arXiv subjects

Graeme Smith

Publications and source records attributed to Graeme Smith.

At least 19 recordsLinked to original sources

arXiv2026

No advantage from classical assistance for energy-constrained bosonic dephasing channels

We prove that four capacities of single-mode bosonic dephasing channels coincide under an average photon-number constraint: the unassisted quantum capacity, the unassisted private capacity, the two-way classically assisted quantum capacity, and the two-way public-classically assisted private capacity. The assistance may be interactive: the parties can exchange classical messages between channel uses and choose subsequent inputs based on earlier outcomes. For every finite value of the constraint, their common value is the coherent information optimized over Fock-diagonal input states satisfying the constraint. The proof uses a relative entropy comparison with the completely dephasing channel to derive chain rules for the Rains relative entropy and the relative entropy of entanglement. These chain rules give an upper bound on the rates achievable by adaptive protocols whose mean input photon number is constrained on average over all channel uses. We also show that both chain rules are attained by canonical purifications of finite-energy Fock-diagonal states.

quant-ph↗

arXiv2026

Nonadditivity in fermionic quantum Shannon theory

We study collective state preparation and channel encoding in fermionic systems under parity superselection and composition governed by the canonical anticommutation relations. For a two-mode Gaussian state $τ$, we obtain the exact entanglement of formation, $E_{\mathrm F}^{\mathrm{phys}}(τ^{\otimes m})=\lceil m/2\rceil\log2$ for every $m\geq1$. Two copies have the same formation value as one, violating additivity and strong superadditivity, while regularization halves the single-copy value. For an associated Gaussian channel, we determine the minimum output entropy and Holevo information at every blocklength and prove nonadditivity of both. Together, these results give exact answers to the fermionic counterparts of the four additivity questions associated with Shor and Hastings. One physical use carries no classical information, whereas two uses transmit one bit perfectly. The unassisted classical and zero-error classical capacities both equal one half bit per mode. A sharp finite-block bound gives a strong converse: the decoding success probability vanishes at every rate above capacity. These optimizations cover all physical pure-state decompositions and channel inputs, with Gaussian ensembles and classical codes attaining the optima. The formation and minimum output entropy formulas hold for every Rényi order $α\in(0,\infty]$. We also determine the unassisted quantum and zero-error quantum capacities, both equal to one half logical qubit per mode, and prove a strong converse: entanglement fidelity vanishes at every rate above capacity. For a noisy Gaussian family, we determine the one- and two-copy formation values and prove strict nonadditivity at full rank. For $τ$, Bell violation under local parity-preserving measurements first appears at three copies.

quant-ph↗

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 show that any shared state yielding positive private information can serve as a sensing resource after appropriate local coherent processing, and derive a quantitative lower bound on the locally accessible sensing capability after assistance. We further show that classical correlations alone provide no analogous guarantee. 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.

quant-ph↗

arXiv2026

What Must a Quantum-Memory Decoder Know About Temporally Correlated Noise?

What must a quantum error-correction decoder know about temporally correlated noise, and what does it cost to learn? We study this question for fixed stabilizer memory experiments with known system-environment interactions. We formulate calibration in terms of the fidelity differences that select a Pauli recovery and relate missing information to the resulting fidelity loss. Our main example uses weak coherent $X$ rotations in a class of CSS codes including Shor, Steane, and odd-distance rotated surface codes. All physical qubits share a sign either fixed throughout a run or independently redrawn each interval. The two models have identical syndrome statistics and the same spatiotemporal Pauli process (SPP), obtained by Pauli-twirling every noise interval. Yet at suitable storage times, they require different logical corrections. In the weak-noise limit, each model is almost perfectly correctable when known. Without model information, even the best final recovery has a worst-case fidelity loss approaching $1/2$ relative to the noise-aware optimum, despite access to the full syndrome record. For this pair of models, at fixed code and fixed positive target loss below $1/2$, we prove matching calibration bounds. With logical preparation and final readout, complete QEC cycles require a number of noise intervals scaling as the inverse rotation angle raised to the code's $X$ distance. Allowing two uninterrupted intervals before one extraction reduces the optimal cost to inverse-square scaling. Physical Pauli twirling of every noise interval changes both recovery performance and its information requirements. Discarding the record of applied random Pauli operations makes the SPP sufficient for optimal recovery. Keeping this record can improve the attainable fidelity, but reaching that optimum may require additional noise information.

