Abstract
Authentication of quantum sources is a crucial task in building reliable and efficient protocols for quantum-information processing. Steady progress vis-\`{a}-vis verification of quantum devices in the scenario with fully characterized measurement devices has been observed in recent years. When it comes to the scenario with uncharacterized measurements, the so-called black-box scenario, practical verification methods are still rather scarce. Development of self-testing methods is an important step forward, but these results so far have been used for reliable verification only by considering the asymptotic behavior of large, identically and independently distributed (IID) samples of a quantum resource. Such strong assumptions deprive the verification procedure of its truly device-independent character. In this paper, we develop a systematic approach to device-independent verification of quantum states free of IID assumptions in the finite copy regime. Remarkably, we show that device-independent verification can be performed with optimal sample efficiency. Finally, for the case of independent copies, we develop a device-independent protocol for quantum state certification: a protocol in which a fragment of the resource copies is measured to warrant the rest of the copies to be close to some target state.
Highlights
All the copies are consumed in the process of verification, and they cannot be reused. We address this issue and construct a protocol for DI certification: from the copies emitted by the source, some fraction is randomly chosen to be measured, the same way they would be measured in the DI quantum state verification, while all the remaining copies are preserved to be used in some other protocol of interest
We developed a protocol for sampleefficient device-independent quantum state verification and certification
We managed to adapt the procedure to the certification scenario where not all copies are consumed through verification in cases where different copies are not identical, but are independent from each other
Summary
Entangled states have been identified as a key resource in applications of quantum technologies, such as quantum communication [1], computation [2], cryptography [3], and sensing [4]. Self-testing tools find direct application even in cryptographic protocols, where earlier they were deemed inappropriate because of the IID assumption they invoke Based on these results we design a DI certification protocol in which a certificate about the unmeasured copies can be guaranteed based on the DI verification procedure performed on the measured copies. This is done by joining together insights from quantum state verification methods with those native to self-testing, and building a general protocol for sample-efficient DI quantum state verification and certification
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