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arXiv:1612.08551 · Physical Review X

Efficient Device-Independent Entanglement Detection for Multipartite Systems

F. Baccari, D. Cavalcanti, P. Wittek, A. Acín

Published Jun 14, 2017• 44 citations
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Abstract

Quantum entanglement lies at the heart of proposals for encoding and manipulating information in a quantum computer, but detecting its presence in large ensembles of particles remains challenging. A new technique for entanglement detection promises to be both computationally and experimentally efficient in systems involving tens of particles.

DOI
10.1103/physrevx.7.021042

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Quantum entanglement lies at the heart of proposals for encoding and manipulating information in a quantum computer, but detecting its presence in large ensembles of particles remains challenging. A new technique for entanglement detection promises to be both computationally and experimentally efficient in systems involving tens of particles.
Entanglement is one of the most studied properties of quantum mechanics for its application in quantum information protocols. Nevertheless, detecting the presence of entanglement in large multipartite sates keeps being a great challenge both from the theoretical and the experimental point of view. Most of the known methods either have computational costs that scale inefficiently with the number of parties or require more information on the state than what is attainable in every-day experiments. We introduce a new technique for entanglement detection that provides several important advantages in these respects. First, its scales efficiently with the number of parties, thus allowing for application to systems composed by up to few tens of parties. Second, it needs only the knowledge of a subset of all possible measurements on the state, therefore being apt for experimental implementation. Moreover, since it is based on the detection of nonlocality, our method is device-independent. We report several examples of its implementation for well-known multipartite states, showing that the introduced technique has a promising range of applications.
Nonlocality detection in multipartite quantum systems is of great interest. The most popular tool to detect nonlocality in quantum systems are Bell inequalities. Most of the provided constructions of multipartite Bell inequalities involve correlations between all parties which quickly becomes computationally intractable and hard to test experimentally in many-body quantum systems. Recently, J. Tura and collaborators have shown in [Science 344.6189 (2014): 1256-1258] that detection of nonlocality in multipartite systems is possible with Bell inequalities involving only one- and two- body correlation functions. However, it is uncertain how efficient these new inequalities are. One of the objectives of the present work is to address this question by numerical means. The other objective is to show that these inequalities can also serve as as device independent witnesses of different forms of entanglement such as genuine multipartite entanglement.
Although the realization of useful quantum computers poses significant challenges, swift progress in emerging quantum technologies is making this goal realistically approachable. In this context, one of the essential resources is quantum entanglement, which allows for quantum computations outperforming their classical counterparts. However, the task of entanglement detection is not always straightforward for several reasons. One of the main challenges is that standardly-used methods rapidly become unfeasible when dealing with quantum states containing more than a few qubits. Typically, this is due to the fact that a vast amount of measurements is needed on many copies of the state. Generally, it is not unusual to deal with a very limited number of state copies in experimental settings - in fact, this may be the case for many large quantum systems. In this article, an overview is provided of a probabilistic approach that enables high-confidence genuine multipartite entanglement detection using an exceptionally low number of state copies. Additionally, a study is presented that shows that this protocol remains efficient also in the presence of noise, thus confirming the practicality of the method for near-term quantum devices and its suitability for complex experimental settings.
Witnessing entanglement is crucial in quantum information processing. With properly preparing ancillary states, it has been shown previously that genuine entanglement can be witnessed without trusting measurement devices. In this work we generalize the scenario and show that generic multipartite entanglement structures, including entanglement of subsystems and entanglement depth, can be witnessed via measurement-device-independent means. As the original measurement-device-independent entanglement witness scheme exploits only one out of four Bell measurement outcomes for each party, a direct generalization to multipartite quantum states will inevitably cause inefficiency in entanglement detection after taking account of statistical fluctuations. To resolve this problem, we also present a way to utilize all the measurement outcomes. The scheme is efficient for multipartite entanglement detection and can be realized with state-of-the-art technologies.
Entanglement is one of the most fascinating features of quantum theory, as it fundamentally distinguishes quantum systems from classical systems. It not only might play a role in natural processes, but provides an especially powerful resource for a plethora of quantum information protocols, including quantum state teleportation, superdense coding as well as quantum computation schemes. However, for larger systems involving more than two parties, it is a challenging task to verify and characterize entanglement. In this thesis, efficient means for detecting genuine multipartite entanglement in multiqubit quantum systems will be derived, demonstrated, and discussed. Beyond that, methods for quantum state and process tomography will be introduced, which allow to analyze and investigate prepared multipartite states or even the performance of whole setups. Some typical obstacles for reliable state tomography will be pointed out, together with new means to understand experimentally obtained data. Finally, the measurement problem, which describes the unavoidable backaction of a measurement process to the quantum state under investigation, will be illustrated. Together with the discussion of different methods of quantum measurements, the optimal measurement instruments for binary qubit measurements will be derived. These optimal measurement instruments allow to perform a quantum measurement, providing a tunable amount of information about the quantum state, while avoiding any unnecessary disturbance to the state. This set of optimal instruments will be compared to other measurement schemes, such as measurements based on the optimal quantum cloning protocol.