arXiv subjects

Graeme Smith

Publications and source records attributed to Graeme Smith.

At least 37 records · Page 2Linked to original sources

arXiv2025

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.

quant-ph↗

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.

quant-ph↗

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.

quant-ph↗

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.

quant-ph↗

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.

quant-ph↗

arXiv2024

Quantification of Entanglement and Coherence with Purity Detection

Entanglement and coherence are fundamental properties of quantum systems, promising to power near future quantum technologies, such as quantum computation, quantum communication and quantum metrology. Yet, their quantification, rather than mere detection, generally requires reconstructing the spectrum of quantum states, i.e., experimentally challenging measurement sets that increase exponentially with the system size. Here, we demonstrate quantitative bounds to operationally useful entanglement and coherence that are universally valid, analytically computable, and experimentally friendly. Specifically, our main theoretical results are lower and upper bounds to the coherent information and the relative entropy of coherence in terms of local and global purities of quantum states. To validate our proposal, we experimentally implement two purity detection methods in an optical system: shadow estimation with random measurements and collective measurements on pairs of state copies. The experiment shows that both the coherent information and the relative entropy of coherence of pure and mixed unknown quantum states can be bounded by purity functions. Our research offers an efficient means of verifying large-scale quantum information processing.

quant-ph↗

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.

quant-ph↗

arXiv2024

The QAOA with Few Measurements

The Quantum Approximate Optimization Algorithm (QAOA) was originally developed to solve combinatorial optimization problems, but has become a standard for assessing the performance of quantum computers. Fully descriptive benchmarking techniques are often prohibitively expensive for large numbers of qubits ($n \gtrsim 10$), so the QAOA often serves in practice as a computational benchmark. The QAOA involves a classical optimization subroutine that attempts to find optimal parameters for a quantum subroutine. Unfortunately, many optimizers used for the QAOA require many shots ($N \gtrsim 1000$) per point in parameter space to get a reliable estimate of the energy being minimized. However, some experimental quantum computing platforms such as neutral atom quantum computers have slow repetition rates, placing unique requirements on the classical optimization subroutine used in the QAOA in these systems. In this paper we investigate the performance of two choices of gradient-free classical optimizer for the QAOA - dual annealing and natural evolution strategies - and demonstrate that optimization is possible even with $N=1$ and $n=16$.

quant-ph↗

arXiv2024

Local measurement strategies for multipartite entanglement quantification

Despite multipartite entanglement being a global property of a quantum state, a number of recent works have made it clear that it can be quantified using only local measurements. This is appealing because local measurements are the easiest to implement on current quantum hardware. However, it remains an open question what protocol one should use in order to minimize the resources required to estimate multipartite entanglement from local measurements alone. In this work, we construct and compare several estimators of multipartite entanglement based solely on the data from local measurements. We first construct statistical estimators for a broad family of entanglement measures using local randomized measurement (LRM) data before providing a general criterion for the construction of such estimators in terms of projective 2-designs. Importantly, this allows us to de-randomize the multipartite estimation protocol based on LRMs. In particular, we show how local symmetric informationally complete POVMs enable multipartite entanglement quantification with only a single measurement setting. For all estimators, we provide both the classical post-processing cost and rigorous performance guarantees in the form of analytical upper bounds on the number of measurements needed to estimate the measures to any desired precision.

quant-ph↗

arXiv2023

Information Fragility or Robustness Under Quantum Channels

Quantum states naturally decay under noise. Many earlier works have quantified and demonstrated lower bounds on the decay rate, showing exponential decay in a wide variety of contexts. Here we study the converse question: are there uniform upper bounds on the ratio of post-noise to initial information quantities when noise is sufficiently weak? In several scenarios, including classical, we find multiplicative converse bounds. However, this is not always the case. Even for simple noise such as qubit dephasing or depolarizing, mutual information may fall by an unbounded factor under arbitrarily weak noise. As an application, we find families of channels with non-zero private capacity despite arbitrarily high probability of transmitting an arbitrarily good copy of the input to the environment.

quant-ph↗

arXiv2023

Quantum and private capacities of low-noise channels

We determine both the quantum and the private capacities of low-noise quantum channels to leading orders in the channel's distance to the perfect channel. It has been an open problem for more than 20 years to determine the capacities of some of these low-noise channels such as the depolarizing channel. We also show that both capacities are equal to the single-letter coherent information of the channel, again to leading orders. We thus find that, in the low noise regime, super-additivity and degenerate codes have negligible benefit for the quantum capacity, and shielding does not improve the private capacity beyond the quantum capacity, in stark contrast to the situation when noisier channels are considered.

quant-ph↗

arXiv2023

On the separation of correlation-assisted sum capacities of multiple access channels

The capacity of a channel characterizes the maximum rate at which information can be transmitted through the channel asymptotically faithfully. For a channel with multiple senders and a single receiver, computing its sum capacity is possible in theory, but challenging in practice because of the nonconvex optimization involved. To address this challenge, we investigate three topics in our study. In the first part, we study the sum capacity of a family of multiple access channels (MACs) obtained from nonlocal games. For any MAC in this family, we obtain an upper bound on the sum rate that depends only on the properties of the game when allowing assistance from an arbitrary set of correlations between the senders. This approach can be used to prove separations between sum capacities when the senders are allowed to share different sets of correlations, such as classical, quantum or no-signalling correlations. We also construct a specific nonlocal game to show that the approach of bounding the sum capacity by relaxing the nonconvex optimization can give arbitrarily loose bounds. Owing to this result, in the second part, we study algorithms for non-convex optimization of a class of functions we call Lipschitz-like functions. This class includes entropic quantities, and hence these results may be of independent interest in information theory. Subsequently, in the third part, we show that one can use these techniques to compute the sum capacity of an arbitrary two-sender MACs to a fixed additive precision in quasi-polynomial time. We showcase our method by efficiently computing the sum capacity of a family of two-sender MACs for which one of the input alphabets has size two. Furthermore, we demonstrate with an example that our algorithm may compute the sum capacity to a higher precision than using the convex relaxation.

