operations, one ancillary mode, and perfect quantum memories-though without access to entanglement. Our approach considers a previously unstudied security aspect to quantum ranging. It also provides a framework to quantify the precision with which a prover's position can be verified in QPV, which previously has been assumed to be infinite.

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arXiv2025

Detecting speculative data flow vulnerabilities using weakest precondition reasoning

Speculative execution is a hardware optimisation technique where a processor, while waiting on the completion of a computation required for an instruction, continues to execute later instructions based on a predicted value of the pending computation. It came to the forefront of security research in 2018 with the disclosure of two related attacks, Spectre and Meltdown. Since then many similar attacks have been identified. While there has been much research on using formal methods to detect speculative execution vulnerabilities based on predicted control flow, there has been significantly less on vulnerabilities based on predicted data flow. In this paper, we introduce an approach for detecting the data flow vulnerabilities, Spectre-STL and Spectre-PSF, using weakest precondition reasoning. We validate our approach on a suite of litmus tests used to validate related approaches in the literature.

cs.LO↗

arXiv2025

Gaussian quantum data hiding

Quantum data hiding encodes a hidden classical bit to a pair of quantum states that is difficult to distinguish using a particular set of measurement, denoted as $M$. In this work, we explore quantum data hiding in two contexts involving Gaussian operations or states. First, we consider the set of measurement $M$ as Gaussian local quantum operations and classical communication, a new set of operations not previously discussed in the literature for data hiding. We hide one classical bit in the two different mixture of displaced two-mode squeezed states. Second, we consider the set of measurement $M$ as general Gaussian measurement and construct the data hiding states using two-mode thermal states. This data hiding scheme is effective in the weak strength limit, providing a new example compared to existing discussions for the set of general Gaussian measurement.

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arXiv2025

Measuring Non-Gaussian Magic in Fermions: Convolution, Entropy, and the Violation of Wick's Theorem and the Matchgate Identity

Classically hard to simulate quantum states, or "magic states", are prerequisites to quantum advantage, highlighting an apparent separation between classically and quantumly tractable problems. Classically simulable states such as Clifford circuits on stabilizer states, free bosonic states, free fermions, and matchgate circuits are all in some sense Gaussian. While free bosons and fermions arise from quadratic Hamiltonians, recent works have demonstrated that bosonic and qudit systems converge to Gaussians and stabilizers under convolution. In this work, we similarly identify convolution for fermions and find efficient measures of non-Gaussian magic in pure fermionic states. We demonstrate that three natural notions for the Gaussification of a state, (1) the Gaussian state with the same covariance matrix, (2) the fixed point of convolution, and (3) the closest Gaussian in relative entropy, coincide by proving a central limit theorem for fermionic systems. We then utilize the violation of Wick's theorem and the matchgate identity to quantify non-Gaussian magic in addition to a SWAP test.

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arXiv2024

Uniform Additivity of Tripartite Optimized Correlation Measures

Information theory provides a framework for answering fundamental questions about the optimal performance of many important quantum communication and computational tasks. In many cases, the optimal rates of these tasks can be expressed in terms of regularized formulas that consist of linear combinations of von Neumann entropies optimized over state extensions. However, evaluation of regularized formulas is often intractable, since it involves computing a formula's value in the limit of infinitely many copies of a state. To find optimized, linear entropic functions of quantum states whose regularized versions are tractable to compute, we search for linear combinations of entropies on tripartite quantum states that are additive. We use the method of \cite{cross2017uniform}, which considers bipartite formulas, to identify convex polyhedral cones of uniformly additive \emph{tripartite} correlation measures. We rely only on strong subadditivity of the von Neumann entropy and use these cones to prove that three previously established tripartite optimized correlation measures are additive.

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arXiv2024

Reverse-type Data Processing Inequality

The quantum data processing inequality asserts that two quantum states become harder to distinguish when a noisy channel is applied. On the other hand, a reverse quantum data processing inequality characterizes whether distinguishability is preserved after the application of a noisy channel. In this work, we explore these concepts through contraction and expansion coefficients of the relative entropy of quantum channels. Our first result is that quantum channels with an input dimension greater than or equal to the output dimension do not have a non-zero expansion coefficient, which means that they cannot admit a reverse data-processing inequality. We propose a comparative approach by introducing a relative expansion coefficient, to assess how one channel expands relative entropy compared to another. We show that this relative expansion coefficient is positive for three important classes of quantum channels: depolarizing channels, generalized dephasing channels, and amplitude damping channels. As an application, we give the first rigorous construction of level-1 less noisy quantum channels that are non-degradable.

quant-ph↗

arXiv2024

Additivity of quantum capacities in simple non-degradable quantum channels

Quantum channel capacities give the fundamental performance limits for information flow over a communication channel. However, the prevalence of superadditivity is a major obstacle to understanding capacities, both quantitatively and conceptually. In contrast, examples exhibiting additivity, though relatively rare, offer crucial insights into the origins of nonadditivity and form the basis of our strongest upper bounds on capacity. Degradable channels, whose coherent information is provably additive, stand out as among the few classes of channels for which the quantum capacity is exactly computable. In this paper, we introduce two families of non-degradable channels whose coherent information remains additive, making their quantum capacities tractable. First, we demonstrate that channels capable of ``outperforming" their environment, under conditions weaker than degradability, can exhibit either strong or weak additivity of coherent information. Second, we explore a complementary construction that modifies a channel to preserve coherent information additivity while destroying the ``outperforming" property. We analyze how structural constraints guarantee strong and weak additivity and investigate how relaxing these constraints leads to the failure of strong additivity, with weak additivity potentially persisting.

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arXiv2024

Security Assumptions in Dispersive-Optics QKD

Quantum key distribution (QKD) seeks to provide a method of generating cryptographically-secure keys between remote parties while guaranteeing unconditional security. Implementations of high-dimensional QKD using dispersive-optics (DO-QKD) have been proposed to allow for multiple secure bits to be transmitted per photon while remaining cost-effective and scalable using existing telecommunication technology [1]. In the recent literature, there have been a number of experimental realizations of DO-QKD systems [2-6], with security analysis based on the treatment in Ref. [1]. Here we demonstrate that in the case of finite dispersion, the model assumed for the eavesdropper's attack in Ref. [1] is non-optimal for the eavesdropper, which leads to a significant overestimation of the secure key rate between parties. We consider an alternative attack model that Alice and Bob find indistinguishable from the Ref. [1] model, as long as they are restricted to making the measurements typical in DO-QKD. We provide concrete examples where a significant gap exists between the Holevo information, and therefore the secret key rate, predicted by the two models. We further analyze the experiment in Ref. [2] as an example of a case where secure key is predicted according to the Ref. [1] model, but where in fact there is zero secure key rate when considering the full set of collective attacks that an eavesdropper may perform.

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