Certification of quantum entanglement under realistic device imperfections is central to quantum communication, cryptography, and quantum networks. Despite the nonclassical nature of entanglement and contextuality, we empirically verify that standard Conformal Prediction(CP)retainsitscoverageguaranteesintheCHSHscenario, astheoreticallyexpected under (context-conditional) exchangeability. We introduce an LHV-Calibrated Anomaly Detection framework achieving an ROC AUC ≈0.96 (Scenario A) and AUC ≈0.83 using only CP-derived features (Scenario B). Validation on IBM quantum hardware (Shw ≈2.53) confirms these results under Noisy Intermediate-Scale Quantum (NISQ) conditions, relative to an explicit LHV null manifold. Finally, we prove a no-go theorem for product-threshold Conformal Entanglement Witnesses (CEW), explaining their limited power. Our results suggest that, at least in the CHSH setting considered here, CP is best viewed as a robust statistical wrapper around quantum devices, rather than a fragile entanglement witness. To facilitate reproducibility, all code, data, and experiment configurations are available at https://github.com/detasar/QCE.
Certification of quantum entanglement under realistic device imperfections is central to quantum communication, cryptography, and quantum networks. Despite the nonclassical nature of entanglement and contextuality, we empirically verify that standard Conformal Prediction(CP)retainsitscoverageguaranteesintheCHSHscenario, astheoreticallyexpected under (context-conditional) exchangeability. We introduce an LHV-Calibrated Anomaly Detection framework achieving an ROC AUC ≈0.96 (Scenario A) and AUC ≈0.83 using only CP-derived features (Scenario B). Validation on IBM quantum hardware (Shw ≈2.53) confirms these results under Noisy Intermediate-Scale Quantum (NISQ) conditions, relative to an explicit LHV null manifold. Finally, we prove a no-go theorem for product-threshold Conformal Entanglement Witnesses (CEW), explaining their limited power. Our results suggest that, at least in the CHSH setting considered here, CP is best viewed as a robust statistical wrapper around quantum devices, rather than a fragile entanglement witness. To facilitate reproducibility, all code, data, and experiment configurations are available at https://github.com/detasar/QCE.
Quantum computing introduces unique forms of randomness arising from measurement processes, gate noise, and hardware imperfections. Ensuring reliable uncertainty quantification in such quantum-driven or quantum-derived predictions is an emerging challenge. In classical machine learning, conformal prediction has proven to be a robust framework for distribution-free uncertainty calibration, often focusing on univariate or low-dimensional outputs. Recent advances (e.g., [1–3]) have extended conformal methods to handle multi-output or multi-dimensional responses, addressing sophisticated tasks such as time-series, image classification sets, and quantum-generated probability distributions. However, bridging the gap between these powerful conformal frameworks and the high-dimensional, noise-prone distributions typical of quantum measurement scenarios remains largely open. In this paper, we propose a unified approach to harness quantum conformal methods for multi-output distributions, with a particular emphasis on two experimental paradigms: (i) a standard 2-qubit circuit scenario producing a four-dimensional outcome distribution, and (ii) a multi-basis measurement setting that concatenates measurement probabilities in different bases (Z, X, Y) into a twelve-dimensional output space. By combining a multi-output regression model (e.g., random forests) with distributional conformal prediction, we validate coverage and interval-set sizes on both simulated quantum data and multi-basis measurement data. Our results confirm that classical conformal prediction can effectively provide coverage guarantees even when the target probabilities derive from inherently quantum processes. Such synergy opens the door to next-generation quantum-classical hybrid frameworks, providing both improved interpretability and rigorous coverage for quantum machine learning tasks. All codes and full reproducible Colab notebooks are made available at https://github.com/detasar/QECMMOU.
Abstract In the noisy intermediate‐scale quantum (NISQ) era, multipartite entanglement in realistic noisy environments exhibits complex structures. Characterizing entanglement structures—particularly entanglement depth and intactness—has become increasingly essential for quantum information processing tasks. Traditional methods like standard entanglement witnesses assume that experimenters can exactly implement specific quantum measurements. Even minor inaccuracies in standard witness can introduce significant errors in entanglement detection. Certification methods are proposed with relaxed assumptions about the system and measurements for entanglement structures. First, entanglement states are classified with the same intactness into three distinct types based on their depth. Next, analytical witnesses are derived to detect the entanglement structure of general n‐qubit systems in both device‐independent and semi‐device‐independent scenarios, where some observables are untrusted while others remain reliable. Furthermore, this framework is extended to account for small measurement imperfections, ensuring robustness in practical settings. It is demonstrated that this witness can detect larger entanglement regions compared to previous Bell‐type inequalities. Remarkably, for Type I 4‐partite quantum states, this entanglement witness with measurement imperfections is identical to both device‐dependent and semi‐device‐independent approaches.