cs.IT↗

arXiv2023

Generic nonadditivity of quantum capacity in simple channels

Determining capacities of quantum channels is a fundamental question in quantum information theory. Despite having rigorous coding theorems quantifying the flow of information across quantum channels, their capacities are poorly understood due to super-additivity effects. Studying these phenomena is important for deepening our understanding of quantum information, yet simple and clean examples of super-additive channels are scarce. Here we study a family of channels called platypus channels. Its simplest member, a qutrit channel, is shown to display super-additivity of coherent information when used jointly with a variety of qubit channels. Higher-dimensional family members display super-additivity of quantum capacity together with an erasure channel. Subject to the "spin-alignment conjecture" introduced in the companion paper [IEEE Trans. Inf. Theory 69(6), pp. 3825-3849, 2023; arXiv:2202.08380], our results on super-additivity of quantum capacity extend to lower-dimensional channels as well as larger parameter ranges. In particular, super-additivity occurs between two weakly additive channels each with large capacity on their own, in stark contrast to previous results. Remarkably, a single, novel transmission strategy achieves super-additivity in all examples. Our results show that super-additivity is much more prevalent than previously thought. It can occur across a wide variety of channels, even when both participating channels have large quantum capacity.

quant-ph↗

arXiv2023

The platypus of the quantum channel zoo

Understanding quantum channels and the strange behavior of their capacities is a key objective of quantum information theory. Here we study a remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic quantum information-theoretic features. As the simplest example from this family, we focus on a qutrit-to-qutrit channel that is intuitively obtained by hybridizing together a simple degradable channel and a completely useless qubit channel. Such hybridizing makes this channel's capacities behave in a variety of interesting ways. For instance, the private and classical capacity of this channel coincide and can be explicitly calculated, even though the channel does not belong to any class for which the underlying information quantities are known to be additive. Moreover, the quantum capacity of the channel can be computed explicitly, given a clear and compelling conjecture is true. This "spin alignment conjecture," which may be of independent interest, is proved in certain special cases and additional numerical evidence for its validity is provided. Finally, we generalize the qutrit channel in two ways, and the resulting channels and their capacities display similarly rich behavior. In the companion paper [Phys. Rev. Lett. 130, 200801 (2023); arXiv:2202.08377], we further show that the qutrit channel demonstrates superadditivity when transmitting quantum information jointly with a variety of assisting channels, in a manner unknown before.

quant-ph↗

arXiv2023

Opportunities and Limitations in Broadband Sensing

We consider estimating the magnitude of a monochromatic AC signal that couples to a two-level sensor. For any detection protocol, the precision achieved depends on the signal's frequency and can be quantified by the quantum Fisher information. To study limitations in broadband sensing, we introduce the integrated quantum Fisher information and derive inequality bounds that embody fundamental tradeoffs in any sensing protocol. These inequalities show that sensitivity in one frequency range must come at a cost of reduced sensitivity elsewhere. For many protocols, including those with small phase accumulation and those consisting of $π$-pulses, we find the integrated Fisher information scales linearly with $T$. We also find protocols with substantial phase accumulation can have integrated QFI that grows quadratically with $T$, which is optimal. These protocols may allow the very rapid detection of a signal with unknown frequency over a very wide bandwidth.

quant-ph↗

arXiv2022

Phase Transitions of Correlations in Black Hole Geometries

We study the holographic realization of optimized correlation measures -- measures of quantum correlation that generalize elementary entropic formulas -- in two-dimensional thermal states dual to spacetimes with a black hole horizon. We consider the symmetric bipartite optimized correlation measures: the entanglement of purification, Q-correlation, R-correlation, and squashed entanglement, as well as the mutual information, a non-optimized correlation measure, and identify the bulk surface configurations realizing their geometric duals over the parameter space of boundary region sizes and the black hole radius. This parameter space is divided into phases associated with given topologies for these bulk surface configurations, and first-order phase transitions occur as a new topology of bulk surfaces becomes preferred. The distinct phases can be associated with different degrees of correlation between the boundary regions and the thermal environment. The Q-correlation has the richest behavior, with a structure of nested optimizations leading to two topologically distinct bulk surface configurations being equally valid as geometric duals at generic points in the phase diagram.

hep-th↗

arXiv2021

Towards Demonstrating Fault Tolerance in Small Circuits Using Bacon-Shor Codes

Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily studies of quantum memory[1, 2], an important first step towards quantum computation, where the objective is to increase the lifetime of the encoded quantum information. Additionally, several works have explored the implementation of logical gates[3-5]. In this work we study a next step - fault-tolerantly implementing quantum circuits. We choose the $[[4, 1, 2]]$ Bacon-Shor subsystem code, which has a particularly simple error-detection circuit. Through both numerics and site-counting arguments, we compute pseudo-thresholds for the Pauli error rate $p$ in a depolarizing noise model, below which the encoded circuits outperform the unencoded circuits. These pseudo-threshold values are shown to be as high as $p=3\%$ for short circuits, and $p=0.6\%$ for circuits of moderate depth. Additionally, we see that multiple rounds of stabilizer measurements give an improvement over performing a single round at the end. This provides a concrete suggestion for a small-scale fault-tolerant demonstration of a quantum algorithm that could be accessible with existing hardware.

quant-ph↗