arXiv subjects

Mariami Gachechiladze

Publications and source records attributed to Mariami Gachechiladze.

At least 19 recordsLinked to original sources

arXiv2026

Information Causality Characterizes the Set of Quantum Correlations in the Simplest Bell Scenario

Information causality (IC) was introduced as a physical principle constraining correlations in non-signaling theories. Whether it can recover the exact quantum correlation boundary, beyond Uffink's inequality, has remained an open question. Here, we combine its generalized formulation for correlated inputs with a new communication protocol to derive quantum Bell inequalities that exactly characterize the quantum correlations in the simplest bipartite Bell scenario, with two binary measurements. In particular, we derive the Tsirelson-Landau-Masanes criterion directly from IC. Thus, the generalized IC implies macroscopic locality, while we also present macroscopically local correlations that violate the generalized IC. This establishes that generalized IC is a strictly stronger principle in this scenario. Together with our earlier result that generalized IC implies a nontrivial communication complexity principle, these findings strengthen the role of information causality in explaining the limits of quantum nonlocality and provide a systematic route to deriving tighter bounds on the set of quantum correlations in more general Bell scenarios.

quant-ph↗

arXiv2026

An infinite hierarchy of multi-copy quantum learning tasks

Learning properties of quantum states from measurement data is a fundamental challenge in quantum information. The sample complexity of such tasks depends crucially on the measurement primitive. While shadow tomography achieves sample-efficient learning by allowing entangling measurements across many copies, it requires prohibitively deep circuits. At the other extreme, two-copy measurements already yield exponential advantages over single-copy strategies in tasks such as Pauli tomography. In this work we show that such sharp separations extend far beyond the two-copy regime: for every prime c we construct explicit learning tasks of degree c, which are exponentially hard with (c - 1)-copy measurements but efficiently solvable with c-copy measurements. Our protocols are not only sample-efficient but also realizable with shallow circuits. Extending further, we show that such finite-degree tasks exist for all square-free integers c, pointing toward a general principle underlying their existence. Together, our results reveal an infinite hierarchy of multi-copy learning problems, uncovering new phase transitions in sample complexity and underscoring the role of reliable quantum memory as a key resource for exponential quantum advantage.

quant-ph↗

arXiv2026

Sound and Efficient Certification of High-Quality Qubit Operations: Theory and Experiment

Can a high-quality quantum gate be certified when uncharacterized state-preparation and measurement errors are dominant? Can this be achieved with low experimental overhead? Here, we introduce a sound black-box certification protocol for a single-qubit gate based on a small set of fixed, deterministic sequences. From the data, the protocol derives finite-sample bounds on the gate's rotation eigenvalue, a gauge-invariant property. Its phase reveals the accuracy of the rotation angle, while its modulus quantifies the loss of coherence under repeated gate applications. We implement the protocol on a $^{40}\mathrm{Ca}^{+}$ trapped-ion processor and certify the $\sqrt{\mathrm{X}}$-gate rotation eigenvalue using $22\,000$ circuit executions, and demonstrate the robustness of certification to state-preparation and measurement errors by deliberately degrading the readout. Finally, we prove that these spectral constraints imply, up to a physically meaningful unitary change of basis, a rigorous average gate-fidelity lower bound for every time-independent qubit model compatible with the data. In both readout settings, the spectral bounds yield the same fidelity certificate of $99.94(3)\%$ with $99\%$ confidence. Our results establish a new standard for quantum-gate certification by combining soundness and experimental efficiency without requiring trusted reference operations, randomized circuits, or model fitting.

quant-ph↗

arXiv2026

Bounds on Nonlocality and Random Access Codes from Extended Information Causality Principle

Information Causality was introduced as a physical principle for constraining the set of nonlocal correlations. In recent work, we proposed an extension of Information Causality that allows correlations among Alice's inputs. This extended principle yields tighter constraints than the original formulation and recovers part of the quantum boundary in certain Bell scenarios. In this work, we further investigate the implications of extended Information Causality and apply it to scenarios beyond binary inputs and outputs. We derive a family of quantum Bell inequalities that strengthen previously known constraints on quantum correlations. Using these inequalities, we obtain an improved analytical bound for the Collins-Gisin family of Bell inequalities. We also apply Information Causality to entanglement-assisted random access codes and derive new theory-independent analytical bounds on the winning probability. For this latter task, we prove that, despite being stronger in general, the extended principle does not improve the bounds obtained from the original Information Causality principle. This suggests that the existing Information Causality bounds are optimal for this class of random access codes.

