arXiv subjects

René Schwonnek

Publications and source records attributed to René Schwonnek.

At least 19 recordsLinked to original sources

arXiv2026

Reliable Entropy Estimation from Observed Statistics for Device-Independent Quantum Cryptography

This paper introduces a numerical framework for establishing lower bounds on the conditional von-Neumann entropy in device-independent quantum cryptography and randomness extraction scenarios. Leveraging a hierarchy of semidefinite programs derived from the Navascués-Pironio-Acin (NPA) hierarchy, our tool enables efficient computation of entropy bounds based solely on observed statistics, assuming the validity of quantum mechanics. The method's computational efficiency is ensured by its reliance on projective operators within the non-commutative polynomial optimization problem. The method facilitates provable bounds for extractable randomness in noisy scenarios and aligns with modern entropy accumulation theorems. Consequently, the framework offers an adaptable tool for practical quantum cryptographic protocols, expanding secure communication possibilities in untrusted environments.

quant-ph↗

arXiv2026

Computing key rates for one-sided device-independent quantum key distribution

The defining feature of one-sided device-independent quantum key distribution is its asymmetric trust model in which only one party is characterized. This scenario sets an interesting middle ground between high key rates achievable by characterizing devices and the security of full device-independence. Here, we provide new tools, methods, and benchmarks for calculating key rates in this setting. To achieve this, we develop and compare two extensions of the NPA hierarchy and derive finite-size security bounds against general attacks with arbitrary device memory. The latter is based on the Generalized Entropy Accumulation Theorem. We then investigate the performance of various protocols: the BB84 protocol both with and without losses, a qutrit mutually unbiased bases protocol, and protocols based on Bell inequalties such as CHSH and $I_{3322}$. We find that the choice of which party is characterized can strongly affects the key rate, surprisingly without a universal ordering. Our work thus offers a general toolbox for calculating key rates for one-sided device-independent QKD protocols.

quant-ph↗

arXiv2026

Optimal strategies for shadow tomography with limited resources

Shadow tomography addresses the task of efficiently predicting many expectation values of an unknown quantum state from randomized measurements on comparatively few copies. Existing analyses promise large scaling advantages, but the optimal strategies realizing these guarantees are not always known, and the required measurements are potentially challenging to implement on current hardware. We address this gap for Pauli observables by computing optimal sample-complexity parameters and constructing optimal measurement strategies under realistic resource constraints. We focus on memoryless protocols, where each copy is measured only once, and on measurements with bounded interaction range. Our approach reduces the problem to the analysis of graph parameters of the frustration graph encoding the Pauli anticommutation relations. We provide efficient numerical methods for the general case and analytically prove that Clifford measurements are optimal in many situations. This includes all perfect graphs, all single-qubit, all two-qubit measurement scenarios, and more. Applied to Hamiltonian energy estimation, our framework yields constructive strategies and improved variance bounds for molecular benchmarks.

quant-ph↗

arXiv2026

One for All: Universal Quantum Conic Programming Framework for Hard-Constrained Combinatorial Optimization Problems

We present a unified quantum-classical framework for addressing NP-complete constrained combinatorial optimisation problems, generalising the recently proposed Quantum Conic Programming (QCP) approach. Accordingly, it inherits many favourable properties of the original proposal such as preventing barren plateaus and NP-hard parameter optimisation. By collecting the entire classical feasibility structure in a single constraint, we enlarge QCP's scope to arbitrary hard-constrained problems. Yet, we prove that the additional restriction is mild enough to still allow for an efficient parameter optimisation via the formulation of a generalised eigenvalue problem (GEP) of adaptable dimension. Our rigorous proof further fills some apparent gaps in prior derivations of GEPs from parameter optimisation problems. We further detail a measurement protocol for formulating the classical parameter optimisation that does not require us to implement any problem-specific objective Hamiltonian or a quantum feasibility oracle. Lastly, we prove that, even under the influence of noise, QCP's parameterised ansatz class always captures the optimum attainable within its generated subcone. All of our results hold true for arbitrarily-constrained combinatorial optimisation problems.

