Abstract Quantum steering is the ability that one system affects another one without delay by performing local measurements, which has garnered significant attention in the field of quantum information science. Here, we propose a linear network to realize tunable quantum steering with adjustable measurements. We show that forward steering of the first entangled source can be perfectly transferred to the state of two endpoints, regardless of measurements in the quantum network. However, for the backward steering between two endpoints, it displays a four-leaf clovers with rich symmetries with measurement parameters { θ j } j = 1 N − 1 and is dependent on the parameters { β j } j = 2 N of the input state. By tuning the measurements far away from or close to the optimal values, one-way or two-way steering can be controllably realized. In addition, the error between the actual and optimal measurements is also taken into account in our proposal. The result indicates that a smaller error is beneficial for predicting two-way steering involving multiple measurements. Our proposal offers a promising way to realize the quantum steering transfer within linear networks.
Abstract Quantum steering is the ability that one system affects another one without delay by performing local measurements, which has garnered significant attention in the field of quantum information science. Here, we propose a linear network to realize tunable quantum steering with adjustable measurements. We show that forward steering of the first entangled source can be perfectly transferred to the state of two endpoints, regardless of measurements in the quantum network. However, for the backward steering between two endpoints, it displays a four-leaf clovers with rich symmetries with measurement parameters { θ j } j = 1 N − 1 and is dependent on the parameters { β j } j = 2 N of the input state. By tuning the measurements far away from or close to the optimal values, one-way or two-way steering can be controllably realized. In addition, the error between the actual and optimal measurements is also taken into account in our proposal. The result indicates that a smaller error is beneficial for predicting two-way steering involving multiple measurements. Our proposal offers a promising way to realize the quantum steering transfer within linear networks.
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.
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.
Quantum resource swapping is crucial for establishing quantum networks and achieving efficient quantum communication and it allows quantum resources to be shared and allocated between nodes in a quantum network, thereby enhancing network flexibility and quantum information processing capabilities. Quantum steering is a special type of quantum correlation that exhibits unique asymmetry compared with quantum entanglement and Bell nonlocality. This asymmetry enables quantum steering swapping to establish one-way or two-way asymmetry quantum steering between two independent optical modes, which is crucial for constructing asymmetric quantum networks. In this work, an all-optical quantum steering swapping scheme is proposed based on tripartite entangled state and bipartite entangled state. The all-optical scheme does not involve optic-electro conversion nor electro-optic conversion, but utilizes a low-noise, high-bandwidth four-wave mixing process to achieve the function of Bell state measurement in traditional schemes without measurement. After the steering swapping operation, the two originally independent entangled states without direct interaction generate quantum steering. In this work, two swapping schemes in the four-wave mixing processes, combined with linear beam splitter and nonlinear beam splitter, are investigated. By analyzing the steering characteristics of the output modes, both schemes exhibit varieties of multipartite steering types. By adjusting the transmissivity of the linear beam splitter and the gain of the four-wave mixing process, the steering relationship can be flexibly manipulated to achieve one-way and two-way asymmetry steering. This provides new possibilities for one-way quantum communication and quantum information processing, making the utilization of quantum resources more efficient and controllable. Through in-depth analysis of the steering characteristics after swapping, it is found that compared with the linear beam splitter scheme, the nonlinear beam splitter scheme not only significantly improves the capability of quantum steering, but also allows for more flexible manipulation of monogamy relations of quantum steering. By optimizing the gain parameters of the nonlinear beam splitter, the precise manipulation of the monogamy relations can be achieved over a wider range. This not only expands broader application prospects for information processing and quantum communication in quantum networks, but also lays an important foundation for building efficient and secure quantum information processing systems.
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 steering is the phenomenon whereby one party (Alice) proves entanglement by ``steering'' the system of another party (Bob) into distinct ensembles of states, by performing different measurements on her subsystem. Here, we investigate steering in a network scenario involving n parties, who each perform local measurements on part of a global quantum state, that is produced using only two-party entangled states, and mixing with ancillary separable states. We introduce three scenarios which can be straightforwardly implemented in standard quantum optics architecture, which we call random 2n-pair entanglement, random pair entanglement, and semirandom pair entanglement. We study steerability of the states across two-party marginals which arise in the three scenarios, and analytically derive the necessary and sufficient steering criteria for different sets of measurement settings. Strikingly, using the semirandom pair entanglement construction, one party can steer every one of the $n\ensuremath{-}1$ other parties, for arbitrarily large n, using only two measurements. Finally, exploiting symmetry, we study various small network configurations (three or four parties) in the three scenarios, under different measurements and produced by different two-party entangled states.
Einstein-Podolsky-Rosen (EPR) steering describes the ability of one party to remotely affect another's state through local measurements. One of the most distinguishable properties of EPR steering is its asymmetric aspect. Steering can work in one direction but fail in the opposite direction. This type of one-way steering, which is different from the symmetry concepts of entanglement and Bell nonlocality, has garnered much interest. However, an experimental demonstration of genuine one-way EPR steering in the simplest scenario, i.e., one that employs two-qubit systems, is still lacking. In this Letter, we experimentally demonstrate one-way EPR steering with multimeasurement settings for a class of two-qubit states, which are still one-way steerable even with infinite settings. The steerability is quantified by the steering radius, which represents a necessary and sufficient steering criterion. The demonstrated one-way steering in the simplest bipartite quantum system is of fundamental interest and may provide potential applications in one-way quantum information tasks.