In this paper, we propose a unified approach to harness quantum conformal methods for multi-output distributions, with a particular emphasis on two experimental paradigms: (i) a standard 2-qubit circuit scenario producing a four-dimensional outcome distribution, and (ii) a multi-basis measurement setting that concatenates measurement probabilities in different bases (Z, X, Y) into a twelve-dimensional output space. By combining a multioutput regression model (e.g., random forests) with distributional conformal prediction, we validate coverage and interval-set sizes on both simulated quantum data and multi-basis measurement data. Our results confirm that classical conformal prediction can effectively provide coverage guarantees even when the target probabilities derive from inherently quantum processes. Such synergy opens the door to next-generation quantum-classical hybrid frameworks, providing both improved interpretability and rigorous coverage for quantum machine learning tasks. All codes and full reproducible Colab notebooks are made available at https://github.com/detasar/QECMMOU.
Detecting and quantifying quantum entanglement remain significant challenges in the noisy intermediate-scale quantum (NISQ) era. This study presents the implementation of quantum support vector machines (QSVMs) on IBM quantum devices to identify and classify entangled states. By employing quantum variational circuits, the proposed framework achieves a runtime complexity of [Formula: see text], where N is the number of qubits, t is the number of iterations, and ε is the acceptable error margin. We investigate various quantum circuits with multiple blocks and obtain the accuracy of QSVM as measures of expressibility and entangling capability. Our results demonstrate that the QSVM framework achieves over 90% accuracy in distinguishing entangled states, despite hardware noise such as decoherence and gate errors. Benchmarks across superconducting qubit platforms (e.g., IBM Perth, Lagos, and Nairobi) highlight the robustness of the model. Furthermore, the QSVM framework effectively classifies two-qubit states and extends its predictive capabilities to three-qubit entangled states. This work marks a significant advancement in quantum machine learning for entanglement detection.
There always exists an entanglement witness for every entangled quantum state. Negativity of the expectation value of an entanglement witness operator guarantees entanglement of the corresponding state, given that the measurement devices involved are perfect, i.e., the performed measurements actually constitute the witness operator for the state under consideration. In a realistic situation, there are two possible ways of measurements to drive the process away from the ideal one. First, wrong measurements may be performed, and, second, while the measurement operators are implemented correctly, the detection process may be noisy. Entanglement witnesses are prone to both of these imperfections. The concept of measurement-device-independent entanglement witnesses was introduced to remove the first problem. We analyze the ``detection loophole'' in the context of measurement-device-independent entanglement witnesses, which deal with the second problem of imprecise measurements. We obtain an upper bound, a threshold value, on the entanglement witness function in the measurement-device-independent entanglement witness scenario, below which entanglement is guaranteed for given nonideal detector efficiencies, that can involve both lost events and dark counts. We also present a threshold value on the function in the ``worst-case scenario'' where the threshold of the witness operator for guaranteeing entanglement assumes its maximal negative value.
Certifying high-dimensional quantum channels is essential for ensuring the reliability of quantum communication protocols. Existing certification schemes often rely on fully trusted internal devices, which is difficult to achieve in realistic scenarios. Here, we propose a semi-device-independent framework for certifying channel properties directly from observed statistics, assuming only that the system dimension is known. By explicitly incorporating the full set of structural constraints inherent to Choi states, our approach exploits the Choi-Jamiołkowski isomorphism for rigorous certification of quantum channels. The entanglement dimensionality of quantum channels is first certified by introducing a witness and numerically determining its Schmidt-number-dependent bounds. This certification method reproduces known analytical benchmarks and is applied to dephasing and depolarizing noise channels, thereby confirming its validity. To provide a more complete assessment of channel performance, the entanglement fidelity of quantum channels is also certified using a hierarchy of semidefinite programming relaxations based on localizing matrices. Lower bounds on the entanglement fidelity are obtained that are compatible with either the full set of observed statistics or a single witness value.