quant-ph↗

arXiv2026

Device-independent Quantum Key Distribution in the commuting operator framework

Device-independent quantum key distribution (DIQKD) is arguably the gold standard for secure quantum communication, as it aims to rely only on observed input-output statistics of an uncharacterized device which is only assumption to obey the laws of quantum physics. A corresponding security analysis hence demands a description of a quantum experiment from a most general perspective. Under close inspection, existing proof techniques do not always meet this goal as they tend to rely on subtile assumptions on a tensor product structure of the underlying Hilbert space and a 'hidden but finite' dimensionality. In this work, we collect the tools needed for a full analysis of DIQKD in the commuting operator framework, which avoids these subtilities and provides the arguably most general view on a quantum experiment. We rigorously proof the common assumption that in DIQKD measurements can be w.l.o.g. assumed to be projective. Furthermore, we show that task of computing key rates can be casted as a non-commutative polynomial optimization (NPO) problem to which the Navascués-Pironio-Acín (NPA) hierarchy gives a correct and converging relaxation. As a tool, we generalize the integral representation for the relative entropy by Frenkel [Quantum 7, 1102 (2023)] to general von Neumann algebras and apply techniques from Kossmann and Schwonnek [arXiv: 2411.04858] for the approximation in an NPO program.

quant-ph↗

arXiv2026

Symmetry-based quantum algorithms for open-shop scheduling with hard constraints

Encoding hard-constrained optimization problems into a variational quantum algorithm often turns out to be a challenging task. In this work, we provide a solution for the class of open-shop scheduling problems (OSSPs), which we achieve by rigorously employing the symmetries of the classical problem. An established approach for encoding the hard constraints of the closely related traveling salesperson problem (TSP) into mixer Hamiltonians was recently given by Hadfield et al.'s Quantum Alternating Operator Ansatz (QAOA). For the OSSP, which contains TSP as a special case, we show that desired properties of similarly constructed mixers can be directly linked to a purely classical object: the group of feasibility-preserving bit value permutations. We also outline a generic way to construct QAOA-like mixers for these problems. We further propose a new variational quantum algorithm that incorporates the underlying group structure more naturally and, as a proof of principle, implement our new algorithm for a small OSSP instance on an IBM Q System One. Unlike the generic QAOA, our algorithm allows for bounding the amount and the domain of parameters necessary to reach every feasible solution from above: Optimizing at most quadratically many parameters should suffice to reach the optimum with certainty.

quant-ph↗

arXiv2026

Device independent quantum key distribution with robust self-tests

Device-independent quantum key distribution (DIQKD) provides a model of quantum key distribution with minimal assumptions and highly abstract theoretical building blocks. Although DIQKD frees us from detailed discussions of specific device models and associated error parameters, it replaces them with fundamental assumptions about the validity of quantum experiments. In this work, we propose a way to lift a protocol based on DIQKD-style assumptions to a device-dependent QKD protocol by performing local self-tests in the laboratories of the two key-generating parties. In particular, we consider routed Bell-test setups as a means of self-testing the local parties in earnest and develop a rigorous mathematical framework showing that the underlying optimization problems can indeed be transferred to the device-dependent QKD setting. As an application, we illustrate many of the relevant techniques through the case study of a routed BB84 protocol.

quant-ph↗

arXiv2026

Routed Bell tests with arbitrarily many local parties

Device-independent quantum key distribution (DIQKD) promises cryptographic security based solely on observed quantum correlations, yet its implementation over long distances remains limited. Routed Bell tests have recently re-emerged as a promising strategy to mitigate this limitation by enabling local self-testing of one party's device. However, extending this idea to self-testing both communicating parties has remained unclear. Here we develop a general $C^*$-algebraic for routed DIQKD with multiple switches and arbitrarily many local test parties, with a conservative, state-dependent definition of Eve. Within this framework, we design and analyse four-party routed protocols that locally self-test both Alice as well as Bob, and numerically bound key rates from the full observed statistics. In the parameter regimes considered, adding a fourth party strictly improves certified key rates and lowers the non-zero key threshold. Randomized key-basis switching further amplifies this advantage. Finally, we investigate a self-test-assisted E91-type protocol that continuously interpolates between the device-dependent Shor-Preskill rate and the device-independent rate derived by [Pironio et al., New J. Phys. 11, 045021 (2009)].

quant-ph↗

arXiv2026

Finite de Finetti for convex bodies and Polynomial Optimization

Leveraging a recently proposed notion of relative entropy in general probabilistic theories (GPT), we prove a finite de Finetti representation theorem for general convex bodies. We apply this result to address a fundamental question in polynomial optimization: the existence of a convergent outer hierarchy for problems with inequality constraints and analytical convergence guarantees. Our strategy generalizes a quantitative monogamy-of-entanglement argument from quantum theory to arbitrary convex bodies, establishing a uniform upper bound on mutual information in multipartite extensions. This leads to a finite de Finetti theorem and, subsequently, a convergent conic hierarchy for a wide class of polynomial optimization problems subject to both equality and inequality constraints. We further provide a constructive rounding scheme that yields certified interior points with controlled approximation error. As an application, we express the optimal GPT value of a two-player non-local game as a polynomial optimization problem, allowing our techniques to produce approximation schemes with finite convergence guarantees.

