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arXiv:1911.05981 · Physical Review Research

Simultaneous certification of entangled states and measurements in bounded dimensional semiquantum games

Xingjian Zhang, Qi Zhao

Published Sep 11, 2020• 4 citations
arXivHTMLPDF

Abstract

Certification of quantum systems and operations is a central task in quantum information processing.Most current schemes rely on a tomography with fully characterized devices, while this may not be met in real experiments.Device characterizations can be removed with device-independent tests, but it is technically challenging at the moment.In this paper, we investigate the problem of certifying entangled states and measurements via semiquantum games, a type of nonlocal quantum games with well characterized quantum inputs, balancing practicality and device independence.We first design a specific bounded-dimensional semiquantum game, with which any pure entangled state and Bell state measurement operators can be simultaneously certified.Afterward via a duality treatment of state and measurement, we interpret the dual form of this game as a source-independent bounded-dimensional entanglement swapping protocol and show the whole process, including any entangled projector and Bell states, can be certified with this protocol.In particular, our results do not require a complete Bell state measurement, which is beneficial for experiments and practical use.

DOI
10.1103/physrevresearch.2.033400

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Certification of quantum systems and operations is a central task in quantum information processing.Most current schemes rely on a tomography with fully characterized devices, while this may not be met in real experiments.Device characterizations can be removed with device-independent tests, but it is technically challenging at the moment.In this paper, we investigate the problem of certifying entangled states and measurements via semiquantum games, a type of nonlocal quantum games with well characterized quantum inputs, balancing practicality and device independence.We first design a specific bounded-dimensional semiquantum game, with which any pure entangled state and Bell state measurement operators can be simultaneously certified.Afterward via a duality treatment of state and measurement, we interpret the dual form of this game as a source-independent bounded-dimensional entanglement swapping protocol and show the whole process, including any entangled projector and Bell states, can be certified with this protocol.In particular, our results do not require a complete Bell state measurement, which is beneficial for experiments and practical use.
Bipartite quantum states with higher Schmidt numbers have been shown to outperform those with lower Schmidt numbers in various quantum information-processing tasks, highlighting the operational advantage of entanglement dimensionality. Certifying the Schmidt number of such states is therefore crucial for efficient resource utilization. Ideally, this certification should rely as little as possible on the certifying devices to ensure robustness against their potential imperfections. Fully device-independent certification via Bell-nonlocal games offers strong robustness but suffers from fundamental limitations: It cannot certify the Schmidt number of all entangled states. We demonstrate that this insufficiency of Bell-nonlocal games is not limited to entangled states that do not exhibit Bell nonlocality. Specifically, we prove the existence of Bell-nonlocal states whose Schmidt number cannot be certified by any Bell-nonlocal game when the parties are restricted to local projective measurements. To overcome this, we develop a measurement-device-independent certification method based on semiquantum nonlocal games, which assume trusted preparation devices but treat measurement devices as black boxes. We prove that for any bipartite state with a Schmidt number exceeding rrr, a semiquantum nonlocal game exists that can certify its Schmidt number. Finally, we provide an explicit construction of such a semiquantum nonlocal game based on an optimal Schmidt number witness operator.
The semi-device-independent framework allows one to draw conclusions about properties of an unknown quantum system under weak assumptions. Here we present a semi-device-independent scheme for the characterization of multipartite entanglement based around a game played by several isolated parties whose devices are uncharacterized beyond an assumption about the dimension of their Hilbert spaces. Our scheme can simultaneously certify that an nnn-partite high-dimensional quantum state features genuine multipartite entanglement, and that a joint measurement on nnn subsystems is entangled. Moreover, it provides a lower bound on the number of entangled measurement operators. These tests are strongly robust to noise, and even optimal for certain classes of states and measurements, as we demonstrate with illustrative examples. Notably, our scheme allows the certification of many entangled states admitting a local model, which therefore cannot violate any Bell inequality.
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.
Bell state measurements, of which the eigenvectors are in an entangled form, are crucial resources in the construction of quantum networks. Therefore, device-independent certification of a Bell state measurement has significance in the quantum information process because it satisfies the exact demand on security. In this study, we implement a proof-of-concept experiment to certify a Bell state measurement device independently in an entanglement swapping process, namely, self-testing. Instead of preparing a tensor product of two singlets with four photons, multiplex encoding in polarization and spatial modes is utilized to produce two pairs of entangled qubits. As a result, we implement a full Bell state measurement and achieve a high degree of Bell violation on the remaining two qubits, which are required for nontrivial self-testing of a Bell state measurement. Furthermore, our results combine the correlations before and after the swapping; thus, the quality of the performed Bell state measurement can be precisely inferred.
Genuine multipartite entanglement represents the strongest type of entanglement, which is an essential resource for quantum information processing. Standard methods to detect genuine multipartite entanglement, e.g., entanglement witnesses, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in an experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected in the experiment, namely, device independently. However, it is difficult to certify genuine entanglement of practical multipartite states in this way, and even more difficult to quantify it, due to the difficulty in identifying optimal multipartite Bell inequalities and protocols tolerant to state impurity. In this Letter, we explore a general and robust device-independent method that can be applied to various realistic multipartite quantum states in arbitrary finite dimension, while merely relying on bipartite Bell inequalities. Our method allows us both to certify the presence of genuine multipartite entanglement and to quantify it. Several important classes of entangled states are tested with this method, leading to the detection of genuinely entangled states. We also certify genuine multipartite entanglement in weakly entangled Greenberger-Horne-Zeilinger states, showing that the method applies equally well to less standard states.
Within the context of semiquantum nonlocal games, the trust can be removed from the measurement devices in an entanglement-detection procedure. Here, we show that a similar approach can be taken to quantify the amount of entanglement. To be specific, first, we show that in this context, a small subset of semiquantum nonlocal games is necessary and sufficient for entanglement detection in the local operations and classical communication paradigm. Second, we prove that the maximum payoff for these games is a universal measure of entanglement which is convex and continuous. Third, we show that for the quantification of negative-partial-transpose entanglement, this subset can be further reduced down to a single arbitrary element. Importantly, our measure is measurement device independent by construction and operationally accessible. Finally, our approach straightforwardly extends to quantify the entanglement within any partitioning of multipartite quantum states.