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Quantum steering from phase measurements with limited resources

Gabriele Bizzarri, Ilaria Gianani, Mylenne Manrique, V. Berardi, Fabio Bruni, Giovanni Capellini, Marco Barbieri

Published Jan 1, 2024• 0 citations
Publisher

Abstract

We extend a metrology-assisted protocol to certify steering, explicitly accounting for experimental imperfections, in a limited resource scenario. Our results provide guidelines to apply such a metrological approach to the validation of quantum channels.
DOI
10.1364/quantum.2024.qm4a.4

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Quantum steering captures the ability of one party, Alice, to control through quantum correlations the state at a distant location, Bob, with superior ability than allowed by a local hidden state model. Verifying the presence of quantum steering has implications for the certification of quantum channels, and its connection to the metrological power of the quantum state has been recently proved. This link is established by means of the violation of a Cramér-Rao bound holding for non-steerable states: its direct assessment would then require operation in the asymptotic regime of a large number of repetitions. Here, we extend previous work to account explicitly for the use of a limited number of resources, and put this modified approach to test in a quantum optics experiment. The imperfections in the apparatus demand an adaptation of the original test in the multiparameter setting. Our results provide guidelines to apply such a metrological approach to the validation of quantum channels.
Quantum steering captures the ability of one party, Alice, to control through quantum correlations the state at a distant location, Bob, with superior ability than allowed by a local hidden state model. Verifying the presence of quantum steering has implications for the operation of quantum communication with limited trust, and its connection to the metrological power of the quantum state has been recently proved. This link is established by means of the violation of a Cramér–Rao bound holding for non-steerable states: its direct assessment would then require operation in the asymptotic regime of a large number of repetitions. Here, we build on previous work to account explicitly for the use of a limited number of resources and put this modified approach to test in a quantum optics experiment. The imperfections in the apparatus demand an adaptation of the original test in the multiparameter setting. Our results provide guidelines to apply such a metrological approach to the validation of quantum channels.
Quantum steering, a fundamental manifestation of nonlocal quantum correlations, plays a vital role in quantum key distribution, quantum randomness generation, and quantum metrology. Reliable experimental detection of quantum steering is therefore a key task in quantum information science, but it is often hindered by measurement imperfections. Here, we introduce a randomized measurement protocol designed to mitigate the effects of imperfect measurements and enhance detection reliability. We theoretically prove that this approach effectively suppresses measurement errors by requiring only local operations on the trusted party; moreover, its dimension-independent nature ensures ready adaptability to quantum systems of arbitrary finite size. We experimentally validate the method using polarization-entangled photons, demonstrating consistent performance under controlled misalignments for both 2- and 3-setting configurations. Our results provide a practical and reliable framework for steering detection in realistic experimental conditions, paving the way for its integration into quantum certification and communication protocols.
Quantum steering is an important correlation in quantum information theory. A recent work [Nat. Commun. 12, 2410 (2021)] showed that quantum steering is also useful for quantum metrology. Here, we extend the exploration of steering-enhanced quantum metrology from single noiseless phase shifts to superpositions of noisy phase shifts. As concrete examples, we consider a control system that manipulates a target system to pass through a superposition of either dephased or depolarized phase shifts channels. We show that using such superpositions of noisy phase shifts can suppress the effects of noise and improve metrology. Furthermore, we also implemented proof-of-principle experiments for a superposition of dephased phase shifts on the IBM quantum experience, demonstrating a clear improvement on metrology.
In this thesis, the certification of quantum resources is discussed. This is crucial for the development of new quantum technologies and consequently for the implementation of quantum protocols. In particular, the connections between measure-and-prepare scenarios and entanglement-based scenarios are utilised. First, measurement incompatibility is investigated in the context of dimension-bounded prepare-and-measure scenarios. Its connection to specific entanglement-based scenarios is explicitly established. Second, the dimensionality of quantum channels is witnessed in a prepare-and-measure setting. The benchmarking methods are developed by leveraging the isomorphism between bipartite states and channels. They are implemented in an experimental collaboration to certify the dimensionality of commercial multimode fibres. Third, states and measurements are certified using quantum networks. The network formalism is significantly simplified by describing it in terms of local maps, thus facilitating the development of a range of benchmarking criteria and the derivation of an activation result. Finally, the practical limitations affecting certification methods is addressed. In particular, methods are presented to treat signalling, which is not taken into account by traditional quantum theory.