math.OC↗

arXiv2026

A Collection of Pinsker-type Inequalities for Quantum Divergences

Pinsker's inequality sets a lower bound on the Umegaki divergence of two quantum states in terms of their trace distance. In this work, we formulate corresponding estimates for a variety of quantum and classical divergences including $f$-divergences like Hellinger and $χ^2$-divergences as well as Rényi divergences and special cases thereof like the Umegaki divergence, collision divergence, max divergence. We further provide a strategy on how to adapt these bounds to smoothed divergences.

quant-ph↗

arXiv2025

Entanglement Detection with Rotationally Covariant Measurements -- From Compton Scattering to Lemonade

The accurate and efficient detection of quantum entanglement remains a central challenge in quantum information science. In this work, we study the detection of entanglement of polarized photons for measurement devices that are solely specified by rotational symmetry. We derive explicit positive operator valued measures (POVMs) showing that from a quantum information perspective any such setting is classified by one real measurable parameter r. In Particular, we give a POVM formulation of the Klein--Nishina formula for Compton scattering of polarized photons. We provide an SDP-based entanglement certification method that operates on the full measured statistics and gives tight bounds, also considering semi-device independent scenarios. Furthermore, we show that, while Bell violations are impossible with rotationally covariant measurements, EPR steering can still be certified under one-sided symmetry constraints. Finally, we present a rotationally covariant showcase experiment, analyzing the scattering of polarized optical light in a selection of soft drinks. Our results suggest that lemonade-based detectors are suitable for entanglement detection.

quant-ph↗

arXiv2025

Simultaneous variances of Pauli strings, weighted independence numbers, and a new kind of perfection of graphs

A set of Pauli stings is well characterized by the graph that encodes its commutatitivity structure, i.e., by its frustration graph. This graph provides a natural interface between graph theory and quantum information, which we explore in this work. We investigate all aspects of this interface for a special class of graphs that bears tight connections between the groundstate structures of a spin systems and topological structure of a graph. We call this class $\hbar$-perfect, as it extends the class of perfect and $h$-perfect graphs. Having an $\hbar$-perfect graph opens up several applications: we find efficient schemes for entanglement detection, a connection to the complexity of shadow tomography, tight uncertainty relations and a construction for computing good lower on bounds ground state energies. Conversely this also induces quantum algorithms for computing the independence number. Albeit those algorithms do not immediately promise an advantage in runtime, we show that an approximate Hamilton encoding of the independence number can be achieved with an amount of qubits that typically scales logarithmically in the number of vertices. We also we also determine the behavior of $\hbar$-perfectness under basic graph operations and evaluate their prevalence among all graphs.

quant-ph↗

arXiv2025

Deep-Circuit QAOA

Despite its popularity, several empirical and theoretical studies suggest that the quantum approximate optimization algorithm (QAOA) has persistent issues in providing a substantial practical advantage. Numerical results for few qubits and shallow circuits are, at best, ambiguous, and the well-studied barren plateau phenomenon draws a rather sobering picture for deeper circuits. However, as more and more sophisticated strategies are proposed to circumvent barren plateaus, it stands to reason which issues are actually fundamental and which merely constitute - admittedly difficult - engineering tasks. By shifting the scope from the usually considered parameter landscape to the quantum state space's geometry we can distinguish between problems that are fundamentally difficult to solve, independently of the parameterization, and those for which there could at least exist a favorable parameterization. Here, we find clear evidence for a 'no free lunch'-behavior of QAOA on a general optimization task with no further structure; individual cases have, however, to be analyzed more carefully. Based on our analysis, we propose and justify a performance indicator for the deep-circuit QAOA that can be accessed by solely evaluating statistical properties of the classical objective function. We further discuss the various favorable properties a generic QAOA instance has in the asymptotic regime of infinitely many gates, and elaborate on the immanent drawbacks of finite circuits. We provide several numerical examples of a deep-circuit QAOA method based on local search strategies and find that - in alignment with our performance indicator - some special function classes, like QUBOs, indeed admit a favorable optimization landscape.

