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arXiv:1912.10605 · Physical Review A

Unified approach to witness non-entanglement-breaking quantum channels

Yi-Zheng Zhen, Yingqiu Mao, Kai Chen, Francesco Buscemi, Oscar Dahlsten

Published Jun 1, 2020• 2 citations
arXivHTMLPDF

Abstract

The ability of quantum devices to preserve or distribute entanglement is essential in employing quantum technologies. Such ability is described and guaranteed by the non-entanglement-breaking (nonEB) feature of participating quantum channels. For quantum information applications relying on entanglement, the certification of the nonEB feature is indispensable in designing, testing, and benchmarking quantum devices. Here, we develop a simple and direct approach for the certification of nonEB quantum channels. By utilizing the prepare-and-measure test, we derive a necessary and sufficient condition for witnessing the nonEB channels, which is applicable in almost all experimental scenarios. The approach not only unifies and simplifies existing methods in the standard scenario and the measurement-device-independent scenario, but also furthers the nonEB channel certification in the semi-device-independent scenario.

DOI
10.1103/physreva.101.062301

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The ability of quantum devices to preserve or distribute entanglement is essential in employing quantum technologies. Such ability is described and guaranteed by the non-entanglement-breaking (nonEB) feature of participating quantum channels. For quantum information applications relying on entanglement, the certification of the nonEB feature is indispensable in designing, testing, and benchmarking quantum devices. Here, we develop a simple and direct approach for the certification of nonEB quantum channels. By utilizing the prepare-and-measure test, we derive a necessary and sufficient condition for witnessing the nonEB channels, which is applicable in almost all experimental scenarios. The approach not only unifies and simplifies existing methods in the standard scenario and the measurement-device-independent scenario, but also furthers the nonEB channel certification in the semi-device-independent scenario.
Ensuring the nonentanglement-breaking (non-EB) property of quantum channels is crucial for the effective distribution and storage of quantum states. However, a practical method for direct and accurate certification of the non-EB feature is highly desirable. Here, we propose and verify a realistic source based measurement device independent certification of non-EB channels. Our method is resilient to repercussions on the certification from experimental conditions, such as multiphotons and imperfect state preparation, and can be implemented with an information incomplete set. We achieve good agreement between experimental outcomes and theoretical predictions, which is validated by the expected results of the ideal semiquantum signaling game, and accurately certify the non-EB channels. Furthermore, our approach is highly robust to effects from noise. Therefore, the proposed approach can be expected to play a significant role in the design and evaluation of realistic quantum channels.
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.
A key aspect in quantum information is to understand the advantage offered by quantum systems over classical ones in communication tasks. In recent years, a fundamental approach to this problem has been developed, focusing on quantum correlations in prepare-and-measure scenarios. Inspired by the developments in Bell nonlocality and device-independent information processing, this line of research aims to characterize the possibilities and limits of quantum systems for communication, in particular to precisely capture the advantage they offer over classical systems. In addition to fundamental insights, these ideas also underpin the concept of semi-device-independent quantum information processing. Exploring trade-offs between security, performance and ease-of-implementation, this approach opens promising directions for novel quantum information processing technologies and devices. A number of protocols and proof-of-principle demonstrations have been reported in recent years, in particular for quantum randomness certification and key distribution. Here, we provide a comprehensive introduction to quantum prepare-and-measure correlations and semi-device independent applications.
High-dimensional entanglement offers significant advantages over its low-dimensional counterpart in various information-processing tasks. However, to harness these advantages, it is crucial that the quantum channels used to store or transmit the subsystems of an entangled system not only preserve entanglement but also maintain its dimensionality above a certain threshold. The maximum entanglement dimension that a channel can preserve is referred to as its effective dimensionality, since the channel cannot be used to transmit information of dimension greater than that in a single use. In this work, we present a method to certify whether a quantum channel can preserve entanglement dimension above a given threshold. Unlike existing approaches, our method is faithful, i.e., it can be applied to any channel, and avoids common assumptions such as preparation of entangled states, auxiliary side channels, or perfect measurement devices. Moreover, the method can be extended to faithfully certify other classes of non-resource-breaking channels, such as non-nonpositive-partial-transpose-breaking channels (non-NPT-breaking channels). Finally, we discuss possible experimental realizations of our certification scheme through explicit examples.
Superdense coding is a paradigmatic protocol in quantum information science, employing a quantum communication channel to send classical information more efficiently. As we show here, it can be understood as a particular case of a prepare and measure experiment, a scenario that has attracted growing attention for its fundamental and practical applications. Formulating superdense coding as a prepare and measure scenario allows us to provide a semi-device-independent witness of entanglement that significantly improves over previous tests. Furthermore, we also show how to adapt our results into self-testing of maximally entangled states and also provide a semidefinite program formulation allowing one to efficiently optimize, for any shared quantum state, the probability of success in the superdense coding protocol.
Certifying the entanglement of quantum states with Bell inequalities allows one to guarantee the security of quantum information protocols independently of imperfections in the measuring devices. Here, we present a similar procedure for witnessing entangled measurements, which play a central role in many quantum information tasks. Our procedure is termed semi-device-independent, as it uses uncharacterized quantum preparations of fixed Hilbert space dimension. Using a photonic setup, we experimentally certify an entangled measurement using only measurement statistics. We also apply our techniques to certify unentangled but nevertheless inherently quantum measurements.