quant-ph↗

arXiv2026

Symmetric hypergraph states: Entanglement quantification and robust Bell nonlocality

Quantum hypergraph states are the natural generalization of graph states. Here we investigate and analytically quantify entanglement and nonlocality for large classes of quantum hypergraph states. More specifically, we connect the geometric measure of entanglement of symmetric hypergraphs to their local Pauli stabilizers. As a result we recognize the resemblance between symmetric graph states and symmetric hypergraph states, which explains both, exponentially increasing violation of local realism for infinitely many classes of hypergraph states and its robustness towards particle loss.

quant-ph↗

arXiv2026

Sound certification of memory-bounded quantum computers

The rapid advancement of quantum hardware calls for the development of reliable methods to certify its correct functioning. However, existing certification tests often fall short: they either rely on flawless state preparation and measurement or lack soundness guarantees, meaning that they do not rule out incorrect implementations of the target operations by a quantum device. We introduce an approach, which we call quantum system quizzing, for the certification of quantum gates in a practical server-user scenario, where a classical user tests the results of quantum computation performed by a quantum server by checking its responses to a set of predesigned small-sized computational problems. Importantly, this approach does not require trusted state preparation and measurement and is thus inherently free from the associated systematic errors. For a wide range of relevant gate sets, including a universal one, we prove our certification protocol to be sound; i.e., it is guaranteed to reject any incorrect gate implementation, under the assumptions of a known Hilbert space dimension and context independence of error. A major technical challenge that we are first to resolve is recovering the tensor product structure of a multi-qubit system in the memory-bounded single-device setup. Finally, we prove the robustness of our protocol and validate its sample and computational efficiency through extensive numerical experiments. Our protocol is platform-agnostic and introduces a new paradigm for benchmarking and comparing diverse quantum architectures.

quant-ph↗

arXiv2026

Communication complexity bounds from information causality

Communication complexity, which quantifies the minimum communication required for distributed computation, offers a natural setting for investigating the capabilities and limitations of quantum mechanics in information processing. We introduce an information-theoretic approach to study one-way communication complexity based solely on the axioms of mutual information. Within this framework, we derive an extended statement of the information causality principle, which recovers known lower bounds on the communication complexities for a range of functions in a simplified manner and leads to new results. We further prove that the extended information causality principle is at least as strong as the principle of non-trivial communication complexity in bounding the strength of quantum correlations attainable in Bell experiments. Our study establishes a new route for exploring the fundamental limits of quantum technologies from an information-theoretic viewpoint.

quant-ph↗

arXiv2025

Certifying Quantum Gates via Automata Advantage

There is growing interest in developing rigorous tests of quantumness that are feasible even before practical quantum advantages become a reality. Such tests not only aim to certify the quantum nature of a system but also serve as benchmarks for precise quantum control. In this work, we argue that promise problems, studied in the theory of finite automata, provide a natural framework for designing sound tests of quantum gate quality. Soundness, the property that only implementations of sufficiently high quality can pass the test, is a central requirement for meaningful certification. We study several promise problems relevant to quantum gate testing and establish separations between the memory resources required by quantum and classical finite automata to solve them. These separations form the theoretical basis for using promise problems as tests of quantumness. Finally, we show how results from automata theory, in particular the minimality of automata, can be used to derive soundness guarantees.

quant-ph↗

arXiv2025

Scaling Bound Entanglement through Local Extensions

Entanglement is a central resource in quantum information science, yet its structure in high dimensions remains notoriously difficult to characterize. One of the few general results on high-dimensional entanglement is given by peel-off theorems, which relate the entanglement of a state to that of its lower-dimensional local projections. We build on this idea by introducing local extensions, the inverse process to peel-off projections, which provide a systematic way to construct higher-dimensional entangled states from lower-dimensional ones. This dual perspective leads to general bounds on how the Schmidt number can change under projections and extensions, and reveals new mechanisms for generating bound entangled states of higher dimensionality. As a concrete application, we construct a positive-partial-transpose state of Schmidt number three in local dimensions $4\times 5$, the smallest system known to host such entanglement. We further extend this approach to identify an elegant family of generalized grid states with increasing Schmidt number, including explicit examples of a $7\times 7$ state with Schmidt number four and a $9\times 9$ state with Schmidt number five, suggesting $(d+1)/2$ scaling in odd local dimensions $d\times d$. Taken together, our results provide a constructive toolkit for probing the scaling of bound entanglement in high dimensions.