quant-ph↗

arXiv2026

A depolarizing choir sings in Gaussian harmony

We study the noise threshold for positive quantum capacity for the qubit depolarizing channel. We explore analytically the action of the qubit depolarizing channel on the symmetric subspaces of the input qubits, in the limit of asymptotically many uses of the channel. We observe the emergence of a bosonic Gaussian channel. Furthermore, the codes previously developed for the depolarizing channel can be translated to codes for the emergent Gaussian channel, and it is easier to further optimize these codes for the simpler emergent Gaussian channel. Translating these codes back to the depolarizing channel leads to extremely good input states for the coherent information of the depolarizing channel producing new lower bounds on the noise threshold for positive capacity. In addition to improved lower bounds on the threshold, this newly found link between depolarizing noise and Gaussian channels offers a novel perspective contributing to our understanding of these symmetric codes.

quant-ph↗

arXiv2026

From Permutation Symmetry to Communication Bounds and Additivity

Correlations across channel uses can improve quantum communication rates, making optimization over arbitrarily large blocks a central difficulty in determining quantum capacity. We show how full permutation invariance limits this advantage for every finite-dimensional memoryless channel. The optimized coherent information per use converges to the single-use maximum and consequently attains its supremum at a finite block length. Thus finite-block superadditivity remains possible, while the asymptotic optimization reduces to a single channel use. We also establish a strong converse for pure-source entanglement generation with permutation-invariant inputs: at any fixed rate above the single-use coherent-information maximum, the fidelity tends to zero. Beyond these communication bounds, we identify a common structure underlying completely bounded norms and the sandwiched Rényi channel quantities governing discrimination against a replacer and entanglement-assisted communication. De Finetti reduction and permutation covariance yield systematic alternative proofs of their known multiplicativity and additivity results within a shared variational framework. We further show that, for permutation-invariant inputs, correlations cannot sustain an asymptotic reduction in output entropy per use below the single-use minimum. This entropy limit holds for Rényi orders greater than one and for the von Neumann entropy, extending the role of symmetry from communication bounds to the control of output entropy.

quant-ph↗

arXiv2026

Quantum Broadcast Channels with Mutually Confidential Messages

We study the transmission of two independent confidential classical messages over a quantum broadcast channel, one for each receiver. Each message must remain secret from the other receiver, including when that receiver knows its own message. For classical inputs and quantum outputs, we establish the classical Marton-type inner bound under average reliability and conditional strong secrecy. The encoder selects pairs of codewords from independently generated codebooks using normalized likelihood weights. We prove reliability through a change-of-distribution argument. Our main technical result is a bipartite classical-quantum resolvability theorem that accounts for the dependence created by pair selection and establishes secrecy for the same encoder. We also obtain a multi-letter capacity characterization and extend it to arbitrary quantum inputs under secrecy against the other receiver, together with the Stinespring environment. We recover confidential capacity regions for deterministic classical and degraded classical-quantum channels, with an explicit evaluation for the classical Blackwell channel. For coherent isometric extensions of injective deterministic classical broadcast channels, we show that the confidential classical capacity region equals that of the corresponding classical channel. We then compare confidential classical communication with quantum transmission. For the coherent isometric extension of the Blackwell channel, we determine the unassisted quantum-capacity region and show that some achievable confidential classical rate pairs lie outside it. The Platypus channel provides another example of this separation.

quant-ph↗

arXiv2026

No cardinality bound for squashed entanglement

Squashed entanglement is an additive bipartite entanglement measure. For a state $ρ_{AB}$, it is defined as the infimum of all conditional mutual information $I(A:B\mid E)$ evaluated on extensions $ρ_{ABE}$. It was unresolved whether there is a bound on the dimension of the conditioning system, $E$, needed for this optimization. We show that no such cardinality bound is possible. Explicitly, we find that the squashed entanglement for a partially dephased Bell pair on two qubits cannot be achieved for any finite dimensional extension $E$. A crucial ingredient of this proof is a direct sum step, which in a sense, symmetrizes two purifying systems while keeping the conditional mutual information unchanged and the coherence no worse.

quant-ph↗

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 $ρ_{AB}$ 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.

quant-ph↗

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.

quant-ph↗

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.

quant-ph↗

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

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.

quant-ph↗

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 Rényi-2 result. As an application, we obtain additivity results for generalized direct-sum channels and their corresponding Choi states.

quant-ph↗

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.

quant-ph↗

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↗

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 $χ^2$ 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.

quant-ph↗

arXiv2025

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↗