quant-ph↗

arXiv2025

Optimising the relative entropy under semidefinite constraints

Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing provable upper and lower bounds is the central result of this work. Our primordial motivation stems from the essential task of estimating secret key rates for QKD from the measurement statistics of a real device. Further applications include the computation of channel capacities, the estimation of entanglement measures and many more. We build on a recently introduced integral representation of quantum relative entropy by [Frenkel, Quantum 7, 1102 (2023)] and provide reliable bounds as a sequence of semidefinite programs (SDPs). Our approach ensures provable sublinear convergence in the discretization, while also maintaining resource efficiency in terms of SDP matrix dimensions. Additionally, we can provide gap estimates to the optimum at each iteration stage.

quant-ph↗

arXiv2025

From barren plateaus through fertile valleys: Conic extensions of parameterised quantum circuits

Optimisation via parameterised quantum circuits is the prevalent technique of near-term quantum algorithms. However, the omnipresent phenomenon of barren plateaus - parameter regions with vanishing gradients - sets a persistent hurdle that drastically diminishes its success in practice. In this work, we introduce an approach - based on non-unitary operations - that favours jumps out of a barren plateau into a fertile valley. These operations are constructed from conic extensions of parameterised unitary quantum circuits, relying on mid-circuit measurements and a small ancilla system. We further reduce the problem of finding optimal jump directions to a low-dimensional generalised eigenvalue problem. As a proof of concept we incorporate jumps within state-of-the-art implementations of the Quantum Approximate Optimisation Algorithm (QAOA). We demonstrate the extensions' effectiveness on QAOA through extensive simulations, showcasing robustness against barren plateaus and highly improved sampling probabilities of optimal solutions.

quant-ph↗

arXiv2025

Specifying the Intrinsic Back-action of a General Measurement

Understanding the invasive nature of quantum measurement and its implications in quantum foundations and information science demands a mathematically rigorous and physically well-grounded characterization of intrinsic back-action in general measurement processes. However, such a framework remains elusive, leaving a critical gap in quantum theory. Here, we address this issue by conceptualizing a general quantum measurement as a reduction of extended projection measurements ensured by Naimark's theorem and, derive a state-updating rule for the concerned measurement as a reduction of the projective measurements postulate. Our framework provides a detailed analysis by explicitly decomposing the disturbance effects into two distinct contributions: those arising from the measurement elements themselves and those resulting from the dilation process. Notably, this formulation naturally recovers the projection postulate in the case of projective measurements. Beyond providing insights into joint measurability, non-disturbance, our rule establishes quantitaive connections between intrinsic disturbance and other fundamental quantum features, such as randomness, uncertainty, and information gain.

quant-ph↗

arXiv2024

Bounding the joint numerical range of Pauli strings by graph parameters

The interplay between the quantum state space and a specific set of measurements can be effectively captured by examining the set of jointly attainable expectation values. This set is commonly referred to as the (convex) joint numerical range. In this work, we explore geometric properties of this construct for measurements represented by tensor products of Pauli observables, also known as Pauli strings. The structure of pairwise commutation and anticommutation relations among a set of Pauli strings determines a graph $G$, sometimes also called the frustration graph. We investigate the connection between the parameters of this graph and the structure of minimal ellipsoids encompassing the joint numerical range. Such an outer approximation can be very practical since ellipsoids can be handled analytically even in high dimensions. We find counterexamples to a conjecture from [C. de Gois, K. Hansenne and O. Gühne, arXiv:2207.02197], and answer an open question in [M. B. Hastings and R. O'Donnell, Proc. STOC 2022, pp. 776-789], which implies a new graph parameter that we call $β(G)$. Besides, we develop this approach in different directions, such as comparison with graph-theoretic approaches in other fields, applications in quantum information theory, numerical methods, properties of the new graph parameter, etc. Our approach suggests many open questions that we discuss briefly at the end.

quant-ph↗

arXiv2023

Hierarchies for Semidefinite Optimization in $\mathcal{C}^\star$-Algebras

Semidefinite Optimization has become a standard technique in the landscape of Mathematical Programming that has many applications in finite dimensional Quantum Information Theory. This paper presents a way for finite-dimensional relaxations of general cone programs on $\mathcal{C}^\star$-algebras which have structurally similar properties to ordinary cone programs, only putting the notion of positivity at the core of optimization. We show that well-known hierarchies for generalized problems like NPA but also Lasserre's hierarchy and to some extend symmetry reductions of generic SDPs by de-Klerk et al. can be considered from a general point of view of $\mathcal{C}^\star$-algebras in combination to optimization problems.

math.OC↗