quant-ph↗

arXiv2025

Classical certification of quantum gates under the dimension assumption

The rapid advancement of quantum hardware necessitates the development of reliable methods to certify its correct functioning. However, existing certification tests fall short, as they either suffer from systematic errors or do not guarantee that only a correctly functioning quantum device can pass the test. We introduce a certification method for quantum gates tailored for a practical server-user scenario, where a classical user tests the results of exact quantum computations performed by a quantum server. This method is free from the systematic state preparation and measurement (SPAM) errors. For single-qubit gates, including those that form a universal set for single-qubit quantum computation, we demonstrate that our approach offers soundness guarantees based solely on the dimension assumption. Additionally, for a highly-relevant phase gate - which corresponds experimentally to a $π/2$-pulse - we prove that the method's sample complexity scales as $\mathrm{O}(\varepsilon^{-1})$ relative to the average gate infidelity $\varepsilon$. By combining the SPAM-error-free and sound notion of certification with practical applicability, our approach paves the way for promising research into efficient and reliable certification methods for full-scale quantum computation.

quant-ph↗

arXiv2025

An Efficient Quantum Classifier Based on Hamiltonian Representations

Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks. However, many studies rely on toy datasets or heavy feature reduction, raising concerns about their scalability. Progress is further hindered by hardware limitations and the significant costs of encoding dense vector representations on quantum devices. To address these challenges, we propose an efficient approach called Hamiltonian classifier that circumvents the costs associated with data encoding by mapping inputs to a finite set of Pauli strings and computing predictions as their expectation values. In addition, we introduce two classifier variants with different scaling in terms of parameters and sample complexity. We evaluate our approach on text and image classification tasks, against well-established classical and quantum models. The Hamiltonian classifier delivers performance comparable to or better than these methods. Notably, our method achieves logarithmic complexity in both qubits and quantum gates, making it well-suited for large-scale, real-world applications. We make our implementation available on GitHub.

quant-ph↗

arXiv2024

Information causality as a tool for bounding the set of quantum correlations

Information causality was initially proposed as a physical principle aimed at deriving the predictions of quantum mechanics on the type of correlations observed in the Bell experiment. In the same work, information causality was famously shown to imply the Uffink inequality that approximates the set of quantum correlations and rederives Tsirelson's bound of the Clauser-Horne-Shimony-Holt inequality. This result found limited generalizations due to the difficulty of deducing implications of the information causality principle on the set of nonlocal correlations. In this paper, we present a simple technique for obtaining polynomial inequalities from information causality bounding the set of physical correlations in any bipartite Bell scenario. This result makes information causality an efficient tool for approximating the set of quantum correlations. To demonstrate our method, we derive a family of inequalities which non-trivially constrains the set of nonlocal correlations in Bell scenarios with binary outcomes and equal number of measurement settings. Finally, we propose an improved statement of the information causality principle and obtain a tighter constraint for the simplest Bell scenario, that goes beyond the Uffink inequality and recovers a part of the boundary of the quantum set.

quant-ph↗

arXiv2024

High Schmidt number concentration in quantum bound entangled states

A deep understanding of quantum entanglement is vital for advancing quantum technologies. The strength of entanglement can be quantified by counting the degrees of freedom that are entangled, which results in a quantity called Schmidt number. A particular challenge is to identify the strength of entanglement in quantum states which remain positive under partial transpose (PPT), otherwise recognized as undistillable states. Finding PPT states with high Schmidt number has become a mathematical and computational challenge. In this work, we introduce efficient analytical tools for calculating the Schmidt number for a class of bipartite states, called generalized grid states. Our methods improve the best known bounds for PPT states with high Schmidt number. Most notably, we construct a Schmidt number three PPT state in five dimensional systems and a family of states with a Schmidt number of $(d+1)/2$ for odd $d$-dimensional systems, representing the best-known scaling of the Schmidt number in a local dimension. Additionally, these states possess intriguing geometrical properties, which we utilize to construct indecomposable entanglement witnesses.

quant-ph↗

arXiv2023

Deterministic Ansätze for the Measurement-based Variational Quantum Eigensolver

Measurement-based quantum computing (MBQC) is a promising approach to reducing circuit depth in noisy intermediate-scale quantum algorithms such as the Variational Quantum Eigensolver (VQE). Unlike gate-based computing, MBQC employs local measurements on a preprepared resource state, offering a trade-off between circuit depth and qubit count. Ensuring determinism is crucial to MBQC, particularly in the VQE context, as a lack of flow in measurement patterns leads to evaluating the cost function at irrelevant locations. This study introduces MBVQE-ansätze that respect determinism and resemble the widely used problem-agnostic hardware-efficient VQE ansatz. We evaluate our approach using ideal simulations on the Schwinger Hamiltonian and $XY$-model and perform experiments on IBM hardware with an adaptive measurement capability. In our use case, we find that ensuring determinism works better via postselection than by adaptive measurements at the expense of increased sampling cost. Additionally, we propose an efficient MBQC-inspired method to prepare the resource state, specifically the cluster state, on hardware with heavy-hex connectivity, requiring a single measurement round, and implement this scheme on quantum computers with $27$ and $127$ qubits. We observe notable improvements for larger cluster states, although direct gate-based implementation achieves higher fidelity for smaller instances.

