Abstract As a key element in quantum repeaters, entanglement swapping establishes entanglement between two independent entangled states. Besides entanglement, quantum steering has been identified as an essential quantum resource and has broad applications in quantum communication. Although entanglement swapping has been realized experimentally, quantum steering swapping still remains a challenge since the condition of quantum steering is stronger than that of entanglement. In this article, quantum steering swapping between a three‐mode and a two‐mode Gaussian entangled state in a lossy channel is demonstrated. By choosing the optimum gain in the classical channel that corresponds to the maximum transmission distance, the one‐way and two‐way steerabilities in a new three‐mode Gaussian state located in distant nodes are achieved. The obtained collective steerability from two users to one user has potential application in quantum secret sharing. The results make a crucial step toward applications of quantum steering in asymmetric quantum information processing.
Abstract As a key element in quantum repeaters, entanglement swapping establishes entanglement between two independent entangled states. Besides entanglement, quantum steering has been identified as an essential quantum resource and has broad applications in quantum communication. Although entanglement swapping has been realized experimentally, quantum steering swapping still remains a challenge since the condition of quantum steering is stronger than that of entanglement. In this article, quantum steering swapping between a three‐mode and a two‐mode Gaussian entangled state in a lossy channel is demonstrated. By choosing the optimum gain in the classical channel that corresponds to the maximum transmission distance, the one‐way and two‐way steerabilities in a new three‐mode Gaussian state located in distant nodes are achieved. The obtained collective steerability from two users to one user has potential application in quantum secret sharing. The results make a crucial step toward applications of quantum steering in asymmetric quantum information processing.
Einstein-Podolsky-Rosen (EPR) steering is a quantum mechanical phenomenon that allows one party to steer the state of a distant party by exploiting their shared entanglement. It has potential applications in secure quantum communication. In this paper, we present two swapping schemes of Gaussian EPR steering, single-channel and dual-channel schemes, by the technique of entanglement swapping. Two space-separated independent EPR steering states without a direct interaction present EPR steering after deterministic swapping. By comparing the EPR steering of the single-channel and dual-channel schemes, we show that the transmission distance of the single-channel scheme is much longer than that of the symmetric dual-channel scheme. Different from entanglement swapping, one-way EPR steering is presented after swapping over lossy channels. The most interesting thing is that the change of the EPR steering direction is observed in the dual-channel scheme. We also show that excess noise in a quantum channel will shorten the transmission distance of the swapping, even leading to the sudden death of EPR steering. The presented schemes provide a technical reference for remote quantum communications with EPR steering.
Multipartite Einstein-Podolsky-Rosen (EPR) steering is a useful quantum resource for quantum communication in quantum networks. It has potential applications in secure quantum communication, such as one-sided device-independent quantum key distribution and quantum secret sharing. By distributing optical modes of a multipartite entangled state to space-separated quantum nodes, a local quantum network can be established. Based on the existing multipartite EPR steering in a local quantum network, secure quantum communication protocol can be accomplished. In this manuscript, we present swapping schemes for EPR steering between two space-separated Gaussian multipartite entangled states, which can be used to connect two space-separated quantum networks. Two swapping schemes, including the swapping between a tripartite Greenberger-Horne-Zeilinger (GHZ) entangled state and an EPR entangled state and that between two tripartite GHZ entangled states, are analyzed. Various types of EPR steering are presented after the swapping of two space-separated independent multipartite entanglement states without direct interaction, which can be used to implement quantum communication between two quantum networks. The presented schemes provide technical reference for more complicated quantum networks with EPR steering.
As two valuable quantum resources, Einstein-Podolsky-Rosen entanglement and steering play important roles in quantum-enhanced communication protocols. Distributing such quantum resources among multiple remote users in a network is a crucial precondition underlying various quantum tasks. We experimentally demonstrate the deterministic distribution of two- and three-mode Gaussian entanglement and steering by transmitting separable states in a network consisting of a quantum server and multiple users. In our experiment, entangled states are not prepared solely by the quantum server, but are created among independent users during the distribution process. More specifically, the quantum server prepares separable squeezed states and applies classical displacements on them before spreading out, and users simply perform local beam-splitter operations and homodyne measurements after they receive separable states. We show that the distributed Gaussian entanglement and steerability are robust against channel loss. Furthermore, one-way Gaussian steering is achieved among users that is useful for further directional or highly asymmetric quantum information processing.
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.
Steering is a type of nonseparable quantum correlation, where its inherent asymmetric feature makes it distinct from Bell nonlocality and entanglement. In this paper, we investigate quantum steering in a two-mode Gaussian state [Formula: see text] coupled to a two-mode vacuum reservoir. The mode [Formula: see text] ([Formula: see text]) is emitted during the first (second) transition of a nondegenerate three-level cascade laser. By means of the master equation of the state [Formula: see text], we derive the analytical expression of the steady-state covariance matrix of the modes [Formula: see text] and [Formula: see text]. Using realistic experimental parameters, we show that the state [Formula: see text] can exhibit asymmetric steering. Furthermore, by an appropriate choice of the physical parameters of the state [Formula: see text], we show that one-way steering can be achieved. Essentially, we demonstrate that one-way steering can, in general, occur only from [Formula: see text]. Besides, we perform a comparative study between the steering of the two laser modes and their Gaussian Rényi-2 entanglement. As a result, we found that the entanglement and steering behave similarly in the same circumstances, i.e. both of them decay under dissipation effect; moreover, they can be well enhanced by inducing more and more quantum coherence in the state [Formula: see text]. In particular, we found that the steering remains always less than the Gaussian Rényi-2 entanglement.
Abstract Einstein–Podolsky–Rosen (EPR) steering is one of the most intriguing features of quantum mechanics and an important resource for quantum communication. For practical applications, it remains a challenge to protect EPR steering from decoherence due to its intrinsic difference from entanglement. Here, we experimentally demonstrate the distillation of Gaussian EPR steering and entanglement in lossy and noisy environments using measurement-based noiseless linear amplification. Different from entanglement distillation, the extension of steerable region happens in the distillation of EPR steering, besides the enhancement of steerabilities. We demonstrate that the two-way or one-way steerable region is extended after the distillation of EPR steering when the NLA is implemented based on Bob’s or Alice’s measurement results. We also show that the NLA helps to extract the secret key from the insecure region in one-sided device-independent quantum key distribution with EPR steering. Our work paves the way for quantum communication exploiting EPR steering in practical quantum channels.