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AVS Quantum Science

Quantum steering from phase measurements with limited resources

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

Published May 16, 2024• 3 citations
Publisher

Abstract

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.

DOI
10.1116/5.0205469

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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 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 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 entanglement is a key resource for foundational quantum information and communication tasks, such as teleportation, entanglement swapping and quantum key distribution [1]. Quantum steering is a quantum correlation that is distinct from other nonclassical correlations such as Bell nonlocality [2] and entanglement. Steering describes the effect of measuring one system, let's say Alice, and affecting the measurement results on the other system, let's say Bob. Moving through the hierarchy of nonlocal classes, from Bell nonlocality towards nonsepa-rability, requires an increasing number of parties and apparatus that need to be trusted but gives access to protocols which are more robust to noise for projective measurements [3,4]. In a quantum steering task [5] the correlations of Alice and Bob's measurement outcomes are tested against a classical probability bound which can be only violated if the state shared between the parties is quantum steerable.
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.
We consider a quantum steering scenario where Alice prepares a bipartite state, sends one subsystem to Bob through a quantum channel, and aims to convince him that their shared state is entangled. Bob, however, will never be convinced if the channel is steering-breaking, that is, if the channel destroys steerability for any input state. To verify that a channel renders a state useless for demonstrating steering, one must consider all possible measurements performed by Alice and check if the conditional states Bob receives admit a local-hidden-state (LHS) model. This is generally a hard problem since it requires considering an infinite number of measurement combinations. Here, we show that the method proposed in [Phys. Rev. Lett. 117, 190401 (2016); Phys. Rev. Lett. 117, 190402 (2016)] can be utilized to tackle this problem. Furthermore, owing to the intimate relation between steering and measurement incompatibility, our approach can faithfully certify whether a channel destroys incompatibility for any set of measurements. Finally, we propose an experimental criterion for certifying steering- and incompatibility-breaking channels, which may be of independent interest.
Quantum steering is a kind of bipartite quantum correlations where one party's measurement remotely alters the state of another party. In an adversarial scenario, there could be a hidden variable introducing a bias in the choice of measurement settings of the parties. However, observers without access to the hidden variable are unaware of this bias. The main focus of this work is to analyze quantum steering without assuming that the parties freely choose their measurement settings. For this, we introduce the measurement-dependent (MD-)steering scenario where the measurement settings chosen by the parties are biased by an adversary. In such a scenario, we present a class of inequalities to test for MD-steerable correlations. Further, we discuss the implications of violating such inequalities in certifying randomness from quantum extremal behaviors. We also assume that an adversary might prepare an assemblage as a mixture of MD-steerable and MD-unsteerable assemblages and provide a bound on the measurement dependence for the observed correlation to remain MD-steerable.