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Entropy

Experimentally Self-Testing Partially Entangled Two-Qubit States on an Optical Platform

Xin Zhao, Yan‐Han Yang, Li-Ming Zhao, Ming‐Xing Luo

Published Jan 9, 2026• 0 citations
Publisher

Abstract

We demonstrate a complete and experimentally validated self-testing protocol for two-qubit partially entangled states, which avoids the need for full tomographic reconstruction. Using a room-temperature type-II PPKTP polarization-entangled source and a free-space optical setup, we implement both quantum state tomography and optimal generalized Bell measurements within a single system. Our approach achieves high-fidelity self-testing of non-maximally entangled states under black-box assumptions, establishing a solid foundation for device-independent quantum information processing applications.

DOI
10.3390/e28010079

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We demonstrate a complete and experimentally validated self-testing protocol for two-qubit partially entangled states, which avoids the need for full tomographic reconstruction. Using a room-temperature type-II PPKTP polarization-entangled source and a free-space optical setup, we implement both quantum state tomography and optimal generalized Bell measurements within a single system. Our approach achieves high-fidelity self-testing of non-maximally entangled states under black-box assumptions, establishing a solid foundation for device-independent quantum information processing applications.
Self-testing is a device-independent approach to estimate the state and measurement operators without the need to assume the dimension of our quantum system. In this paper, we show that one can self-test black boxes into any pure entangled two-qubit state by performing simple Bell-type experiments. The approach makes use of only one family of Bell inequalities with two inputs and two outputs. Furthermore, we outline the sufficient conditions for one to self-test any dimensional bipartite entangled state. All these methods are robust to small but inevitable experimental errors.
Abstract Quantum tomography is currently the mainly employed method to characterize a quantum system and therefore plays a fundamental role when trying to characterize the action of a particular channel. Nonetheless, quantum tomography works on the premise of a full characterization and description of the devices preparing the quantum state and realizing the measurements. Such an assumption was recently relaxed in Dall’Arno et al (arXiv: 1805.01159 ) and Dall’Arno et al (2017 Proc. R. Soc. A 473 20160721), where a theoretical framework for the device-independent inference of quantum channels was developed and experimentally implemented with superconducting qubits. Here, based on such a framework, we present a complete experimental test on a photonic setup of two semi-device-independent protocols that can be employed for the validation of the tomographic reconstruction or the characterization of a given quantum channel, not relying on many assumptions on the adopted device. Our implementation paves the way to the development of new experimental methods not relying on the assumptions typically taken for granted in all the previous protocols.
Previous theoretical works showed that all pure two-qubit entangled states can generate one bit of local randomness and can be self-tested through the violation of proper Bell inequalities. We report an experiment in which nearly pure partially entangled states of photonic qubits are produced to investigate these tasks in a practical scenario. We show that small deviations from the ideal situation make low entangled states impractical to self-testing and randomness generation using the available techniques. Our results show that in practice lower entanglement implies lower randomness generation, recovering the intuition that maximally entangled states are better candidates for device-independent quantum information processing.
Abstract Quantum nonlocality has recently been intensively studied in connection to device-independent quantum information processing, where the extremal points of the set of quantum correlations play a crucial role through self-testing. In most protocols, the proofs for self-testing rely on the maximal violation of the Bell inequalities, but there is another known proof based on the geometry of state vectors to self-test a maximally entangled state. We present a geometrical proof in the case of partially entangled states. We show that, when a set of correlators in the simplest Bell scenario satisfies a condition, the geometry of the state vectors is uniquely determined. The realization becomes self-testable when another unitary observable exists on the geometry. Applying this proven fact, we propose self-testing protocols by intentionally adding one more measurement. This geometrical scheme for self-testing is superior in that, by using this as a building block and repeatedly adding measurements, a realization with an arbitrary number of measurements can be self-tested. Besides the application, we also attempt to describe nonlocal correlations by guessing probabilities of distant measurement outcomes. In this description, the quantum set is also convex, and a large class of extremal points is identified by the uniqueness of the geometry.
We assess the quality of a source of allegedly pure two-qubit states using both standard tomography and methods inspired by device-independent self-testing. Even when the detection and locality loopholes are open, the latter methods can dispense with modeling of the system and the measurements. However, due to finite sample fluctuations, the estimated probability distribution usually does not satisfy the no-signaling conditions exactly. We implement data analysis that is robust against these fluctuations. We demonstrate a high ratio ${f}_{s}/{f}_{t}\ensuremath{\approx}0.988$ between the fidelity estimated from self-testing and that estimated from full tomography, proving the high performance of self-testing methods.
Quantum entanglement is the key resource for quantum information processing. Device-independent certification of entangled states is a long standing open question, which arouses the concept of self-testing. The central aim of self-testing is to certify the state and measurements of quantum systems without any knowledge of their inner workings, even when the used devices cannot be trusted. Specifically, utilizing Bell's theorem, it is possible to place a boundary on the singlet fidelity of entangled qubits. Here, beyond this rough estimation, we experimentally demonstrate a complete self-testing process for various pure bipartite entangled states up to four dimensions, by simply inspecting the correlations of the measurement outcomes. We show that this self-testing process can certify the exact form of entangled states with fidelities higher than 99.9% for all the investigated scenarios, which indicates the superior completeness and robustness of this method. Our work promotes self-testing as a practical tool for developing quantum techniques.