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arXiv:2506.23637 · Physical Review A

Topologically noise-robust network steering without inputs

Dhruv Baheti, Shubhayan Sarkar

Published Nov 25, 2025• 1 citation
arXivHTMLPDF

Abstract

Quantum networks with independent sources allow observing quantum nonlocality or steering with just a single measurement per node of the network, or without any inputs. Inspired by the recently introduced notion of swap-steering, we consider here the triangle network scenario without inputs, where one of the parties is trusted to perform a well-calibrated measurement. In this scenario, we first propose a linear witness to detect triangle network swap-steering. Then, by using the correlations that achieve the maximum value of this inequality, and assuming that all the sources are the same, we can self-test the state generated by the sources and the measurements of the untrusted party. We then extend this framework to ring networks with an arbitrary number of nodes with one of them being trusted. Interestingly, this is the first example of a topologically robust, that is, one can observe steerability without assuming the network structure of the network, as well as noise-robust quantum advantage in a network. Additionally, by allowing the trusted party to perform tomography of their subsystems, we demonstrate that every bipartite entangled state will result in swap-steerable correlations in the ring network. For this purpose, we construct linear witnesses to detect ring network swap-steering corresponding to every bipartite entangled state.

DOI
10.1103/r9py-kcgj

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Quantum networks with independent sources allow observing quantum nonlocality or steering with just a single measurement per node of the network, or without any inputs. Inspired by the recently introduced notion of swap-steering, we consider here the triangle network scenario without inputs, where one of the parties is trusted to perform a well-calibrated measurement. In this scenario, we first propose a linear witness to detect triangle network swap-steering. Then, by using the correlations that achieve the maximum value of this inequality, and assuming that all the sources are the same, we can self-test the state generated by the sources and the measurements of the untrusted party. We then extend this framework to ring networks with an arbitrary number of nodes with one of them being trusted. Interestingly, this is the first example of a topologically robust, that is, one can observe steerability without assuming the network structure of the network, as well as noise-robust quantum advantage in a network. Additionally, by allowing the trusted party to perform tomography of their subsystems, we demonstrate that every bipartite entangled state will result in swap-steerable correlations in the ring network. For this purpose, we construct linear witnesses to detect ring network swap-steering corresponding to every bipartite entangled state.
Quantum steering is an asymmetric form of quantum nonlocality where one can detect whether a measurement on one system can steer or change another distant system. It is well-known that there are quantum states that are entangled but unsteerable in the standard quantum steering scenario. Consequently, a long-standing open problem in this regard is whether the steerability of every entangled state can be activated in some way. In this work, we consider quantum networks and focus on the swap-steering scenario without inputs and find linear witnesses of network steerability corresponding to any negative partial transpose (NPT) bipartite state and a large class of bipartite states that violate the computable cross-norm (CCN) criterion. Furthermore, by considering that the trusted party can perform tomography of the incoming subsystems, we construct linear inequalities to witness swap-steerability of every bipartite entangled state. Consequently, for every bipartite entangled state one can now observe a form of quantum steering.
Quantum networks with multiple sources allow the observation of quantum nonlocality without inputs. Consequently, the incompatibility of measurements is not a necessity for observing quantum nonlocality when one has access to multiple quantum sources. Here we investigate the minimal scenario without inputs where one can observe any form of quantum nonlocality. We show that even two parties with two sources that might be classically correlated can witness a form of quantum nonlocality, in particular quantum steering, in networks without inputs if one of the parties is trusted, that is, performs a fixed known measurement. We term this effect as swap-steering. The scenario presented in this work is minimal to observe such an effect. Consequently, a scenario exists where one can observe quantum steering but not Bell non-locality. We further construct a linear witness to observe swap-steering. Interestingly, this witness enables self-testing of the quantum states generated by the sources and the local measurement of the untrusted party. This in turn allows certifying two bits of randomness that can be obtained from the measurement outcomes of the untrusted device without the requirement of initially feeding the device with randomness.
The development of large-scale quantum networks promises to bring a multitude of technological applications as well as shed light on foundational topics, such as quantum nonlocality. It is particularly interesting to consider scenarios where sources within the network are statistically independent, which leads to so-called network nonlocality, even when parties perform fixed measurements. Here we promote certain parties to be trusted and introduce the notion of network steering and network local hidden state (NLHS) models within this paradigm of independent sources. In one direction, we show how the results from Bell nonlocality and quantum steering can be used to demonstrate network steering. We further show that it is a genuinely novel effect by exhibiting unsteerable states that nevertheless demonstrate network steering based upon entanglement swapping yielding a form of activation. On the other hand, we provide no-go results for network steering in a large class of scenarios by explicitly constructing NLHS models.
Quantum nonlocality and its asymmetric counterpart, quantum steering, are among the most intriguing manifestations of quantum mechanics. From a theoretical perspective, they are not only of fundamental significance but also hold promise for a wide range of applications. However, the stringent technological requirements for their experimental observation in a loophole-free way have largely restricted their realization to foundational demonstrations. A major challenge in these setups is the limited detection efficiency of current detectors as to observe nonlocality or steering in the standard scenarios, one requires detectors above a certain critical efficiency which can only be achieved with superconducting detectors. Considering the simplest quantum network, we demonstrate here that quantum steering between two parties, can be demonstrated for any non-zero detection efficiency, if the sources in the network generate states above a critical visibility well-within the current practical limits. This form of quantum steering in networks, is termed swap-steering. Moreover, when the sources are perfect, swap-steering can be observed using any entangled measurement on the untrusted side, even with arbitrarily low detection efficiency. Consequently, two major loopholes, the detection-loophole as well as free-will loophole can be closed easily in quantum steering experiments, when implemented using networks.
Entanglement is a key resource to demonstrate quantum advantage over classical strategies. Entanglement in quantum states is one of the most well-explored areas in quantum physics. However, a rigorous approach to understanding and detecting entanglement in composite quantum measurements is lacking. In this work, we focus on composite quantum measurements and classify them into two classes: entangled and separable measurements. As done for quantum states, we define analogously a notion of witness that can be used to detect entanglement in composite quantum measurements. Here, one does not need to trust the measurement to witness its entanglement but must trust the quantum states. We then further extend this approach to show that any entangled measurement provides an advantage in network quantum steering without inputs, also known as swap steering. Consequently, this provides a way to witness entanglement in any quantum measurement in a one-sided device-independent way. Finally, we consider the star network scenario and show that any rank-one projective entangled quantum measurement gives a quantum advantage. Thus, one can detect the entanglement in any rank-one projective measurement in a device-independent way.
We consider quantum steering certification in multipartite networks, with a focus on minimal trust scenarios: all-except-one parties are untrusted and treated device-independently. We show that it is always possible to lift steering certification to the measurement-device-independent regime, in which even the (last) trusted party can treat their local hardware as a black-box, except for a set of fiduciary quantum states used as the inputs to the experiment. This holds both for finite-dimensional systems as well as for bosonic continuous-variable systems, which we characterize in terms of semi-quantum games in the bipartite case. Additionally, we introduce measurement-device-independent network steering protocols based entirely on Gaussian operations -- which cannot be used for fully device-independent protocols, and thus become instead a viable option for minimal trust certification as soon as a single trusted input is inserted in the network. Our results present a basis for steering-based applications (such as randomness generation) with minimal trust beyond full nonlocality and with feasible experimental requirements.