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arXiv:1801.10446 · Physical Review A

Self-testing of Pauli observables for device-independent entanglement certification

Joseph Bowles, Ivan Šupić, Daniel Cavalcanti, Antonio Acín

Published Oct 29, 2018• 77 citations
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Abstract

We present self-testing protocols to certify the presence of tensor products of Pauli measurements on maximally entangled states of local dimension ${2}^{n}$ for $n\ensuremath{\in}\mathbb{N}$. This provides self-tests of sets of informationally complete measurements in arbitrarily high dimension. We then show that this can be used for the device-independent certification of the entanglement of all bipartite entangled states by exploiting a connection to measurement-device-independent entanglement witnesses and quantum networks. This work extends a more compact parallel work on the same subject [Bowles et al., Phys. Rev. Lett. 121, 180503 (2018)] and provides all the required technical proofs.

DOI
10.1103/physreva.98.042336

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We present self-testing protocols to certify the presence of tensor products of Pauli measurements on maximally entangled states of local dimension 2n{2}^{n}2n for n\ensuremath∈Nn\ensuremath{\in}\mathbb{N}n\ensuremath∈N. This provides self-tests of sets of informationally complete measurements in arbitrarily high dimension. We then show that this can be used for the device-independent certification of the entanglement of all bipartite entangled states by exploiting a connection to measurement-device-independent entanglement witnesses and quantum networks. This work extends a more compact parallel work on the same subject [Bowles et al., Phys. Rev. Lett. 121, 180503 (2018)] and provides all the required technical proofs.
Self-testing protocols are methods to determine the presence of shared entangled states in a device independent scenario, where no assumptions on the measurements involved in the protocol are made. A particular type of self-testing protocol, called parallel self-testing, can certify the presence of copies of a state, however such protocols typically suffer from the problem of requiring a number of measurements that increases with respect to the number of copies one aims to certify. Here we propose a procedure to transform single-copy self-testing protocols into a procedure that certifies the tensor product of an arbitrary number of (not necessarily equal) quantum states, without increasing the number of parties or measurement choices. Moreover, we prove that self-testing protocols that certify a state and rank-one measurements can always be parallelized to certify many copies of the state. Our results suggest a method to achieve device-independent unbounded randomness expansion with high-dimensional quantum states.
We present a method to certify the entanglement of all entangled quantum states in a device-independent way. This is achieved by placing the state in a quantum network and constructing a correlation inequality based on an entanglement witness for the state. Our method is device independent, in the sense that entanglement can be certified from the observed statistics alone, under minimal assumptions on the underlying physics. Conceptually, our results borrow ideas from the field of self-testing to bring the recently introduced measurement-device-independent entanglement witnesses into the fully device-independent regime.
Characterizing large quantum systems with minimal assumptions is a central challenge in quantum information science. Self-testing provides the strongest form of certification by identifying the underlying quantum state solely from observed measurement statistics. However, existing self-testing methods for generic nnn-partite states face a scalability barrier, requiring exponentially many samples in the system size. In this work, we overcome this barrier by introducing a protocol that robustly self-tests almost all nnn-qubit states with only polynomial sample complexity. The key ingredient is an efficient scheme for device-independently evaluating multipartite Pauli measurements, which can be implemented using only a linear number of ancillary Bell pairs together with standard projective and Bell measurements, well within the reach of current quantum technology. Beyond self-testing states, our scheme provides a general framework for implementing a wide range of learning and certification protocols in the device-independent setting, thereby opening a scalable route to device-independent quantum information processing in large-scale quantum networks.
While quantum networks have been extensively studied as a natural extension of the standard Bell scenario with a richer correlation structure, general constructions of nonlinear Bell inequalities with self-testing properties are still largely lacking. In this work, we present a general method for constructing such inequalities in the simplest network scenario, in which two independent sources distribute bipartite quantum states to three spatially separated observers. These inequalities allow for arbitrary numbers of binary measurements and are maximally violated by maximally entangled states of the corresponding local dimensions together with sets of pairwise anticommuting Clifford observables. Importantly, their maximal quantum values can be determined analytically, which makes them particularly promising for device-independent applications. In particular, we prove that these Bell inequalities can be used to device-independently certify the underlying quantum network, including both the quantum states produced by the sources and the observables measured by all parties. To the best of our knowledge, this is the first self-testing result for quantum networks that relies solely on the maximal violation of a nonlocality witness.
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.
With advances in experimental quantum computing, the requirement for verifying the correctness of quantum computation is urgent. The recent protocols of device-independent verifiable blind quantum computation provide a fruitful solution. However, all existing approaches have relatively high overhead. In this paper, we present a parallel self-testing technology to extract the presence of tensor products of Pauli observables on maximally entangled state. We then utilize our parallel self-testing to propose a device-independent verification protocol. Finally, compared to other existing protocols, our scheme has a lower overhead, which costs Bell pairs, where n is the size of original computation.