quant-ph↗

arXiv2023

Entanglement witnessing with untrusted detectors

We consider the problem of entanglement detection in the presence of faulty, potentially malicious detectors. A common - and, as of yet, the only - approach to this problem is to perform a Bell test in order to identify nonlocality of the measured entangled state. However, there are two significant drawbacks in this approach: the requirement to exceed a critical, and often high, detection efficiency, and much lower noise tolerance. In this paper, we propose an alternative approach to this problem, which is resilient to the detection loophole and is based on the standard tool of entanglement witness. We discuss how the two main techniques to detection losses, namely the discard and assignment strategies, apply to entanglement witnessing. We demonstrate using the example of a two-qubit Bell state that the critical detection efficiency can be significantly reduced compared to the Bell test approach.

quant-ph↗

arXiv2022

A convergent inflation hierarchy for quantum causal structures

A causal structure is a description of the functional dependencies between random variables. A distribution is compatible with a given causal structure if it can be realized by a process respecting these dependencies. Deciding whether a distribution is compatible with a structure is a practically and fundamentally relevant, yet very difficult problem. Only recently has a general class of algorithms been proposed: These so-called inflation techniques associate to any causal structure a hierarchy of increasingly strict compatibility tests, where each test can be formulated as a computationally efficient convex optimization problem. Remarkably, it has been shown that in the classical case, this hierarchy is complete in the sense that each non-compatible distribution will be detected at some level of the hierarchy. An inflation hierarchy has also been formulated for causal structures that allow for the observed classical random variables to arise from measurements on quantum states - however, no proof of completeness of this quantum inflation hierarchy has been supplied. In this paper, we construct a first version of the quantum inflation hierarchy that is provably convergent. From a technical point of view, convergence proofs are built on de Finetti Theorems, which show that certain symmetries (which can be imposed in convex optimization problems) imply independence of random variables (which is not directly a convex constraint). A main technical ingredient to our proof is a Quantum de Finetti Theorem that holds for general tensor products of $C^*$-algebras, generalizing previous work that was restricted to minimal tensor products.

quant-ph↗

arXiv2022

Quantum Bell inequalities from Information Causality -- tight for Macroscopic Locality

In a Bell test, the set of observed probability distributions complying with the principle of local realism is fully characterized by Bell inequalities. Quantum theory allows for a violation of these inequalities, which is famously regarded as Bell nonlocality. However, finding the maximal degree of this violation is, in general, an undecidable problem. Consequently, no algorithm can be used to derive quantum analogs of Bell inequalities, which would characterize the set of probability distributions allowed by quantum theory. Here we present a family of inequalities, which approximate the set of quantum correlations in Bell scenarios where the number of settings or outcomes can be arbitrary. We derive these inequalities from the principle of Information Causality, and thus, we do not assume the formalism of quantum mechanics. Moreover, we identify a subspace in the correlation space for which the derived inequalities give the necessary and sufficient conditions for the principle of Macroscopic Locality. As a result, we show that in this subspace, the principle of Information Causality is strictly stronger than the principle of Macroscopic Locality.

quant-ph↗

arXiv2021

Causal inference with imperfect instrumental variables

Instrumental variables allow for quantification of cause and effect relationships even in the absence of interventions. To achieve this, a number of causal assumptions must be met, the most important of which is the independence assumption, which states that the instrument and any confounding factor must be independent. However, if this independence condition is not met, can we still work with imperfect instrumental variables? Imperfect instruments can manifest themselves by violations of the instrumental inequalities that constrain the set of correlations in the scenario. In this paper, we establish a quantitative relationship between such violations of instrumental inequalities and the minimal amount of measurement dependence required to explain them. As a result, we provide adapted inequalities that are valid in the presence of a relaxed measurement dependence assumption in the instrumental scenario. This allows for the adaptation of existing and new lower bounds on the average causal effect for instrumental scenarios with binary outcomes. Finally, we discuss our findings in the context of quantum mechanics.

stat.ML↗